From 3e886e1254f4ea25d40fe428693bf5e45fffdcc3 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Thu, 3 Jul 2025 18:25:57 +0200 Subject: [PATCH 01/17] add roxygen style documentation and vignettes --- .gitignore | 4 +- DESCRIPTION | 5 +- NAMESPACE | 43 ++--- NAMESPACE.backup | 29 ++++ R/AIC.drcOrdinal.R | 5 +- R/BCa.R | 4 + R/BIC.drcOrdinal.R | 3 + R/MACurve.R | 60 +++++++ R/PAV.R | 22 +++ R/bmd.R | 172 +++++++++++++++++++ R/bmdBoot.R | 130 +++++++++++++- R/bmdHetVar.R | 117 ++++++++++++- R/bmdHetVarMA.R | 116 ++++++++++++- R/bmdIso.R | 124 ++++++++++++++ R/bmdIsoBoot.R | 136 +++++++++++++++ R/bmdMA.R | 208 +++++++++++++++++++++++ R/bmdMACurve.R | 4 + R/bmdOrdinal.R | 111 ++++++++++++ R/bmdOrdinalDeltaCI.R | 2 +- R/bmdOrdinalMA.R | 106 ++++++++++++ R/bmdProfileCI.R | 2 +- R/bmdProfileCIgrid.R | 2 +- R/bootDataGen.R | 4 + R/bootDataGenHetVar.R | 2 +- R/bootDataGenOrdinal.R | 4 + R/coef.drcHetVar.R | 5 +- R/drmHetVar.R | 74 +++++++- R/drmMMRE.R | 60 ++++++- R/drmOrdinal.R | 46 +++++ R/expandBinomial.R | 25 +++ R/getBmrScaledList.R | 2 +- R/getBmrScaledRepar.R | 2 +- R/getFctDerivx.R | 2 +- R/getStackingWeights.R | 40 +++++ R/invBmd.R | 4 + R/logLik.drcHetVar.R | 7 + R/logLik.drcOrdinal.R | 3 + R/monotonicityTest.R | 47 +++++ R/plot.bmd.R | 38 +++++ R/plot.drcHetVar.R | 5 +- R/plot.drcOrdinal.R | 3 + R/print.bmd.R | 2 +- R/print.bmdHetVar.R | 2 +- R/print.bmdOrdinal.R | 5 +- R/print.drcHetVar.R | 5 +- R/print.drcMMRE.R | 5 +- R/print.drcOrdinal.R | 3 + R/qplotBmd.R | 40 +++++ R/qplotDrc.R | 122 +++++++++++++ R/shirleyTest.R | 2 +- R/trendTest.R | 56 +++++- R/tukeytrendfit.R | 2 +- R/williamsTest.R | 2 +- bmd.Rproj | 1 - man/AIC.drcHetVar.Rd | 11 ++ man/AIC.drcOrdinal.Rd | 11 ++ man/BCa.Rd | 8 +- man/BIC.drcHetVar.Rd | 11 ++ man/BIC.drcOrdinal.Rd | 11 ++ man/MACurve.Rd | 66 ++++--- man/PAV.Rd | 48 +++--- man/bmd.Rd | 300 +++++++++++++++++++------------- man/bmdBoot.Rd | 224 ++++++++++++++---------- man/bmdHetVar.Rd | 167 ++++++++++-------- man/bmdHetVarMA.Rd | 167 ++++++++++-------- man/bmdIso.Rd | 192 ++++++++++++--------- man/bmdIsoBoot.Rd | 202 +++++++++++++--------- man/bmdMA.Rd | 349 +++++++++++++++++++++++--------------- man/bmdMACurve.Rd | 8 +- man/bmdOrdinal.Rd | 215 +++++++++++++---------- man/bmdOrdinalMA.Rd | 187 +++++++++++--------- man/bootDataGen.Rd | 8 +- man/bootDataGenOrdinal.Rd | 12 +- man/coef.drcHetVar.Rd | 11 ++ man/drmHetVar.Rd | 71 ++++---- man/drmMMRE.Rd | 75 ++++---- man/drmOrdinal.Rd | 80 +++++---- man/expandBinomial.Rd | 52 +++--- man/getStackingWeights.Rd | 48 +++--- man/invBmd.Rd | 20 ++- man/logLik.drcHetVar.Rd | 11 ++ man/logLik.drcOrdinal.Rd | 11 ++ man/monotonicityTest.Rd | 87 ++++++---- man/plot.bmd.Rd | 53 +++--- man/plot.drcHetVar.Rd | 11 ++ man/plot.drcOrdinal.Rd | 11 ++ man/print.bmdOrdinal.Rd | 11 ++ man/print.drcHetVar.Rd | 11 ++ man/print.drcMMRE.Rd | 11 ++ man/print.drcOrdinal.Rd | 11 ++ man/qplotBmd.Rd | 68 ++++---- man/qplotDrc.Rd | 176 +++++++++++-------- man/trendTest.Rd | 81 +++++---- man/vcov.drcMMRE.Rd | 11 ++ tests/testthat.R | 2 +- tests/testthat/test-bmd.R | 2 +- vignettes/.gitignore | 2 + vignettes/bmd_Package.Rmd | 107 ++++++++++++ 98 files changed, 3996 insertions(+), 1260 deletions(-) create mode 100644 NAMESPACE.backup create mode 100644 man/AIC.drcHetVar.Rd create mode 100644 man/AIC.drcOrdinal.Rd create mode 100644 man/BIC.drcHetVar.Rd create mode 100644 man/BIC.drcOrdinal.Rd create mode 100644 man/coef.drcHetVar.Rd create mode 100644 man/logLik.drcHetVar.Rd create mode 100644 man/logLik.drcOrdinal.Rd create mode 100644 man/plot.drcHetVar.Rd create mode 100644 man/plot.drcOrdinal.Rd create mode 100644 man/print.bmdOrdinal.Rd create mode 100644 man/print.drcHetVar.Rd create mode 100644 man/print.drcMMRE.Rd create mode 100644 man/print.drcOrdinal.Rd create mode 100644 man/vcov.drcMMRE.Rd create mode 100644 vignettes/.gitignore create mode 100644 vignettes/bmd_Package.Rmd diff --git a/.gitignore b/.gitignore index 61fb704..0b05f50 100644 --- a/.gitignore +++ b/.gitignore @@ -2,4 +2,6 @@ .Rhistory .RData .Ruserdata -cache/ \ No newline at end of file +cache/ +bmd.Rproj +inst/doc diff --git a/DESCRIPTION b/DESCRIPTION index 504c091..686986a 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -25,7 +25,9 @@ Suggests: tidyr, numDeriv, drcData, - testthat (>= 3.0.0) + testthat (>= 3.0.0), + knitr, + rmarkdown Remotes: doseresponse/drc, doseresponse/drcData @@ -36,3 +38,4 @@ Config/testthat/edition: 3 RoxygenNote: 7.3.2 Depends: R (>= 3.5) +VignetteBuilder: knitr diff --git a/NAMESPACE b/NAMESPACE index 6ccfdc1..f785f83 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -1,29 +1,16 @@ -import(drc, ggplot2, dplyr) -importFrom("graphics", "lines") -importFrom("stats", "aggregate", "approx", "as.formula", "coef", - "complete.cases", "confint", "constrOptim", "df.residual", - "dnorm", "fitted", "lm", "model.frame", "model.matrix", - "optim", "pnorm", "predict", "qchisq", "qnorm", "qt", - "quantile", "rbinom", "resid", "residuals", "rnorm", "sd", - "uniroot", "update", "var", "vcov", "AIC", "BIC", "logLik") -importFrom("utils", "setTxtProgressBar", "txtProgressBar") -export(bmd, bmdBoot, bmdIso, bmdIsoBoot, PAV, bmdMA, bootDataGen, bmdMACurve, BCa, invBmd, expandBinomial, - getStackingWeights, drmOrdinal, bmdOrdinal, bmdOrdinalMA, - qplotDrc, qplotBmd, MACurve, monotonicityTest, trendTest, bmdHetVar, drmHetVar, drmMMRE, bmdHetVarMA) +# Generated by roxygen2: do not edit by hand -## S3 methods -S3method(logLik, drcOrdinal) -S3method(logLik, drcHetVar) -S3method(AIC, drcOrdinal) -S3method(AIC, drcHetVar) -S3method(BIC, drcOrdinal) -S3method(BIC, drcHetVar) -S3method(plot, drcOrdinal) -S3method(print, drcOrdinal) -S3method(print, bmdOrdinal) -S3method(print, drcHetVar) -S3method(plot, bmd) -S3method(plot, drcHetVar) -S3method(vcov, drcMMRE) -S3method(print, drcMMRE) -S3method(coef, drcHetVar) \ No newline at end of file +S3method(AIC,drcHetVar) +S3method(AIC,drcOrdinal) +S3method(BIC,drcHetVar) +S3method(BIC,drcOrdinal) +S3method(coef,drcHetVar) +S3method(logLik,drcHetVar) +S3method(logLik,drcOrdinal) +S3method(plot,drcHetVar) +S3method(plot,drcOrdinal) +S3method(print,bmdOrdinal) +S3method(print,drcHetVar) +S3method(print,drcMMRE) +S3method(print,drcOrdinal) +S3method(vcov,drcMMRE) diff --git a/NAMESPACE.backup b/NAMESPACE.backup new file mode 100644 index 0000000..6ccfdc1 --- /dev/null +++ b/NAMESPACE.backup @@ -0,0 +1,29 @@ +import(drc, ggplot2, dplyr) +importFrom("graphics", "lines") +importFrom("stats", "aggregate", "approx", "as.formula", "coef", + "complete.cases", "confint", "constrOptim", "df.residual", + "dnorm", "fitted", "lm", "model.frame", "model.matrix", + "optim", "pnorm", "predict", "qchisq", "qnorm", "qt", + "quantile", "rbinom", "resid", "residuals", "rnorm", "sd", + "uniroot", "update", "var", "vcov", "AIC", "BIC", "logLik") +importFrom("utils", "setTxtProgressBar", "txtProgressBar") +export(bmd, bmdBoot, bmdIso, bmdIsoBoot, PAV, bmdMA, bootDataGen, bmdMACurve, BCa, invBmd, expandBinomial, + getStackingWeights, drmOrdinal, bmdOrdinal, bmdOrdinalMA, + qplotDrc, qplotBmd, MACurve, monotonicityTest, trendTest, bmdHetVar, drmHetVar, drmMMRE, bmdHetVarMA) + +## S3 methods +S3method(logLik, drcOrdinal) +S3method(logLik, drcHetVar) +S3method(AIC, drcOrdinal) +S3method(AIC, drcHetVar) +S3method(BIC, drcOrdinal) +S3method(BIC, drcHetVar) +S3method(plot, drcOrdinal) +S3method(print, drcOrdinal) +S3method(print, bmdOrdinal) +S3method(print, drcHetVar) +S3method(plot, bmd) +S3method(plot, drcHetVar) +S3method(vcov, drcMMRE) +S3method(print, drcMMRE) +S3method(coef, drcHetVar) \ No newline at end of file diff --git a/R/AIC.drcOrdinal.R b/R/AIC.drcOrdinal.R index 987bab8..b70815f 100644 --- a/R/AIC.drcOrdinal.R +++ b/R/AIC.drcOrdinal.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export AIC.drcOrdinal <- function(object, ..., k = 2) { dots <- list(...) if (!is.null(dots$epsilon)){ @@ -8,4 +11,4 @@ AIC.drcOrdinal <- function(object, ..., k = 2) { n.parameters <- sum(sapply(object$drmList, function(mod) length(mod$coefficients))) -2 * logLik(object, epsilon = epsilon) + k * n.parameters -} \ No newline at end of file +} diff --git a/R/BCa.R b/R/BCa.R index 2947263..ce6e380 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,3 +1,7 @@ +#' Help funtion to bmdBoot +#' +#' +#' BCa <- function(obs, data, bootSample, bootjack, level){ R <- length(bootSample) b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) diff --git a/R/BIC.drcOrdinal.R b/R/BIC.drcOrdinal.R index 3457d0e..40a7942 100644 --- a/R/BIC.drcOrdinal.R +++ b/R/BIC.drcOrdinal.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export BIC.drcOrdinal <- function(object, ...){ dots <- list(...) if (!is.null(dots$epsilon)){ diff --git a/R/MACurve.R b/R/MACurve.R index 46d219d..b3d7244 100644 --- a/R/MACurve.R +++ b/R/MACurve.R @@ -1,3 +1,63 @@ +#' Model-average dose-response curves +#' +#' Computing weighted average response estimates across multiple dose-response +#' curves. +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' @param x a vector of dose values for which the weighted average of response +#' estimates are to be computed +#' @param modelList list of models of class \code{drc} +#' @param modelWeights character string specifying the type of weights used, +#' "AIC", "BIC" or "Stack", or a vector of the same length as the modelList +#' with user defined weights +#' @param stackingSeed integer or NULL: Random seed to use in the data split in +#' the estimation of the Stacking Weights, when \code{modelWeights = "Stack"}. +#' The global seed is reset to the initial value after estimation of the +#' weights, so this option does not interfere with a globally set seed. +#' @param stackingSplits integer or "LOO": When \code{modelWeights = "Stack"}, +#' the Stacking Weights are estimated, which are based on V-fold +#' cross-validation. The stackingSplits argument sets the number V of data +#' splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +#' to setting V equal to the number of observations in the data set. +#' @return numeric +#' @author Jens Riis Baalkilde +#' @keywords models nonlinear model averaging +#' @examples +#' +#' library(bmd) +#' library(drc) +#' library(drcData) +#' library(ggplot2) +#' +#' # fit models to aconiazide data +#' aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3()) +#' aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3()) +#' aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3()) +#' aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3()) +#' +#' # plot the MA curve +#' plot(aconiazide.LL.3, type = "obs") +#' curve( +#' MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,aconiazide.W1.3, aconiazide.W2.3), +#' modelWeights = "AIC"), +#' add = TRUE) +#' +#' # or plot using ggplot2 +#' qplotDrc(aconiazide.LL.3, type = "obs") + +#' geom_function(fun = function(x){ +#' MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3, +#' aconiazide.W1.3, aconiazide.W2.3), +#' modelWeights = "AIC") +#' }) +#' +#' MACurve <- function(x, modelList, modelWeights, stackingSeed = 1, stackingSplits = 2){ diff --git a/R/PAV.R b/R/PAV.R index ced17b6..4e30bae 100644 --- a/R/PAV.R +++ b/R/PAV.R @@ -1,3 +1,25 @@ +#' Pool-adjacent-violators monotonizing +#' +#' The function monotonizes a sequence of probabilities or means based on the +#' pool-adjacent-violators algorithm. +#' +#' For details on how the pool-adjacent-violators algorithm is defined see +#' Silvapulle and Sen (2004). +#' +#' Formula should be specified as in the form number/total ~ dose for binomial +#' data and response ~ for continuous data. +#' +#' @param formula an object of class "formula" expressing dose-response +#' relationship. Details of model specification are given under 'Details' +#' @param data data frame containing the variables in the formula +#' @param type character string specifying the type of data used in the model, +#' "continuous" or "binomial" or "Poisson" +#' @return A vector containing the monotonized sequence. +#' @author Signe M. Jensen +#' @references Silvapulle, M. J. and Sen, P. K. (2004). Constrained statistical +#' inference: order, inequality, and shape constraints. New York: John Wiley & +#' Sons. +#' @keywords nonparametric isotonic regression PAV<-function(formula,data,type){ object <- formula if( identical(type,"binomial")){ diff --git a/R/bmd.R b/R/bmd.R index 3ce060b..e031311 100644 --- a/R/bmd.R +++ b/R/bmd.R @@ -1,3 +1,175 @@ +#' Benchmark dose estimation +#' +#' Estimation of benchmark doses and benchmark dose lower limit from dose +#' response model fits +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' @param object object of class \code{drc} +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. For binomial data the options are "modelBased" and "absolute". +#' For continuous data the options are "modelBased","absolute", "hybridSD" and +#' "hybridPercentile". For count data (Poisson, negbin1 or negbin2) the options +#' are "modelBased" and "absolute". +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = backg for binomial response and for the "relative", "extra" +#' and "added" definition for continuous or count response data. p0 = 1 - +#' phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +#' f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +#' function and sigma is the SD for the control group. +#' +#' "hybridPercentile" - the background risk is specified by the user in terms +#' of percentile from the control group distribution (assuming a normal +#' distribution). p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. where x0 is +#' the level for which the response is considered adverse, phi is the normal +#' distribution function and sigma is the SD for the control group +#' +#' If not specified, it will be set to "modelBased" for all def excluding +#' "hybridExc" and "hybridAdd", for these the default is "hybridSD". +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk for binomial response (1 for decreasing +#' dose-response models), 2 SD for "hybridSD" background and 0.9 for +#' "hybridPercentile" +#' @param controlSD numeric value specifying the standard deviation of the +#' control group (used in the hybrid approach). If not specified the SD for the +#' control group will be estimated as the square root of the residual variance +#' (assuming variance homogeneity). +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess", "additional" and "point" are for +#' binomial response. "relative", "extra", "added", "hybridExc" (excess +#' hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +#' response. "relative", "extra", and "point" are for count response data. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response data +#' +#' "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +#' continuous and count response data +#' +#' "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +#' continuous and count response data +#' +#' "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +#' response +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +#' (1- p0), where x0 is the level for which the response is considered adverse, +#' phi is the normal distribution function and sigma is the SD for the control +#' group. Works for continuous response +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +#' where x0 is the level for which the response is considered adverse, phi is +#' the normal distribution function and sigma is the SD for the control group. +#' Works for continuous response +#' @param respTrans if the dose-response model is fitted with a transformed +#' response, specifying this option ensures that the background level for the +#' BMD is computed on the original scale. Options include "none" (default), +#' "log" (natural logarithm) and "sqrt"(square root). +#' @param interval character string specifying the type of confidence interval +#' to use: "delta" (default), "inv", "profile" or "profileGrid" +#' +#' "delta" - BMDL is based on the lower limit of a Wald confidence interval +#' based on the delta method +#' +#' "inv" - BMDL is based on inverse regression, that is the dose associated +#' with the upper limit of the pointwise confidence interval of the +#' dose-response curve. Currently not available for a transformed response +#' variable. +#' +#' "profile" - A profile confidence interval is computed by reparametrising the +#' model. Only available for \code{backgType} in ("modelBased", "absolute"), +#' \code{def} in ("excess", "additional","relative", "extra", "point") and +#' dose-response models with model functions of types Log-Logistic, Log-Normal +#' and Weibull 1 and 2. The limits of the confidence interval are searched for +#' within a grid of size specified by the \code{profileGridSize} argument, +#' however the values of the confidence interval are not limited to the values +#' on the grid. +#' +#' "profileGrid" - A profile confidence interval is computed by creating a +#' multi-dimensional grid of parameter values for the model. Then, a confidence +#' region for the parameters in the model is estimated, and the BMD is +#' estimated for all combinations of parameter values within the region. The +#' interval for the BMD is then computed as the minimum and maximum values of +#' BMD values within the region. Note that for models with several parameters +#' (3-5), is might take a while to compute the confidence interval using this +#' method. The number of grid points for each parameter can be specified by the +#' \code{profileGridSize} argument. +#' @param sandwich.vcov logical. If TRUE BMDL is based on confidence intervals +#' based on robust standard errors from the sandwich covariance matrix +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @param profileGridSize integer specifying the number of grid points used for +#' each parameter, when \code{interval} is either "profile" or +#' "profileGridSearch". Defaults to 20 if not specified. +#' @param profileProgressInfo logical. If TRUE, progress info is be printed +#' while computed profile confidence intervals using the \code{profileGrid} +#' method. Default is TRUE. +#' @return A list of four elements: Results contain the estimated BMD and BMDL, +#' bmrScaled is the response value corresponding to the BMD, interval gives the +#' lower (BMDL) and upper (BMDU) end of the confidence interval of BMD, SE +#' gives the standard error of BMD. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @references Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +#' Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +#' \bold{57}, 698--706. +#' +#' Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +#' Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' +#' ## Fitting log-logistic two-parameter model to binomial data +#' deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial") +#' +#' ## BMD for 5% additional risk with estimated background risk +#' bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional") +#' +#' ## BMD for 10% additional risk with 2% background risk +#' bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional") +#' +#' ## BMD for 5% excess risk and background 0 +#' bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess") +#' +#' ## Dose resulting in 12% risk +#' bmd(deguelin.m1, 0.12, def = "point") +#' +#' ## Benchmark doses for a continuous response +#' ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) +#' +#' ## BMD as the dose resulting in a 5% change relative to the mean background level +#' bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE) +#' +#' ## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk +#' bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE) +#' +#' bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg=NA, controlSD=NA, def = c("excess", "additional", diff --git a/R/bmdBoot.R b/R/bmdBoot.R index 5ea7581..e97fdd7 100644 --- a/R/bmdBoot.R +++ b/R/bmdBoot.R @@ -1,3 +1,131 @@ +#' Benchmark dose estimation using bootstrap +#' +#' The function estimates BMD and BMDL using bootstrap based on parametric +#' dose-response models. +#' +#' BMDL is defined as the 5th percentile in the bootstrap distribution. +#' +#' Bootstrapping with the argument boot = "nonparametric" is done by sampling +#' with replacement from the original data set. Bootstrapping with the argument +#' boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +#' assuming equal variance between groups, in case of continuous data. For +#' binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +#' In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +#' resampling always produces 0 or 1, respectively. In this case data is +#' sampled from binom(N_i,(Y_i+1/4)/(N_i+1/2)). Bootstrapping with argument +#' boot = "semiparametric" is done by sampling with replacement from the +#' residuals. +#' +#' All sampling is made within dose groups. +#' +#' @param object object of class \code{drc} +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param R number of bootstrap samples. Default is 1000 +#' @param bootType character string specifying type of bootstrap used. +#' "nonparametric" (default), "semiparametric" or "parametric". "Semiparametric +#' is only available for continuous data and "nonparametric" is at present the +#' only option for count data. See details below +#' @param bmdType Type of estimate for BMD. Default is "orig" the bmd estimate +#' from the original data set. Other choices are "mean" - the mean of the +#' bootstrap estimates, or "median" - the median of the bootstrap estimates +#' @param backgType character string specifying how the background level is +#' specified. For binomial and count data the options are "modelBased" and +#' "absolute". For continuous data the options are "modelBased", "absolute", +#' "hybridSD" and "hybridPercentile" +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = backg for binomial response and for the "relative", "extra" +#' and "added" definition for continuous response. p0 = 1 - phi((back - +#' f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +#' f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +#' function and sigma is the SD for the control group. "hybridPercentile" - +#' the background risk is specified by the user in terms of percentile from the +#' control group distribution (assuming a normal distribution). p0 = 1 - +#' phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +#' response is considered adverse, phi is the normal distribution function and +#' sigma is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background level for binomial response (1 for decreasing +#' dose-response models), 2 SD for "hybridSD" background and 0.9 for +#' "hybridpercentile" +#' @param controlSD numeric value specifying the standard deviation of the +#' control group (used in the hybrid approach). If not specified the SD for the +#' control group will be estimated as the square root of the residual variance +#' (assuming variance homogeneity). +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess" , "additional" and "point" are for +#' binomial response whereas "relative", "extra", "added", "hybridExc" (excess +#' hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +#' response. "relative", "extra", and "point" are for count response data. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response +#' +#' "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +#' continuous response +#' +#' "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +#' count and continuous response +#' +#' "added" - BMR is defined as: BMR= f(BMD) + p0. Works for count and +#' continuous response +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +#' (1- p0), where x0 is the level for which the response is considered adverse, +#' phi is the normal distribution function and sigma is the SD for the control +#' group. Works for continuous response +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +#' where x0 is the level for which the response is considered adverse, phi is +#' the normal distribution function and sigma is the SD for the control group. +#' Works for continuous response +#' @param respTrans if the dose-response model is fitted with a transformed +#' response, specifying this option ensures that the background level for the +#' BMD is computed on the original scale. Options include "none" (default), +#' "log" (natural logarithm) and "sqrt"(square root). +#' @param bootInterval character string indicating type of bootstrap interval +#' used for estimating BMDL. "Percentile" (default) or "BCa" (Bias corrected +#' and adjusted) +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @return A list of three elements: Results contain the estimated BMD and +#' BMDL, bootEst is a vector af all of the estimated BMD values from each +#' bootstrap sample, Interval gives BMDL and BMDU, which is identical to the +#' confidence interval for the percentile interval approach. +#' @author Signe M. Jensen +#' @keywords bootstrap +#' @examples +#' +#' ## Data on root length in ryegrass after exposure to ferulic acid +#' require(drc) +#' require(drcData) +#' data(ryegrass) +#' +#' ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) +#' +#' ## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk +#' bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50) +#' +#' ## BMD from the same definitions but using parametric bootstrap +#' bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50) +#' +#' bmdBoot <- function(object, bmr, R=1000, bootType="nonparametric", bmdType = "orig", backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg=NA, @@ -352,4 +480,4 @@ bmdBoot <- function(object, bmr, R=1000, bootType="nonparametric", bmdType = "or interval = intMat) class(resBMD) <- "bmd" invisible(resBMD) -} \ No newline at end of file +} diff --git a/R/bmdHetVar.R b/R/bmdHetVar.R index e52f69d..c3dd32c 100644 --- a/R/bmdHetVar.R +++ b/R/bmdHetVar.R @@ -1,3 +1,118 @@ +#' Benchmark dose estimation with heterogeneous variance +#' +#' Estimation of benchmark doses and benchmark dose lower limit based on the +#' hybrid method from dose response model fits with the option to specify a +#' heterogeneous variance structure, where the variance depends on the dose +#' level and/or the fitted values +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' REFERENCES TO BE ADDED/WRITTEN +#' +#' @param object dose-response model with a heterogeneous variance structure of +#' class \code{drcHetVar} +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. The options are "absolute", "hybridSD" and "hybridPercentile". +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +#' "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +#' f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +#' distribution function and sigma(0) is the SD for the control group. +#' +#' "hybridPercentile" - the background risk is specified by the user in terms +#' of percentile from the control group distribution (assuming a normal +#' distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +#' the level for which the response is considered adverse, phi is the normal +#' distribution function and sigma(0) is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 2 SD +#' for "hybridSD" background and 0.9 for "hybridPercentile" +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +#' (additional hybrid), available. +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +#' p0)/ (1- p0), where x0 is the level for which the response is considered +#' adverse, phi is the normal distribution function and sigma(BMD) is the SD at +#' the benchmark dose. +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +#' p0, where x0 is the level for which the response is considered adverse, phi +#' is the normal distribution function and sigma(BMD) is the SD at the +#' benchmark dose. +#' @param interval character string specifying the type of confidence interval +#' to use: "boot" (default) or "none" +#' +#' "boot" - BMDL is based on percentile bootstrapping. +#' +#' "none" - no confidence interval is computed. +#' @param R number of bootstrap samples. Ignored if \code{interval = "none"} +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @param bootType character string specifying the type of bootstrap samples. +#' Options are "nonparametric" (observations are drawn without replacement from +#' the original data set), "semi-parametric" (standardised residuals are drawn +#' with replacement and subsequently rescaled according to the model) and +#' "parametric" (new observations are simulated from the distribution given by +#' the fitted model). +#' @param progressInfo logical. If TRUE, progress info is be printed while +#' bootstrap confidence intervals are estimated. Default is TRUE. +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @return A list of five elements: Results contain the estimated BMD and BMDL, +#' bmrScaled is the response value corresponding to the BMD, interval gives the +#' lower (BMDL) and upper (BMDU) end of the confidence interval of BMD +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' library(bmd) +#' # install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT. +#' +#' # ryegrass data +#' set.seed(123) +#' ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), +#' data = ryegrass, fct = LL.4()) +#' plot(ryegrass.LL.4.hetVar) +#' bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, +#' display = TRUE) # increase R +#' bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, +#' def = "hybridExc", R = 50, level = 0.95, +#' bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap +#' +#' # barley data +#' set.seed(123) +#' barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4()) +#' plot(barley.LL.4.hetVar) +#' bmdHetVar(barley.LL.4.hetVar, bmr = 0.1, backgType = "hybridSD", backg = 1, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) +#' +#' # GiantKelp data +#' set.seed(123) +#' GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), +#' data = GiantKelp, fct = LL.4()) +#' plot(GiantKelp.LL.4.hetVarSq) +#' bmdHetVar(GiantKelp.LL.4.hetVarSq, bmr = 0.1, backgType = "hybridSD", backg = 1, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) +#' +#' GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), +#' data = GiantKelp, fct = LL.4()) +#' plot(GiantKelp.LL.4.hetVarLogSq) +#' bmdHetVar(GiantKelp.LL.4.hetVarLogSq, bmr = 0.1, backgType = "hybridSD", backg = 1, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) +#' +#' bmdHetVar <- function(object, bmr, backgType = c("absolute", "hybridSD", "hybridPercentile"), backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), R = 1000, level = 0.95, bootType = "nonparametric", progressInfo = TRUE, display = TRUE){ ### Assertions ### # object @@ -171,4 +286,4 @@ bmdHetVar <- function(object, bmr, backgType = c("absolute", "hybridSD", "hybrid model = object) class(resBMD) <- c("bmdHetVar", "bmd") invisible(resBMD) -} \ No newline at end of file +} diff --git a/R/bmdHetVarMA.R b/R/bmdHetVarMA.R index 060c0aa..8a6da69 100644 --- a/R/bmdHetVarMA.R +++ b/R/bmdHetVarMA.R @@ -1,3 +1,117 @@ +#' Benchmark dose estimation with heterogeneous variance based on model +#' averaging (MA) +#' +#' Estimation of benchmark doses and benchmark dose lower limit based on the +#' hybrid method from a list of dose response model fits with the option to +#' specify a heterogeneous variance structure, where the variance depends on +#' the dose level and/or the fitted values +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' REFERENCES TO BE ADDED/WRITTEN +#' +#' @param modelList a list of dose-response models with a heterogeneous +#' variance structure of class \code{drcHetVar} +#' @param modelWeights character string specifying the type of weights used, +#' "AIC" or "BIC", or a numeric vector of the same length as the modelList with +#' user defined weights +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. The options are "absolute", "hybridSD" and "hybridPercentile". +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +#' "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +#' f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +#' distribution function and sigma(0) is the SD for the control group. +#' +#' "hybridPercentile" - the background risk is specified by the user in terms +#' of percentile from the control group distribution (assuming a normal +#' distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +#' the level for which the response is considered adverse, phi is the normal +#' distribution function and sigma(0) is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 2 SD +#' for "hybridSD" background and 0.9 for "hybridPercentile" +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +#' (additional hybrid), available. +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +#' p0)/ (1- p0), where x0 is the level for which the response is considered +#' adverse, phi is the normal distribution function and sigma(BMD) is the SD at +#' the benchmark dose. +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +#' p0, where x0 is the level for which the response is considered adverse, phi +#' is the normal distribution function and sigma(BMD) is the SD at the +#' benchmark dose. +#' @param interval character string specifying the type of confidence interval +#' to use: "boot" (default) or "none" +#' +#' "boot" - BMDL is based on nonparametric percentile bootstrapping. +#' +#' "none" - no confidence interval is computed. +#' @param R number of bootstrap samples. Ignored if \code{interval = "none"} +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @param progressInfo logical. If TRUE, progress info is be printed while +#' bootstrap confidence intervals are estimated. Default is TRUE. +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @return A list of four elements: Results contain the estimated BMD and BMDL, +#' Boot.samples.used gives the number of boot samples that resulted in +#' succesful estimations and were accordingly used in the estimation of BMDL +#' (and BMDU), Interval gives BMDL and BMDU, which is identical to the +#' confidence interval for the percentile interval approach, and modelWeights +#' includes the estimated weights. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' library(bmd) +#' # install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT. +#' +#' # ryegrass data +#' set.seed(123) +#' ryegrass.hetVar.list <- list( +#' drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LL.4()), +#' drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LN.4()), +#' drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W1.4()), +#' drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W2.4())) +#' bmdHetVarMA(ryegrass.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridPercentile", +#' backg = 0.1, def = "hybridExc", R = 100, level = 0.95) +#' bmdHetVarMA(ryegrass.hetVar.list, modelWeights = c(0.4, 0.2, 0.1, 0.3), bmr = 0.1, +#' backgType = "hybridPercentile", backg = 0.1, +#' def = "hybridExc", R = 50, level = 0.95) # user-defined weights +#' +#' # barley data +#' set.seed(123) +#' barley.hetVar.list <- list(drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), +#' data = barley, fct = LL.4()), +#' drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), +#' data = barley, fct = W2.4())) +#' bmdHetVarMA(barley.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", backg = 2, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) +#' +#' # GiantKelp data +#' set.seed(123) +#' GiantKelp.hetVar.list <- list( +#' drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), data = GiantKelp, fct = LL.4()), +#' drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), data = GiantKelp, fct = LL.4())) +#' bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", +#' backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, +#' display = TRUE) +#' +#' bmdHetVarMA <- function(modelList, modelWeights = c("AIC", "BIC"), bmr, backgType = c("absolute", "hybridSD", "hybridPercentile"), backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), R = 1000, level = 0.95, progressInfo = TRUE, display = TRUE){ ### Assertions ### # modelList @@ -122,4 +236,4 @@ bmdHetVarMA <- function(modelList, modelWeights = c("AIC", "BIC"), bmr, backgTyp modelWeights = modelWeights0) class(resBMD) <- c("bmdHetVar", "bmd") invisible(resBMD) -} \ No newline at end of file +} diff --git a/R/bmdIso.R b/R/bmdIso.R index 9982f4d..e084b57 100644 --- a/R/bmdIso.R +++ b/R/bmdIso.R @@ -1,3 +1,127 @@ +#' Benchmark dose estimation from isotonic regression +#' +#' The function monotonizes the sequence of response values based on the +#' pool-adjacent violators algorithm and based on these use linear +#' interpolating splines to build an isotonic regression model. From this model +#' a benchmark dose is estimated. +#' +#' Formula should be specified as in the form number/total ~ dose for binomial +#' data. For details about the use of isotonic regression for BMD estimation +#' see Piegorsch et al. (20014) and Lin et al. (2015). +#' +#' @param formula an object of class "formula" expressing the dose-response +#' relationship. Details of model specification are given under 'Details' +#' @param data data frame containing the variables in the model +#' @param type character string specifying the type of data used in the model. +#' "continuous", "binomial" or "Poisson" +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param p0 background probability for hybrid definitions +#' @param backgType character string specifying how the background level is +#' specified. For binomial data the options are "modelBased" and "absolute". +#' For continuous data the options are "absolute", "hybridSD" and +#' "hybridPercentile" +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = backg for binomial response and for the "relative" and +#' "added" definition for continuous response. p0 = 1 - phi((back - +#' f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +#' f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +#' function and sigma is the SD for the control group. "hybridPercentile" - +#' the background risk is specified by the user in terms of percentile from the +#' control group distribution (assuming a normal distribution). p0 = 1 - +#' phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +#' response is considered adverse, phi is the normal distribution function and +#' sigma is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk for binomial response (1 for decreasing +#' dose-response models), 2 SD for "hybridSD" background and 0.9 for +#' "hybridpercentile" +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess", "additional" and "point" are for +#' binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +#' "hybridAdd" (additional hybrid), and "point" are for continuous response. +#' "relative", "extra", and "point" are for count response data. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response +#' +#' "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +#' continuous response +#' +#' "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +#' response +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +#' (1- p0), where x0 is the level for which the response is considered adverse, +#' phi is the normal distribution function and sigma is the SD for the control +#' group. Works for continuous response +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +#' where x0 is the level for which the response is considered adverse, phi is +#' the normal distribution function and sigma is the SD for the control group. +#' Works for continuous response +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @return A matrix with two columns, one containing BMD and the other +#' containing BMDL. +#' @author Signe M. Jensen +#' @references Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +#' (2014). Benchmark dose analysis via nonparametric regression modeling. Risk +#' Analysis, 34(1), 135-151 +#' +#' Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +#' benchmark dose estimation with continuous dose-response data. Scandinavian +#' Journal of Statistics, 42, 713-731 +#' @keywords nonparametric isotonic regression +#' @examples +#' +#' ## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014) +#' formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0), +#' tumor.incidence = c(0, 0, 0, 3, 21, 150), +#' total = c(122, 27, 126, 113, 34, 182)) +#' +#' # Estimating BMD from isotonic regression using excess risk definition and a BMR=0.1 +#' bmdIso(tumor.incidence/total ~ conc, +#' data=formaldehyde, +#' type="binomial", +#' bmr=0.1, +#' backgType = "modelBased", +#' def = "excess") +#' +#' +#' ## Data on root length in ryegrass after exposure to ferulic acid +#' require(drc) +#' require(drcData) +#' data(ryegrass) +#' +#' # As isotonic regression only wors for increasing dose-response relationship +#' # the association is turned +#' ryegrass1<-ryegrass +#' ryegrass1$rootl<-100-ryegrass1$rootl +#' +#' # Estimating BMD from isotonic regression using relative risk definition +#' # and a BMR=0.05 +#' bmdIso(rootl ~ conc, +#' data=ryegrass1, +#' type="continuous", +#' bmr=0.05, +#' backgType = "modelBased", +#' def = "relative") +#' bmdIso <- function(formula, data, type, bmr, p0, backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), backg=NA, def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point"), display=FALSE){ object <- formula PAV.p <- PAV(object, data, type) diff --git a/R/bmdIsoBoot.R b/R/bmdIsoBoot.R index 67f17a9..7c40973 100644 --- a/R/bmdIsoBoot.R +++ b/R/bmdIsoBoot.R @@ -1,3 +1,139 @@ +#' Benchmark dose estimation from isotonic regression +#' +#' The function estimates BMD and BMDL using bootstrap based on isotonic +#' regression. +#' +#' BMD and BMDL is defined as the median and the 5th percentile in the +#' bootstrap distribution, respectively. +#' +#' Formula should be specified as in the form number/total ~ dose for binomial +#' data. +#' +#' Bootstrapping with the argument boot = "resample" is done by sampling with +#' replacement from the original data set. Bootstrapping with the argument boot +#' = "pseudorandom" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming +#' equal variance between groups, in case of continuous data. For binomial +#' data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of +#' Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always +#' produces 0 or 1, respectively. In this case data is sampled from +#' binom(N_i,(Y_i+1/3)/(N_i+1/3)). +#' +#' All sampling is made within dose groups. +#' +#' For details about the use of isotonic regression for BMD estimation see +#' Piegorsch et al. (20014) and Lin et al. (2015). +#' +#' @param formula an object of class "formula" expressing dose-response +#' relationship. Details of model specification are given under 'Details' +#' @param data data frame containing the variables in the model +#' @param type character string specifying the type of data used in the model. +#' "continuous" or "binomial" or "Poisson" +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param R number of bootstrap samples +#' @param boot character string specifying type of bootstrap used. "resample" +#' or "pseudorandom". Only option for count data is "resample" +#' @param backgType character string specifying how the background level is +#' specified. For binomial data the options are "modelBased" and "absolute". +#' For continuous data the options are "modelBased", "absolute", "hybridSD" and +#' "hybridPercentile" +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument: p0 = backg for binomial response and for the "relative" and +#' "added" definition for continuous response. p0 = 1 - phi((back - +#' f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +#' f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +#' function and sigma is the SD for the control group. "hybridPercentile" - +#' the background risk is specified by the user in terms of percentile from the +#' control group distribution (assuming a normal distribution). p0 = 1 - +#' phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +#' response is considered adverse, phi is the normal distribution function and +#' sigma is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk for binomial response (1 for decreasing +#' dose-response models), 2 SD for "hybridSD" background and 0.9 for +#' "hybridpercentile" +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess", "additional" and "point" are for +#' binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +#' "hybridAdd" (additional hybrid), and "point" are for continuous response. +#' "relative", "extra", and "point" are for count response data. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response +#' +#' "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +#' continuous response +#' +#' "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +#' response +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +#' (1- p0), where x0 is the level for which the response is considered adverse, +#' phi is the normal distribution function and sigma is the SD for the control +#' group. Works for continuous response +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +#' where x0 is the level for which the response is considered adverse, phi is +#' the normal distribution function and sigma is the SD for the control group. +#' Works for continuous response +#' @return A matrix with two columns, one containing BMD and the other +#' containing BMDL. +#' @author Signe M. Jensen +#' @references Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +#' (2014). Benchmark dose analysis via nonparametric regression modeling. Risk +#' Analysis, 34(1), 135-151 +#' +#' Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +#' benchmark dose estimation with continuous dose-response data. Scandinavian +#' Journal of Statistics, 42, 713-731 +#' @keywords nonparametric isotonic regression bootstrap +#' @examples +#' +#' ## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014) +#' formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0), +#' tumor.incidence = c(0, 0, 0, 3, 21, 150), +#' total = c(122, 27, 126, 113, 34, 182)) +#' +#' # BMD and BMDL from isotonic regression using excess risk definition and a BMR=0.1 +#' bmdIsoBoot(tumor.incidence/total ~ conc, +#' data=formaldehyde, +#' type="binomial", +#' bmr=0.1, +#' backgType = "modelBased", +#' def = "excess") +#' +#' +#' ## Data on root length in ryegrass after exposure to ferulic acid +#' require(drc) +#' data(ryegrass) +#' +#' # As isotonic regression only wors for increasing dose-response relationship +#' # the association is turned +#' ryegrass1<-ryegrass +#' ryegrass1$rootl<-100-ryegrass1$rootl +#' +#' # Estimating BMD from isotonic regression using relative risk definition and a BMR=0.05 +#' bmdIsoBoot(rootl ~ conc, +#' data=ryegrass1, +#' type="continuous", +#' bmr=0.05, +#' backgType = "modelBased", +#' def = "relative", R = 100) +#' bmdIsoBoot <- function(formula, data, type, bmr, R=1000, boot="resample", backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), backg=NA, diff --git a/R/bmdMA.R b/R/bmdMA.R index ec38cbc..beddc13 100644 --- a/R/bmdMA.R +++ b/R/bmdMA.R @@ -1,3 +1,211 @@ +#' Model-averaged benchmark dose estimation +#' +#' Estimation of benchmark doses and benchmark dose lower limit based on model +#' averaging from a user-defined list of dose response model fits +#' +#' This package project is still under development. The aim to provide an R +#' package calculating the benchmark dose (BMD) and the lower limit of the +#' corresponding 95\% confidence interval (BMDL) for continuous and quantal +#' dose-response data for a range of dose-response model based on the available +#' definitions of the benchmark dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' Bootstrapping with the argument boot = "nonparametric" is done by sampling +#' with replacement from the original data set. Bootstrapping with the argument +#' boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +#' assuming equal variance between groups, in case of continuous data. For +#' binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +#' In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +#' resampling always produces 0 or 1, respectively. In this case data is +#' sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)). +#' +#' All sampling is made within dose groups. +#' +#' @param modelList list of models of class \code{drc} +#' @param modelWeights character string specifying the type of weights used, +#' "AIC", "BIC" or "Stack" (Baalkilde, J. R., Hansen, N. R., and Jensen, S. M., +#' 2025), or a vector of the same length as the modelList with user defined +#' weights +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. For binomial data the options are "modelBased" and "absolute". +#' For continuous data the options are "absolute", "hybridSD" and +#' "hybridPercentile" +#' +#' "modelBased" - the background risk is obtained from the model as the risk +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background risk is specified by the user through the backg +#' argument: p0 = backg for binomial response and for the "relative", "extra" +#' and "added" definition for continuous response. p0 = 1 - phi((back - +#' f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. +#' +#' "hybridSD" - the background risk is specified by the user in terms of number +#' of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +#' f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +#' function and sigma is the SD for the control group. "hybridPercentile" - +#' the background risk is specified by the user in terms of percentile from the +#' control group distribution (assuming a normal distribution). p0 = 1 - +#' phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +#' response is considered adverse, phi is the normal distribution function and +#' sigma is the SD for the control group +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk for binomial response (1 for decreasing +#' dose-response models), 2 SD for "hybridSD" background and 0.9 for +#' "hybridpercentile" +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess" , "additional" and "point" are for +#' binomial response whereas "relative", "extra", "added", "hybridExc" (excess +#' hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +#' response +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for both binomial and continuous +#' response +#' +#' "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +#' continuous response +#' +#' "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +#' continuous response +#' +#' "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +#' response +#' +#' "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +#' (1- p0), where x0 is the level for which the response is considered adverse, +#' phi is the normal distribution function and sigma is the SD for the control +#' group. Works for continuous response +#' +#' "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +#' where x0 is the level for which the response is considered adverse, phi is +#' the normal distribution function and sigma is the SD for the control group. +#' Works for continuous response +#' @param respTrans if the dose-response model is fitted with a transformed +#' response, specifying this option ensures that the background level for the +#' BMD is computed on the original scale. Options include "none" (default), +#' "log" (natural logarithm) and "sqrt"(square root). +#' @param interval character string specifying the type of confidence interval +#' to use for the individual models (no effect when type = "bootstrap" or +#' "curve"): "delta" (default), "sandwich", "inv" or "profile" +#' +#' "delta" - BMDL is based on the lower limit of a Wald confidence interval +#' based on the delta method +#' +#' "sandwich" - BMDL is based on the lower limit of a Wald confidence interval +#' based on the delta method where the sandwich covariance matrix is used +#' +#' "inv" - BMDL is based on inverse regression, that is the dose associated +#' with the upper limit of the point wise confidence interval of the +#' dose-response curve. Not possible if type = "Buckland" +#' +#' "profile" - BMDL is based on the lower limit of a profile likelihood +#' confidence interval. Not possible if type = "Buckland" +#' @param type character string specifying how to estimate BMD and BMDL: +#' "curve", "bootstrap", "Kang" or "Buckland" +#' +#' "curve" - +#' +#' "bootstrap" - +#' +#' "Kang" - +#' +#' "Buckland" - +#' @param bootstrapType character string indicating type of bootstrap sampling +#' to be used if type="bootstrap" or "curve". "nonparametric" (default), or +#' "parametric" (see details) +#' @param bootInterval character string indicating how to estimate the +#' bootstrap confidence intervals used to find BMDL type="bootstrap". +#' "percentile" (default) or "BCa" (Bias corrected and adjusted) +#' @param R number of bootstrap samples to use. Default is 1000 +#' @param level numeric value specifying the level of the confidence interval +#' underlying BMDL. Default is 0.95. Note that the full CI is also computed. +#' The full CI has level 1-2*(1-level) +#' @param stackingSeed integer or NULL: Random seed to use in the data split in +#' the estimation of the Stacking Weights when \code{modelWeights = "Stack"}. +#' The global seed is reset to the initial value after estimation of the +#' weights, so this option does not interfere with a globally set seed. +#' @param stackingSplits integer or "LOO": When \code{modelWeights = "Stack"}, +#' the Stacking Weights are estimated, which are based on V-fold +#' cross-validation. The stackingSplits argument sets the number V of data +#' splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +#' to setting V equal to the number of observations in the data set. +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @param progressInfo logical. If TRUE, a progressbar is shown when computing +#' bootstrap confidence intervals. +#' @return A list of five elements: Results contain the estimated BMD and BMDL, +#' Boot.samples.used gives the number of boot samples that resulted in +#' succesful estimations and were accordingly used in the estimation of BMDL +#' (and BMDU), Interval gives BMDL and BMDU, which is identical to the +#' confidence interval for the percentile interval approach, SE gives the +#' estimated SE for the "Buckland" method, and modelWeights includes the +#' estimated weights. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @references Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +#' Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +#' \bold{57}, 698--706. +#' +#' Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +#' Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +#' +#' Baalkilde, J. R., Hansen, N. R., and Jensen, S. M. (2025) Stacking Weights +#' and Model Space Selection in Frequentist Model Averaging for Benchmark Dose +#' Estimation, \emph{Environmetrics} \bold{36(2)}, e70002. +#' @keywords model averaging nonlinear bootstrap +#' @examples +#' +#' library(drc) +#' library(drcData) +#' +#' ## Fitting 4 different two-parameter models to binomial data +#' deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial") +#' deguelin.m2 <- drm(r/n~dose, weights=n, data=deguelin, fct=W1.2(), type="binomial") +#' deguelin.m3 <- drm(r/n~dose, weights=n, data=deguelin, fct=W2.2(), type="binomial") +#' deguelin.m4 <- drm(r/n~dose, weights=n, data=deguelin, fct=LN.2(), type="binomial") +#' +#' +#' ## Model averaged BMD for 5% additional risk with estimated background risk +#' ## and BMDL based on Buckland et al. +#' bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, +#' backgType = "modelBased", def = "additional", +#' type = "Buckland") +#' +#' ## Model averaged BMD for 5% additional risk with estimated background risk +#' ## and BMDL based on an average of the model curves +#' bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, +#' backgType = "modelBased", def = "additional", +#' type = "curve", bootstrapType = "parametric", bootInterval = "percentile", R=50) +#' +#' +#' ## Fitting 4 different two-parameter models to binomial data +#' ryegrass.m1<-drm(rootl~conc, data=ryegrass, fct=LL.4()) +#' ryegrass.m2<-drm(rootl~conc, data=ryegrass, fct=W1.4()) +#' ryegrass.m3<-drm(rootl~conc, data=ryegrass, fct=W2.4()) +#' ryegrass.m4<-drm(rootl~conc, data=ryegrass, fct=LN.4()) +#' +#' ## Model-averaged BMD and bootstrap BMDL for bmr=5% and using the hybrid approach +#' ## to estimate the background risk. +#' bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="AIC", bmr=0.05, +#' backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", +#' bootstrapType = "nonparametric", bootInterval = "percentile", R = 50) +#' +#' +#' ## Model-averaged BMD using the Stacking Weights +#' bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="Stack", bmr=0.05, +#' backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", +#' bootstrapType = "nonparametric", bootInterval = "percentile", R = 50) +#' +#' bmdMA <- function(modelList, modelWeights, bmr, backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg=NA, diff --git a/R/bmdMACurve.R b/R/bmdMACurve.R index 10ed57d..ea372e3 100644 --- a/R/bmdMACurve.R +++ b/R/bmdMACurve.R @@ -1,3 +1,7 @@ +#' Help funtion to bmdMA +#' +#' +#' bmdMACurve<-function(modelList,modelWeights,bmrScaled0, searchInterval="dataBased"){ nCurves <- ncol(modelList[[1]]$parmMat) diff --git a/R/bmdOrdinal.R b/R/bmdOrdinal.R index a059145..d48bf70 100644 --- a/R/bmdOrdinal.R +++ b/R/bmdOrdinal.R @@ -1,3 +1,114 @@ +#' Benchmark dose estimation for ordinal dose-response models +#' +#' Estimation of benchmark doses and benchmark dose lower limit from ordinal +#' dose response model fits +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous, quantal, quantal and ordinal dose-response data for a range of +#' dose-response models based on the available definitions of the benchmark +#' dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' @param object object of class \code{drcOrdinal} +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. The options are "modelBased" and "absolute". +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument. +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk. +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess", "additional" and "point" are available +#' for ordinal response. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response data. +#' @param interval character string specifying the type of confidence interval +#' to use: "delta" (default), "sandwich", "profile" or "bootstrap" +#' +#' "delta" - BMDL is based on the lower limit of a Wald confidence interval +#' based on the delta method +#' +#' "sandwich" - BMDL is based on the lower limit of a Wald confidence interval +#' based on the delta method, where the sandwich covariance matrix is used +#' +#' "bootstrap" - BMDL is based on bmd estimates on resampled data sets. The +#' type of bootstrap applied can be specified by the "bootType" argument. +#' Default is "nonparametric". +#' +#' "none" - No confidence interval is computed. +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @param R integer specifying the number of data sets resampled from the +#' original data set when computing the confidence interval by bootstrap. +#' @param bootType character string specifying the resampling procedure for the +#' data sets used for bootstrap. +#' +#' "nonparametric" - Bootstrapping is done by sampling with replacement from +#' the original data set. +#' +#' "parametric" - Bootstrapping is done by sampling from a multinomial +#' distribution with probabilites given by the number of observations for each +#' level. If all observations for one group are in the same level, shrinkage is +#' used to avoid that the resampling always produces that particular level. In +#' this case data is sampled from a multinomial distribution with probabilities +#' (1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +#' 1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +#' particular group, and |K| is the number of levels. +#' +#' "model" - New data sets are resampled from the fitted model. +#' +#' "hierarchical" - If the experiment design is hierarchical (i.e. observations +#' are grouped according to a categorical variable, for instance litter), a +#' special resampling procedure is suggested (Blessinger 2020) +#' +#' All resampling is done within the dose values. +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @param progressInfo logical. If TRUE, a progressbar is displayed when +#' calculating bootstrap confidence intervals +#' @return A list of four elements: Results contain the estimated BMD and BMDL, +#' interval gives the lower (BMDL) and upper (BMDU) end of the confidence +#' interval of BMD. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @references Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +#' Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +#' \bold{57}, 698--706. +#' +#' Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +#' Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +#' +#' Blessinger, T. D., Euling, S. Y., Wang, L., Hogan, K. A., Cai, C., +#' Klinefelter, G., Saillenfait, A.M. (2020) \emph{Environment International} +#' \bold{134} +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' data(guthion) +#' +#' guthionS <- subset(guthion, trt == "S") +#' +#' guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), +#' weights = "total", dose = "dose", data = guthionS, fct = LL.2()) +#' bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50) +#' bmdOrdinal <- function(object, bmr, backgType = c("modelBased", "absolute"), backg = NA, def=c("excess", "additional", "point"), interval = c("delta", "sandwich", "profile", "bootstrap"), level = 0.95, R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical"), display = TRUE, progressInfo = TRUE){ interval <- match.arg(interval) diff --git a/R/bmdOrdinalDeltaCI.R b/R/bmdOrdinalDeltaCI.R index 5ae560f..76edd64 100644 --- a/R/bmdOrdinalDeltaCI.R +++ b/R/bmdOrdinalDeltaCI.R @@ -145,4 +145,4 @@ # CI <- tmp$confint[1,2:3] # } # CI -# } \ No newline at end of file +# } diff --git a/R/bmdOrdinalMA.R b/R/bmdOrdinalMA.R index dfda41d..0e5a4e1 100644 --- a/R/bmdOrdinalMA.R +++ b/R/bmdOrdinalMA.R @@ -1,3 +1,109 @@ +#' Benchmark dose estimation for ordinal dose-response models +#' +#' Estimation of benchmark doses and benchmark dose lower limit based on model +#' averaging from a user-defined list of ordinal dose-response model fits +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous, quantal, quantal and ordinal dose-response data for a range of +#' dose-response models based on the available definitions of the benchmark +#' dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' @param modelList A list of ordinal dose-response models of class +#' \code{drcOrdinal} +#' @param modelWeights character string specifying the type of weights used, +#' "AIC" or "BIC", or a numeric vector of the same length as the modelList with +#' user defined weights +#' @param bmr numeric value of benchmark response level for which to calculate +#' the benchmark dose +#' @param backgType character string specifying how the background level is +#' specified. The options are "modelBased" and "absolute". +#' +#' "modelBased" - the background level is obtained from the model as the level +#' for dose 0: p0 = f(0) +#' +#' "absolute" - the background level is specified by the user through the backg +#' argument. +#' @param backg numeric value specifying the background level. Defaults to 0 +#' for "absolute" background risk. +#' @param def character string specifying the definition of the benchmark dose +#' to use in the calculations. "excess", "additional" and "point" are available +#' for ordinal response. +#' +#' "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +#' binomial response. BMR should be between 0 and 1. +#' +#' "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +#' response. BMR should be between 0 and 1. +#' +#' "point" - The response level for which to find BMD is directly defined +#' through the BMR level: BMR = f(BMD). Works for binomial, count and +#' continuous response data. +#' @param type specify the model averaging type used for the confidence +#' intervals. Options are "Kang" (confidence intervals computed as weighted +#' averages of individual confidence intervals) and "bootstrap" +#' @param level numeric value specifying the levle of the confidence interval +#' underlying BMDL. Default is 0.95 +#' @param R integer specifying the number of data sets resampled from the +#' original data set when computing the confidence interval by bootstrap. +#' @param bootType character string specifying the resampling procedure for the +#' data sets used for bootstrap. +#' +#' "nonparametric" - Bootstrapping is done by sampling with replacement from +#' the original data set. +#' +#' "parametric" - Bootstrapping is done by sampling from a multinomial +#' distribution with probabilites given by the number of observations for each +#' level. If all observations for one group are in the same level, shrinkage is +#' used to avoid that the resampling always produces that particular level. In +#' this case data is sampled from a multinomial distribution with probabilities +#' (1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +#' 1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +#' particular group, and |K| is the number of levels. +#' +#' All resampling is done within the dose values. +#' @param display logical. If TRUE the results are displayed; otherwise they +#' are not +#' @param progressInfo logical. If TRUE, a progressbar is displayed when +#' calculating bootstrap confidence intervals +#' @return A list of four elements: Results contain the estimated BMD and BMDL, +#' interval gives the lower (BMDL) and upper (BMDU) end of the confidence +#' interval of BMD. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @references Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +#' Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +#' \bold{57}, 698--706. +#' +#' Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +#' Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' data(guthion) +#' +#' guthionS <- subset(guthion, trt == "S") +#' +#' guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), +#' weights = "total", dose = "dose", data = guthionS, fct = LL.2()) +#' guthionS.LN <- drmOrdinal(levels = c("alive", "moribund", "dead"), +#' weights = "total", dose = "dose", data = guthionS, fct = LN.2()) +#' guthionS.W1 <- drmOrdinal(levels = c("alive", "moribund", "dead"), +#' weights = "total", dose = "dose", data = guthionS, fct = W1.2()) +#' guthionS.W2 <- drmOrdinal(levels = c("alive", "moribund", "dead"), +#' weights = "total", dose = "dose", data = guthionS, fct = W2.2()) +#' +#' bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), +#' modelWeights = "AIC", bmr = 0.1, +#' backgType = "modelBased", def = "excess", type = "Kang") +#' bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), +#' modelWeights = "AIC", bmr = 0.1, +#' backgType = "modelBased", def = "excess", type = "bootstrap", R = 50) +#' bmdOrdinalMA <- function(modelList, modelWeights = c("AIC", "BIC"), bmr, backgType = c("modelBased", "absolute"), backg = NA, def = c("excess", "additional", "point"), type = c("bootstrap", "Kang"), level = 0.95, R = 500, bootType = c("nonparametric", "parametric"), display = TRUE, progressInfo = TRUE){ # assertions if(!all(sapply(modelList, function(object) inherits(object, "drcOrdinal")))){ diff --git a/R/bmdProfileCI.R b/R/bmdProfileCI.R index eedbe67..ad132e2 100644 --- a/R/bmdProfileCI.R +++ b/R/bmdProfileCI.R @@ -42,4 +42,4 @@ bmdProfileCI <- function(object, slope, bmr, backgType, backg, # controlSD, upper = grid[which(grid == max(grid[accept])) + 1])$root |> try(silent = TRUE) |> as.numeric() c(BMDL = CIlower, BMDU = CIupper) -} \ No newline at end of file +} diff --git a/R/bmdProfileCIgrid.R b/R/bmdProfileCIgrid.R index 248fc31..1165313 100644 --- a/R/bmdProfileCIgrid.R +++ b/R/bmdProfileCIgrid.R @@ -112,4 +112,4 @@ bmdProfileCIgrid <- function(object, bmr, backgType = c("modelBased", "absolute" CI <- c(BMDL = min(bmdVals, na.rm = TRUE), BMDU = max(bmdVals, na.rm = TRUE)) CI -} \ No newline at end of file +} diff --git a/R/bootDataGen.R b/R/bootDataGen.R index 1c6bb6e..a16581b 100644 --- a/R/bootDataGen.R +++ b/R/bootDataGen.R @@ -1,3 +1,7 @@ +#' Help funtion to bmdBoot +#' +#' +#' bootDataGen <- function(object, R=1000, bootType="nonparametric",aggregated=TRUE){ if(bootType=="nonparametric"){ if(object$type=="binomial"){ diff --git a/R/bootDataGenHetVar.R b/R/bootDataGenHetVar.R index 5377550..2f4e4b1 100644 --- a/R/bootDataGenHetVar.R +++ b/R/bootDataGenHetVar.R @@ -47,4 +47,4 @@ bootDataGenHetVar <- function(object, R=1000, bootType=c("nonparametric", "semip } return(tmp.data) -} \ No newline at end of file +} diff --git a/R/bootDataGenOrdinal.R b/R/bootDataGenOrdinal.R index 9594c5f..cf3a7a0 100644 --- a/R/bootDataGenOrdinal.R +++ b/R/bootDataGenOrdinal.R @@ -1,3 +1,7 @@ +#' Help funtion to bmdOrdinal and bmdOrdinalMA +#' +#' +#' bootDataGenOrdinal <- function(object, R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical")){ bootType <- match.arg(bootType) diff --git a/R/coef.drcHetVar.R b/R/coef.drcHetVar.R index 9cb2bcb..19d95a6 100644 --- a/R/coef.drcHetVar.R +++ b/R/coef.drcHetVar.R @@ -1,7 +1,10 @@ + +#' @title S3 method +#' @export coef.drcHetVar <- function(object, ...){ curvePar <- object$curvePar names(curvePar) <- paste0("Curve:", names(curvePar)) sigmaPar <- object$sigmaPar names(sigmaPar) <- paste0("Sigma:", names(sigmaPar)) c(curvePar, sigmaPar) -} \ No newline at end of file +} diff --git a/R/drmHetVar.R b/R/drmHetVar.R index 25ebf0e..23602a5 100644 --- a/R/drmHetVar.R +++ b/R/drmHetVar.R @@ -1,3 +1,75 @@ +#' Dose response modeling with heterogeneous variance +#' +#' Fit a dose-response model with heterogeneous variance dependending on dose +#' level. +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' REFERENCES TO BE ADDED/WRITTEN +#' +#' @param formula formula for the dose-response relationship +#' @param var.formula one-sided formula specifying the dependance of the dose +#' values and/or the fitted values on the point-wise standard error +#' @param data data.frame containing the observations +#' @param fct a list with three or more elements specifying the non-linear +#' function, the accompanying self starter function, the names of the parameter +#' in the non-linear function and, optionally, the first and second derivatives +#' as well as information used for calculation of ED values. Currently +#' available functions include, among others, the four- and five-parameter +#' log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +#' drc::getMeanFunctions for a full list. +#' @param curveStart numerical of length equal to the number of parameters for +#' the curve. Starting values for the curve parameters (optional). +#' @return dose-response model with a heterogeneous variance structure of class +#' \code{drcHetVar}. +#' +#' The primary objective is to use this model for benchmark dose estimation +#' based on the hybrid method with a heterogeneous variance structure. This can +#' be done using the \code{bmdHetVar} function. +#' +#' A plot method is available, which can be useful for assessing the fit of the +#' variance structure. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' library(bmd) +#' # install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT. +#' +#' # ryegrass data +#' set.seed(123) +#' ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), +#' data = ryegrass, fct = LL.4()) +#' plot(ryegrass.LL.4.hetVar) +#' bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, +#' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) +#' bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, +#' def = "hybridExc", R = 50, level = 0.95, +#' bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap +#' +#' # barley data +#' set.seed(123) +#' barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4()) +#' plot(barley.LL.4.hetVar) +#' +#' # GiantKelp data +#' set.seed(123) +#' GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), +#' data = GiantKelp, fct = LL.4()) +#' plot(GiantKelp.LL.4.hetVarSq) +#' +#' GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), +#' data = GiantKelp, fct = LL.4()) +#' plot(GiantKelp.LL.4.hetVarLogSq) +#' +#' +#' +#' drmHetVar <- function(formula, var.formula, data, fct, curveStart = NULL) { call <- match.call() @@ -119,4 +191,4 @@ drmHetVar <- function(formula, var.formula, data, fct, curveStart = NULL) { class(object) <- c("drcHetVar", "drc") return(object) -} \ No newline at end of file +} diff --git a/R/drmMMRE.R b/R/drmMMRE.R index bee7a26..0c87143 100644 --- a/R/drmMMRE.R +++ b/R/drmMMRE.R @@ -1,3 +1,60 @@ +#' Dose response modeling with hierarchical variance structure +#' +#' Fits a meta-analytic hierarchical dose-response model. +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' Fitting the meta-analytic model relies on a multivariate meta-analytic model +#' provided by the function \code{rma.mv} in the "metafor" package, which can +#' be installed by running \code{remotes::install_github("wviechtb/metafor")} +#' +#' Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor +#' package. Journal of Statistical Software, 36(3), 1-48. +#' doi:10.18637/jss.v036.i03 +#' +#' @param formula a symbolic description of the model to be fit of the form +#' 'response ~ dose' +#' @param exp_id the name of the column in the data set that specifies the +#' hierarchical structure of the data +#' @param data a data frame containing the variables in the model. +#' @param fct a list with three or more elements specifying the non-linear +#' function, the accompanying self starter function, the names of the parameter +#' in the non-linear function and, optionally, the first and second derivatives +#' as well as information used for calculation of ED values. Currently +#' available functions include, among others, the four- and five-parameter +#' log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +#' drc::getMeanFunctions for a full list. +#' @param type a character string specifying the distribution of the data. The +#' default is "continuous", corresponding to assuming a normal distribution. +#' "binary" imply a binomial distribution. +#' @return meta-analytic dose-response model with a hierarchical variance +#' structure of class \code{drcMMRE}. +#' +#' The primary objective is to use this model for benchmark dose estimation +#' based on dose-response data with a heterogeneous variance structure. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' library(metafor) +#' library(bmd) +#' +#' set.seed(1) +#' data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2), +#' y = rep(drcData::ryegrass$rootl, 2) + +#' c(rnorm(n = nrow(drcData::ryegrass), mean = 2, sd = 0.5), +#' rnorm(n = nrow(drcData::ryegrass), mean = 2.7, sd = 0.7)), +#' EXP_ID = rep(as.character(1:2), each = nrow(drcData::ryegrass))) +#' +#' modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4()) +#' bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative") +#' +#' drmMMRE <- function(formula, exp_id, data, fct, type = c("continuous", "binomial")){ call_expr <- match.call() @@ -103,7 +160,8 @@ drmMMRE <- function(formula, exp_id, data, fct, type = c("continuous", "binomial object } - +#' @title S3 method +#' @export vcov.drcMMRE <- function(object, ...){ vcov(object$MV_MA_model) } diff --git a/R/drmOrdinal.R b/R/drmOrdinal.R index 08a711d..1b1b946 100644 --- a/R/drmOrdinal.R +++ b/R/drmOrdinal.R @@ -1,3 +1,49 @@ +#' Fitting ordinal dose-response models +#' +#' A model fitting function for analysis of ordinal dose-response data. +#' +#' This functions fits a dose-response model for ordinal dose-response data by +#' fitting a series of binomial dose-response models. +#' +#' @param levels a character vector of the levels of the response variable in +#' increasing order, as they appear in the supplied data set +#' @param dose a character string specifying the column with the dose values in +#' the supplied data set +#' @param weights a character string specifying the column containing the +#' number of observations pr. group +#' @param blocks a character string specifying the column containing the blocks +#' of the experiment, if available (optional) +#' @param data a dataframe containing the observations +#' @param fct a list with three or more elements specifying the non-linear +#' function, the accompanying self starter function, the names of the parameter +#' in the non-linear function and, optionally, the first and second derivatives +#' as well, for the individual fitted curves. For more information see the help +#' page for the "drm" function in the "drc" package. Currently available +#' functions for ordinal dose-response models include, among others, the +#' log-logistic models \code{\link[drc]{LL.4}}, the log-normal model +#' \code{\link[drc]{LN.4}} and the two Weibull models \code{\link[drc]{W1.4}} +#' and \code{\link[drc]{W2.4}}. Use \code{\link[drc]{getMeanFunctions}} for a +#' full list. +#' @param p.epsilon numeric value specifying the lower bound for the +#' probabilites for each level returned by the function pFun created when +#' fitting the model. Default value is 10^(-16) +#' @return An object of (S3) class 'drcOrdinal'. +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @references # ADD REFERENCES +#' @keywords models nonlinear +#' @examples +#' +#' library(drc) +#' library(drcData) +#' data(guthion) +#' guthionS <- subset(guthion, trt == "S") +#' +#' guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "total", +#' dose = "dose", data = guthionS, fct = LL.2()) +#' +#' plot(guthionS.LL, xlim = c(15,55)) # uses ggplot +#' +#' drmOrdinal <- function(levels, dose, weights, blocks, data, fct, p.epsilon = 1e-16){ if(missing(blocks)){ blocks = NULL diff --git a/R/expandBinomial.R b/R/expandBinomial.R index 68fe8d7..edda01a 100644 --- a/R/expandBinomial.R +++ b/R/expandBinomial.R @@ -1,3 +1,28 @@ +#' Utility function +#' +#' Utility function for expanding binomial data +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' @param data a data.frame +#' @param number the name of the column in the data set containing the number +#' of affected individuals per dose level +#' @param total the name of the column in the data set containing the total +#' number of individuals per dose level +#' @param dose the name of the column in the data set containing the dose +#' values +#' @param curveid the name of the column in the data set specifying the curveid +#' (if available) +#' @return data.frame +#' @author Signe M. Jensen and Jens Riis Baalkilde +#' @keywords models nonlinear +#' @examples \dontrun{ +#' } +#' +#' expandBinomial <- function(data, number, total, dose, curveid = character(0)){ if(length(curveid) == 0){ df<-data.frame(number = c(rep(rep(1,length(data[,number])), data[,number]), diff --git a/R/getBmrScaledList.R b/R/getBmrScaledList.R index 75f2258..439b008 100644 --- a/R/getBmrScaledList.R +++ b/R/getBmrScaledList.R @@ -270,4 +270,4 @@ getBmrScaledList <- function(object, bmr, backgType = c("modelBased", "absolute" } list(bmrScaledMat = bmrScaledMat, dBmrScaledMat = dBmrScaledMat) -} \ No newline at end of file +} diff --git a/R/getBmrScaledRepar.R b/R/getBmrScaledRepar.R index 277ecc2..d54d8b1 100644 --- a/R/getBmrScaledRepar.R +++ b/R/getBmrScaledRepar.R @@ -179,4 +179,4 @@ getBmrScaledRepar <- function(cdVec, slope, bmr, backgType, } bmrScaled -} \ No newline at end of file +} diff --git a/R/getFctDerivx.R b/R/getFctDerivx.R index 1003f6a..ec8799b 100644 --- a/R/getFctDerivx.R +++ b/R/getFctDerivx.R @@ -151,4 +151,4 @@ getFctDerivx <- function(object){ } derivx -} \ No newline at end of file +} diff --git a/R/getStackingWeights.R b/R/getStackingWeights.R index 80e006f..c3e6b0d 100644 --- a/R/getStackingWeights.R +++ b/R/getStackingWeights.R @@ -200,6 +200,46 @@ getDataSplits <- function(object, nSplits){ splitList } + + +#' Model-average dose-response curves +#' +#' Computing stacking weights. +#' +#' The aim to provide an R package calculating the benchmark dose (BMD) and the +#' lower limit of the corresponding 95\% confidence interval (BMDL) for +#' continuous and quantal dose-response data for a range of dose-response +#' models based on the available definitions of the benchmark dose concepts. +#' +#' Details on the implemented definitions and methods can be found in Crump +#' (2002) +#' +#' @param modelList list of models of class \code{drc} +#' @param nSplits integer. The Stacking Weights are based on V-fold +#' cross-validation. The nSplits argument sets the number V of data splits used +#' in the cross validation. +#' @return numeric +#' @author Jens Riis Baalkilde +#' @keywords models nonlinear model averaging +#' @examples +#' +#' library(bmd) +#' library(drc) +#' library(drcData) +#' +#' # fit models to aconiazide data +#' aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3()) +#' aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3()) +#' aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3()) +#' aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3()) +#' +#' getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, +#' aconiazide.W1.3, aconiazide.W2.3)) +#' getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, +#' aconiazide.W1.3, aconiazide.W2.3), +#' nSplits = 7) +#' +#' getStackingWeights <- function(modelList, nSplits = 2){ if(!requireNamespace("CVXR")){ stop('package "CVXR" must be installed to estimate stacking weights') diff --git a/R/invBmd.R b/R/invBmd.R index e213a3f..cd3388e 100644 --- a/R/invBmd.R +++ b/R/invBmd.R @@ -1,3 +1,7 @@ +#' Help funtion to bmd +#' +#' +#' invBmd <- function(object, bmr, level=0.9, slope, backgType="modelBased", backg=NA, catLev=NA, extFactor=10, def, useSD=useSD, sandwich.vcov=FALSE){ diff --git a/R/logLik.drcHetVar.R b/R/logLik.drcHetVar.R index 8838022..1f4303c 100644 --- a/R/logLik.drcHetVar.R +++ b/R/logLik.drcHetVar.R @@ -1,11 +1,18 @@ + +#' @title S3 method +#' @export logLik.drcHetVar <- function(object, ...){ - object$sumList$numObs/2 * log(2*pi) - object$value/2 } +#' @title S3 method +#' @export AIC.drcHetVar <- function(object, ..., k = 2){ 2*object$sumList$numPar - k*logLik(object) } +#' @title S3 method +#' @export BIC.drcHetVar <- function(object, ...){ object$sumList$numPar*log(object$sumList$numObs) - 2*logLik(object) } diff --git a/R/logLik.drcOrdinal.R b/R/logLik.drcOrdinal.R index b6eda0e..3a24219 100644 --- a/R/logLik.drcOrdinal.R +++ b/R/logLik.drcOrdinal.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export logLik.drcOrdinal <- function(object, ...){ dots <- list(...) if (!is.null(dots$epsilon)){ diff --git a/R/monotonicityTest.R b/R/monotonicityTest.R index c0edd37..0d9891b 100644 --- a/R/monotonicityTest.R +++ b/R/monotonicityTest.R @@ -1,3 +1,50 @@ +#' Test for Monotonicity of Relationship Between Two Variables +#' +#' Conducts a test for monotonicity between a numeric independent variable +#' \code{x} and a numeric dependent variable \code{y} using specified +#' statistical tests. +#' +#' The function tests the monotonicity of the relationship between \code{x} and +#' \code{y} based on the specified test: \itemize{ \item \code{"jonckheere"}: +#' Uses the Jonckheere-Terpstra test to assess monotonic trends. \item +#' \code{"bartholomew"}: Uses Bartholomew's test to assess monotonicity. } +#' +#' The direction of the monotonicity (increasing or decreasing) is determined +#' by the sign of the coefficient from a simple linear model \code{lm(y ~ x)}. +#' +#' @param x A numeric vector or the name of the independent variable (if +#' \code{data} is provided). +#' @param y A numeric vector or the name of the dependent variable (if +#' \code{data} is provided). +#' @param data An optional data frame containing the variables \code{x} and +#' \code{y}. If provided, \code{x} and \code{y} should be column names in +#' \code{data}. +#' @param test A character string specifying the test to use. Must be one of +#' \code{"jonckheere"} (default) or \code{"bartholomew"}. +#' @param level Significance level for the test. Defaults to 0.05. +#' @param ... Additional arguments passed to the underlying test functions. +#' @return A list with the following components: \item{p.value}{The p-value of +#' the test.} \item{acceptMonotonicity}{A logical value indicating whether +#' monotonicity is accepted (\code{TRUE}) or rejected (\code{FALSE}) based on +#' the specified significance level.} +#' @author Jens Riis Baalkilde +#' @seealso \code{.jonckheereTest}, \code{.bartholomewTest} +#' @references A. R. Jonckheere (1954). "A Distribution-Free k-Sample Test +#' Against Ordered Alternatives." D. J. Bartholomew (1961). "Ordered tests in +#' the analysis of variance." OECD (2006). Rapport No. 54, Annexes. +#' @keywords monotonicity, trend test +#' @examples +#' +#' # Example with custom data +#' x <- c(1, 2, 3, 4, 5) +#' y <- c(2, 4, 6, 8, 10) +#' result <- monotonicityTest(x, y, test = "jonckheere") +#' print(result) +#' +#' data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) +#' result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew") +#' print(result) +#' monotonicityTest <- function(x, y, data, test = c("jonckheere", "bartholomew"), level = 0.05, ...){ # , "drc", "quad" if(!missing(data)){ x <- data[[x]] diff --git a/R/plot.bmd.R b/R/plot.bmd.R index cbb194f..b93962a 100644 --- a/R/plot.bmd.R +++ b/R/plot.bmd.R @@ -1,3 +1,41 @@ +#' Plotting benchmark doses +#' +#' \code{plot.bmd} displays benchmark dose values with options to plot +#' confidence intervals as well. +#' +#' This function is a simple function to plot benchmark dose values along with +#' the fitted curve. +#' +#' @aliases plot.bmd \method{plot}{bmd} +#' @param x an object of class 'bmd'. +#' @param ... arguments to be passed on to \code{plot.drc}, if \code{add = +#' FALSE} +#' @param interval option to plot only the lower limit of the confidence +#' interval for the benchmark dose ("BMDL", default), both limit of the +#' confidence interval ("twosided"), or no confidence interval ("none"). +#' @return Creates a plot. No value returned. +#' @author Jens Riis Baalkilde. +#' @keywords ggplot +#' @examples +#' +#' library(drc) +#' library(drcData) +#' +#' ## Fitting model and calculating BMD. +#' model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) +#' bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative") +#' +#' ## Plotting +#' plot(bmd0) +#' +#' # Plot both limits of confidence interval +#' plot(bmd0, interval = "twosided") +#' +#' # Pass argument to plot.bmd to plot confidence band around curve +#' plot(bmd0, type = "confidence") +#' +#' +#' plot.bmd <- function(x, ..., interval = c("BMDL", "twosided", "none")){ object <- x model <- object$model diff --git a/R/plot.drcHetVar.R b/R/plot.drcHetVar.R index cafc325..218e3de 100644 --- a/R/plot.drcHetVar.R +++ b/R/plot.drcHetVar.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export plot.drcHetVar <- function(x, ...){ object <- x dots <- list(...) @@ -57,4 +60,4 @@ plot.drcHetVar <- function(x, ...){ (gridExtra::grid.arrange(p1, p2)) invisible(list(p1,p2)) -} \ No newline at end of file +} diff --git a/R/plot.drcOrdinal.R b/R/plot.drcOrdinal.R index cf9c7ed..ed1375f 100644 --- a/R/plot.drcOrdinal.R +++ b/R/plot.drcOrdinal.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export plot.drcOrdinal <- function(x, ...){ object <- x dots <- list(...) diff --git a/R/print.bmd.R b/R/print.bmd.R index a495841..ee19688 100644 --- a/R/print.bmd.R +++ b/R/print.bmd.R @@ -13,4 +13,4 @@ cat("\n") invisible(object) -} \ No newline at end of file +} diff --git a/R/print.bmdHetVar.R b/R/print.bmdHetVar.R index 065455b..9457125 100644 --- a/R/print.bmdHetVar.R +++ b/R/print.bmdHetVar.R @@ -13,4 +13,4 @@ cat("\n") invisible(object) -} \ No newline at end of file +} diff --git a/R/print.bmdOrdinal.R b/R/print.bmdOrdinal.R index a7357b8..6b974dc 100644 --- a/R/print.bmdOrdinal.R +++ b/R/print.bmdOrdinal.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export print.bmdOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) { object <- x @@ -13,4 +16,4 @@ print.bmdOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) cat("\n") invisible(object) -} \ No newline at end of file +} diff --git a/R/print.drcHetVar.R b/R/print.drcHetVar.R index 81a14c1..09728c5 100644 --- a/R/print.drcHetVar.R +++ b/R/print.drcHetVar.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export print.drcHetVar <- function(x, ..., digits = max(3, getOption("digits") - 3)){ object <- x classList <- class(object) @@ -17,4 +20,4 @@ print.drcHetVar <- function(x, ..., digits = max(3, getOption("digits") - 3)){ # END invisible(object) -} \ No newline at end of file +} diff --git a/R/print.drcMMRE.R b/R/print.drcMMRE.R index f139a66..c13cd88 100644 --- a/R/print.drcMMRE.R +++ b/R/print.drcMMRE.R @@ -1,3 +1,6 @@ + +#' @title S3 method +#' @export print.drcMMRE <- function (x, ..., digits = max(3, getOption("digits") - 3)) { object <- x @@ -14,4 +17,4 @@ print.drcMMRE <- function (x, ..., digits = max(3, getOption("digits") - 3)) } cat("\n") invisible(object) -} \ No newline at end of file +} diff --git a/R/print.drcOrdinal.R b/R/print.drcOrdinal.R index c7cfdf5..508c94c 100644 --- a/R/print.drcOrdinal.R +++ b/R/print.drcOrdinal.R @@ -1,4 +1,7 @@ print.drcOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) +#' @title S3 method +#' @export +print.drcOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) { object <- x classList <- class(object) diff --git a/R/qplotBmd.R b/R/qplotBmd.R index 85947b3..1ea0cc8 100644 --- a/R/qplotBmd.R +++ b/R/qplotBmd.R @@ -1,3 +1,43 @@ +#' Plotting benchmark doses using ggplot2 +#' +#' \code{qplotBmd} displays benchmark dose values with options to plot +#' confidence intervals as well using \code{ggplot2}. +#' +#' This function is a simple function to plot benchmark dose values +#' +#' @param x an object of class 'bmd'. +#' @param ... arguments to be passed on to qplotDrc, if \code{add = FALSE} +#' @param interval option to plot only the lower limit of the confidence +#' interval for the benchmark dose ("BMDL", default), both limit of the +#' confidence interval ("twosided"), or no confidence interval ("none"). +#' @param col logical. If TRUE then multiple curves specified by "curveid" in +#' the dose-response model are distinguised by colours rather than point shapes +#' and line types +#' @param add logical. If TRUE then the functions returns a list of plot layers +#' to be added to an already existing ggplot. +#' @return A \code{ggplot} object. If the option \code{add} is used, a list of +#' \code{ggplot} layers is returned. +#' @author Jens Riis Baalkilde. +#' @keywords ggplot +#' @examples +#' +#' library(drc) +#' library(drcData) +#' +#' ## Fitting model and calculating BMD. +#' model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) +#' bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative") +#' +#' # Plot +#' qplotBmd(bmd0, interval = "twosided", add = FALSE) +#' +#' qplotDrc(model,type="confidence") + +#' qplotBmd(bmd0, interval = "twosided", add = TRUE) +#' +#' qplotBmd(bmd0, interval = "twosided", add = FALSE) +#' +#' +#' qplotBmd <- function(x, ..., interval = c("BMDL", "twosided", "none"), col = FALSE, add = FALSE){ object <- x diff --git a/R/qplotDrc.R b/R/qplotDrc.R index c9a2feb..494c131 100644 --- a/R/qplotDrc.R +++ b/R/qplotDrc.R @@ -1,3 +1,125 @@ +#' Plotting fitted dose-response curves using ggplot2 +#' +#' \code{qplotDrc} displays fitted curves and observations in the same plot +#' window, distinguishing between curves by different plot symbols and line +#' types or colours using \code{ggplot2}. +#' +#' This function largely seeks to mimic the behaviour of the \code{plot} method +#' for the \code{drc} package using the \code{ggplot2} package for plotting. +#' +#' The use of \code{xlim} allows changing the range of the x axis, +#' extrapolating the fitted dose-response curves. Note that changing the range +#' on the x axis may also entail a change of the range on the y axis. +#' +#' See \code{\link{colors}} for the available colours. +#' +#' Suitable labels are automatically provided. +#' +#' The model-based standard errors used for the error bars are calculated as +#' the fitted value plus/minus the estimated error times the 1-(alpha/2) +#' quantile in the t distribution with degrees of freedom equal to the residual +#' degrees of freedom for the model (or using a standard normal distribution in +#' case of binomial and poisson data), where alpha=1-confidence.level. The +#' standard errors are obtained using the predict method with the arguments +#' interval = "confidence" and level=confidence.level. +#' +#' @param x an object of class 'drc'. +#' @param add logical. If TRUE then the functions returns a list of plot layers +#' to be added to an already existing ggplot. +#' @param level vector of curve levels to plot. To plot only the curves +#' specified by their names. +#' @param type a character string specifying how to plot the data. There are +#' currently 5 options: "average" (averages and fitted curve(s); default), +#' "none" (only the fitted curve(s)), "obs" (only the data points), "all" (all +#' data points and fitted curve(s)), "bars" (averages and fitted curve(s) with +#' model-based standard errors (see Details)), and "confidence" (confidence +#' bands for fitted curve(s)). +#' @param gridsize numeric. Number of points in the grid used for plotting the +#' fitted curves. +#' @param xtrans Transformation to use on the x-axis. The default is +#' "pesudo_log", which is a logarithmic transformation with a smooth transition +#' to 0. Other options include (among others) "log" and "identity". Can be +#' overridden by adding a scale using the \code{scale_x_continuous} function. +#' @param xlab an optional label for the x axis. +#' @param xlim a numeric vector of length two, containing the lower and upper +#' limit for the x axis. +#' @param ytrans Transformation to use on the y-axis. The default is no +#' transformation. Other options include (among others) "pseudo_log" and "log" +#' and. Can be overridden by adding a scale using the \code{scale_y_continuous} +#' function. +#' @param ylab an optional label for the y axis. +#' @param ylim a numeric vector of length two, containing the lower and upper +#' limit for the y axis. +#' @param col logical. If TRUE default ggplot colours are used, can be +#' overridden by \code{scale_color_manual}. If FALSE (default) no colours are +#' used. +#' @param normal logical. If TRUE the plot of the normalized data and fitted +#' curves are shown (for details see Weimer et al. (2012) for details). +#' @param normRef numeric specifying the reference for the normalization +#' (default is 1). +#' @param confidence.level confidence level for error bars and confidence +#' bands. Defaults to 0.95. +#' @return A \code{ggplot} object. If the option \code{add} is used, a list of +#' \code{ggplot} layers is returned. +#' @author Jens Riis Baalkilde. Based on \code{plot.drc} by Christian Ritz and +#' Jens C. Streibig with Contributions from Xiaoyan Wang and Greg Warnes. +#' @references Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., +#' Kopp-Schneider, A. (2012) The impact of data transformations on +#' concentration-response modeling. \emph{Toxicology Letters}, \bold{213}, +#' 292--298. +#' @keywords ggplot +#' @examples +#' +#' library(drc) +#' library(drcData) +#' library(ggplot2) +#' +#' ## Fitting models to be plotted below +#' ryegrass.m1 <- drm(rootl~conc, data = ryegrass, fct = LL.4()) +#' ryegrass.m2 <- drm(rootl~conc, data = ryegrass, fct = LL.3()) # lower limit fixed at 0 +#' +#' ## Plotting observations and fitted curve for the first model +#' p <- qplotDrc(ryegrass.m1) +#' p +#' +#' ## Add confidence region for the first model. +#' p + qplotDrc(ryegrass.m1, type="confidence", add = TRUE)$confBandLayer +#' +#' ## Plot both models +#' p + qplotDrc(ryegrass.m2, add = TRUE)$curveLayer +#' +#' ## Fitting model to be plotted below +#' spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4()) +#' +#' ## Plot with no colours +#' qplotDrc(spinach.m1) +#' +#' ## Plot with default colours +#' qplotDrc(spinach.m1, col = TRUE) +#' +#' ## Plot with specified colours +#' qplotDrc(spinach.m1, col = TRUE) + +#' scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", +#' "darkslategray4", "plum4")) +#' +#' ## Plot of curves 1 and 2 only +#' qplotDrc(spinach.m1, level = c(1,4)) +#' +#' ## Plot with confidence regions +#' qplotDrc(spinach.m1, col = TRUE, type = "confidence") +#' +#' ## Plot points and add confidence regions. Confidence regions are coloured by the "fill" aesthetic. +#' ## Customising the x scale by adding a new scale. +#' qplotDrc(spinach.m1, col = TRUE, type = "confidence") + +#' qplotDrc(spinach.m1, col = TRUE, type = "average", add = TRUE)$obsLayer + +#' scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", +#' "darkslategray4", "plum4"))+ +#' scale_fill_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", +#' "darkslategray4", "plum4")) + +#' scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1))) +#' +#' +#' qplotDrc <- function(x, add = FALSE, level = NULL, type = c("average", "all", "bars", "none", "obs", "confidence"), gridsize = 250, xtrans = "pseudo_log", xlab, xlim, ytrans = NULL, ylab, ylim, col = FALSE, diff --git a/R/shirleyTest.R b/R/shirleyTest.R index c6fb520..98cd458 100644 --- a/R/shirleyTest.R +++ b/R/shirleyTest.R @@ -117,4 +117,4 @@ dist = "t'", model = DAT) class(ans) <- "osrt" return(ans) -} \ No newline at end of file +} diff --git a/R/trendTest.R b/R/trendTest.R index 622ebfa..5903093 100644 --- a/R/trendTest.R +++ b/R/trendTest.R @@ -1,3 +1,57 @@ +#' Test for Trend in Relationship Between Two Variables +#' +#' Conducts a test for trends between a numeric independent variable \code{x} +#' and a numeric dependent variable \code{y} using specified statistical tests. +#' +#' The function tests for a trend in the relationship between \code{x} and +#' \code{y} based on the specified test: \itemize{ \item \code{"william"}: +#' Applies Williams' test to assess trend significance. \item +#' \code{"shirley"}: Uses Shirley's test for trend analysis with ordered +#' alternatives. \item \code{"tukey"}: Implements the Tukey trend test using +#' multiple marginal models. } +#' +#' The direction of the trend (increasing or decreasing) is determined by the +#' slope of the linear model \code{lm(y ~ x)}. +#' +#' @param x A numeric vector or the name of the independent variable (if +#' \code{data} is provided). +#' @param y A numeric vector or the name of the dependent variable (if +#' \code{data} is provided). +#' @param data An optional data frame containing the variables \code{x} and +#' \code{y}. If provided, \code{x} and \code{y} should be column names in +#' \code{data}. +#' @param test A character string specifying the test to use. Must be one of +#' \code{"william"}, \code{"shirley"}, or \code{"tukey"} (default). +#' @param level Significance level for the test. Defaults to 0.05. +#' @return A list with the following components: \item{p.values}{A numeric +#' vector of p-values for the tests (if applicable).} \item{decisions}{A +#' character vector indicating whether the trend is \code{"accept"} or +#' \code{"reject"} based on the test results.} \item{acceptTrend}{A logical +#' value indicating whether a trend is accepted (\code{TRUE}) or rejected +#' (\code{FALSE}) based on the specified significance level.} +#' @author Jens Riis Baalkilde +#' @seealso \code{.williamsTest}, \code{.shirleyTest}, \code{.tukeytrendfit} +#' @references Williams, D. A. (1971). "A test for differences between +#' treatment means when several dose levels are compared with a zero dose +#' control." Biometrics, 27(1), 103-117. Shirley, E. (1977). "A non-parametric +#' equivalent of Williams' test for contrasting increasing dose levels of a +#' treatment." Biometrics, 33(2), 386-389. Schaarschmidt, F. et al. (2021). +#' "The Tukey trend test: Multiplicity adjustment using multiple marginal +#' models" Biometrics, 78(2), 789-797. +#' @keywords trend, statistical test +#' @examples +#' +#' # Example with custom data +#' x <- c(1, 2, 3, 4, 5) +#' y <- c(2, 4, 6, 8, 10) +#' result <- trendTest(x, y, test = "tukey") +#' print(result) +#' +#' # Example with a data frame +#' data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) +#' result <- trendTest("x", "y", data = data, test = "shirley") +#' print(result) +#' trendTest <- function(x, y, data, test = c("william", "shirley", "tukey"), level = 0.05){ if(!missing(data)){ x <- data[[x]] @@ -37,4 +91,4 @@ trendTest <- function(x, y, data, test = c("william", "shirley", "tukey"), level } list(p.values = p.values, decisions = decisions, acceptTrend = acceptTrend) -} \ No newline at end of file +} diff --git a/R/tukeytrendfit.R b/R/tukeytrendfit.R index 570f98a..0ee876c 100644 --- a/R/tukeytrendfit.R +++ b/R/tukeytrendfit.R @@ -57,4 +57,4 @@ OUT <- c(list(mmm = MMM, mlf = MLF, df = DF), MODINFO) class(OUT) <- "tukeytrend" return(OUT) -} \ No newline at end of file +} diff --git a/R/williamsTest.R b/R/williamsTest.R index b951eef..179e9fe 100644 --- a/R/williamsTest.R +++ b/R/williamsTest.R @@ -115,4 +115,4 @@ dist = "t'") class(ans) <- "osrt" ans -} \ No newline at end of file +} diff --git a/bmd.Rproj b/bmd.Rproj index c88d76d..b1ded45 100644 --- a/bmd.Rproj +++ b/bmd.Rproj @@ -1,5 +1,4 @@ Version: 1.0 -ProjectId: 17a33614-0dad-4a73-9ef1-82328c71af7f RestoreWorkspace: Default SaveWorkspace: Default diff --git a/man/AIC.drcHetVar.Rd b/man/AIC.drcHetVar.Rd new file mode 100644 index 0000000..d717015 --- /dev/null +++ b/man/AIC.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/logLik.drcHetVar.R +\name{AIC.drcHetVar} +\alias{AIC.drcHetVar} +\title{S3 method} +\usage{ +\method{AIC}{drcHetVar}(object, ..., k = 2) +} +\description{ +S3 method +} diff --git a/man/AIC.drcOrdinal.Rd b/man/AIC.drcOrdinal.Rd new file mode 100644 index 0000000..40e9c1b --- /dev/null +++ b/man/AIC.drcOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/AIC.drcOrdinal.R +\name{AIC.drcOrdinal} +\alias{AIC.drcOrdinal} +\title{S3 method} +\usage{ +\method{AIC}{drcOrdinal}(object, ..., k = 2) +} +\description{ +S3 method +} diff --git a/man/BCa.Rd b/man/BCa.Rd index 92eca9c..40c7c39 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -1,5 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/BCa.R \name{BCa} \alias{BCa} -\title{ +\title{Help funtion to bmdBoot} +\usage{ +BCa(obs, data, bootSample, bootjack, level) +} +\description{ Help funtion to bmdBoot } diff --git a/man/BIC.drcHetVar.Rd b/man/BIC.drcHetVar.Rd new file mode 100644 index 0000000..bb878bf --- /dev/null +++ b/man/BIC.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/logLik.drcHetVar.R +\name{BIC.drcHetVar} +\alias{BIC.drcHetVar} +\title{S3 method} +\usage{ +\method{BIC}{drcHetVar}(object, ...) +} +\description{ +S3 method +} diff --git a/man/BIC.drcOrdinal.Rd b/man/BIC.drcOrdinal.Rd new file mode 100644 index 0000000..78c3c22 --- /dev/null +++ b/man/BIC.drcOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/BIC.drcOrdinal.R +\name{BIC.drcOrdinal} +\alias{BIC.drcOrdinal} +\title{S3 method} +\usage{ +\method{BIC}{drcOrdinal}(object, ...) +} +\description{ +S3 method +} diff --git a/man/MACurve.Rd b/man/MACurve.Rd index d2c274c..6766f25 100644 --- a/man/MACurve.Rd +++ b/man/MACurve.Rd @@ -1,43 +1,50 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/MACurve.R \name{MACurve} \alias{MACurve} -\title{ -Model-average dose-response curves -} -\description{Computing weighted average response estimates across multiple dose-response curves. -} +\title{Model-average dose-response curves} \usage{ MACurve(x, modelList, modelWeights, stackingSeed = 1, stackingSplits = 2) } \arguments{ - \item{x}{a vector of dose values for which the weighted average of response estimates are to be computed} - \item{modelList}{list of models of class \code{drc}} - \item{modelWeights}{character string specifying the type of weights used, "AIC", "BIC" or "Stack", or a vector of the same length as the modelList with user defined weights} - \item{stackingSeed}{integer or NULL: Random seed to use in the data split in the estimation of the Stacking Weights, when \code{modelWeights = "Stack"}. The global seed is reset to the initial value after estimation of the weights, so this option does not interfere with a globally set seed.} - \item{stackingSplits}{integer or "LOO": When \code{modelWeights = "Stack"}, the Stacking Weights are estimated, which are based on V-fold cross-validation. The stackingSplits argument sets the number V of data splits used in the cross validation. The "LOO" (Leave one out) is a shortcut to setting V equal to the number of observations in the data set. } -} +\item{x}{a vector of dose values for which the weighted average of response +estimates are to be computed} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) +\item{modelList}{list of models of class \code{drc}} + +\item{modelWeights}{character string specifying the type of weights used, +"AIC", "BIC" or "Stack", or a vector of the same length as the modelList +with user defined weights} + +\item{stackingSeed}{integer or NULL: Random seed to use in the data split in +the estimation of the Stacking Weights, when \code{modelWeights = "Stack"}. +The global seed is reset to the initial value after estimation of the +weights, so this option does not interfere with a globally set seed.} + +\item{stackingSplits}{integer or "LOO": When \code{modelWeights = "Stack"}, +the Stacking Weights are estimated, which are based on V-fold +cross-validation. The stackingSplits argument sets the number V of data +splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +to setting V equal to the number of observations in the data set.} } \value{ numeric } -\references{ -} - -\author{ Jens Riis Baalkilde -} -\note{ +\description{ +Computing weighted average response estimates across multiple dose-response +curves. } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +Details on the implemented definitions and methods can be found in Crump +(2002) } \examples{ + library(bmd) library(drc) library(drcData) @@ -64,9 +71,12 @@ qplotDrc(aconiazide.LL.3, type = "obs") + modelWeights = "AIC") }) + +} +\author{ +Jens Riis Baalkilde } +\keyword{averaging} +\keyword{model} \keyword{models} \keyword{nonlinear} -\keyword{model averaging} - -\concept{dose-response, MA, Model Averaging} diff --git a/man/PAV.Rd b/man/PAV.Rd index 07dcbda..7362458 100644 --- a/man/PAV.Rd +++ b/man/PAV.Rd @@ -1,40 +1,42 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/PAV.R \name{PAV} \alias{PAV} -\title{ -Pool-adjacent-violators monotonizing -} -\description{The function monotonizes a sequence of probabilities or means based on the pool-adjacent-violators algorithm. -} +\title{Pool-adjacent-violators monotonizing} \usage{ -PAV(formula,data,type) +PAV(formula, data, type) } \arguments{ - \item{formula}{an object of class "formula" expressing dose-response relationship. Details of model specification are given under 'Details'} - \item{data}{data frame containing the variables in the formula} - \item{type}{character string specifying the type of data used in the model, "continuous" or "binomial" or "Poisson"} -} +\item{formula}{an object of class "formula" expressing dose-response +relationship. Details of model specification are given under 'Details'} -\details{ -For details on how the pool-adjacent-violators algorithm is defined see Silvapulle and Sen (2004). +\item{data}{data frame containing the variables in the formula} -Formula should be specified as in the form number/total ~ dose for binomial data and response ~ for continuous data. +\item{type}{character string specifying the type of data used in the model, +"continuous" or "binomial" or "Poisson"} } \value{ A vector containing the monotonized sequence. } -\references{ - Silvapulle, M. J. and Sen, P. K. (2004). Constrained statistical inference: order, inequality, and shape constraints. New York: John Wiley & Sons. +\description{ +The function monotonizes a sequence of probabilities or means based on the +pool-adjacent-violators algorithm. } +\details{ +For details on how the pool-adjacent-violators algorithm is defined see +Silvapulle and Sen (2004). -\author{ Signe M. Jensen +Formula should be specified as in the form number/total ~ dose for binomial +data and response ~ for continuous data. } -\note{ +\references{ +Silvapulle, M. J. and Sen, P. K. (2004). Constrained statistical +inference: order, inequality, and shape constraints. New York: John Wiley & +Sons. } - -\seealso{ +\author{ +Signe M. Jensen } - +\keyword{isotonic} \keyword{nonparametric} -\keyword{isotonic regression} - -\concept{Pool-adjacent-violators} \ No newline at end of file +\keyword{regression} diff --git a/man/bmd.Rd b/man/bmd.Rd index edff726..6f9ba18 100644 --- a/man/bmd.Rd +++ b/man/bmd.Rd @@ -1,157 +1,217 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmd.R \name{bmd} \alias{bmd} -\title{ -Benchmark dose estimation -} -\description{Estimation of benchmark doses and benchmark dose lower limit from dose response model fits -} +\title{Benchmark dose estimation} \usage{ -bmd(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), - backg = NA, controlSD = NA, - def = c("excess", "additional", "relative", "extra", - "added", "hybridExc", "hybridAdd", "point"), - respTrans = c("none", "log", "sqrt"), - interval = c("delta", "sandwich", "inv", "profile", "profileGrid"), - sandwich.vcov = FALSE, display = TRUE, level = 0.95, - profileGridSize = NA, profileProgressInfo = TRUE) +bmd( + object, + bmr, + backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), + backg = NA, + controlSD = NA, + def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd", + "point"), + respTrans = c("none", "log", "sqrt"), + interval = c("delta", "sandwich", "inv", "profile", "profileGrid"), + sandwich.vcov = FALSE, + display = TRUE, + level = 0.95, + profileGridSize = NA, + profileProgressInfo = TRUE +) } - \arguments{ - \item{object}{object of class \code{drc}} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. For binomial data the options are "modelBased" and "absolute". For continuous data the options are "modelBased","absolute", "hybridSD" and "hybridPercentile". For count data (Poisson, negbin1 or negbin2) the options are "modelBased" and "absolute". - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument: - p0 = backg for binomial response and for the "relative", "extra" and "added" definition for continuous or count response data. - p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), - where phi is the normal distribution function and sigma is the SD for the control group. - - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group - - If not specified, it will be set to "modelBased" for all def excluding "hybridExc" and "hybridAdd", for these the default is "hybridSD". - } - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridPercentile"} - - \item{controlSD}{numeric value specifying the standard deviation of the control group (used in the hybrid approach). If not specified the SD for the control group will be estimated as the square root of the residual variance (assuming variance homogeneity).} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are for binomial response. "relative", "extra", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response. "relative", "extra", and "point" are for count response data. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response data - - "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. - Works for continuous and count response data - - "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). - Works for continuous and count response data - - "added" - BMR is defined as: BMR= f(BMD) + p0. - Works for continuous response - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response} - - \item{respTrans}{if the dose-response model is fitted with a transformed response, specifying this option ensures that the background level for the BMD is computed on the original scale. - Options include "none" (default), "log" (natural logarithm) and "sqrt"(square root).} - - \item{interval}{character string specifying the type of confidence interval to use: "delta" (default), "inv", "profile" or "profileGrid" - - "delta" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method - - "inv" - BMDL is based on inverse regression, that is the dose associated with the upper limit of the pointwise confidence interval of the dose-response curve. Currently not available for a transformed response variable. - - "profile" - A profile confidence interval is computed by reparametrising the model. Only available for \code{backgType} in ("modelBased", "absolute"), \code{def} in ("excess", "additional","relative", "extra", "point") and dose-response models with model functions of types Log-Logistic, Log-Normal and Weibull 1 and 2. The limits of the confidence interval are searched for within a grid of size specified by the \code{profileGridSize} argument, however the values of the confidence interval are not limited to the values on the grid. - - "profileGrid" - A profile confidence interval is computed by creating a multi-dimensional grid of parameter values for the model. Then, a confidence region for the parameters in the model is estimated, and the BMD is estimated for all combinations of parameter values within the region. The interval for the BMD is then computed as the minimum and maximum values of BMD values within the region. Note that for models with several parameters (3-5), is might take a while to compute the confidence interval using this method. The number of grid points for each parameter can be specified by the \code{profileGridSize} argument.} - - \item{sandwich.vcov}{logical. If TRUE BMDL is based on confidence intervals based on robust standard errors from the sandwich covariance matrix} - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} - - \item{profileGridSize}{integer specifying the number of grid points used for each parameter, when \code{interval} is either "profile" or "profileGridSearch". Defaults to 20 if not specified. } - - \item{profileProgressInfo}{logical. If TRUE, progress info is be printed while computed profile confidence intervals using the \code{profileGrid} method. Default is TRUE.} -} - -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) +\item{object}{object of class \code{drc}} + +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "modelBased","absolute", "hybridSD" and +"hybridPercentile". For count data (Poisson, negbin1 or negbin2) the options +are "modelBased" and "absolute". + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous or count response data. p0 = 1 - +phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. + +"hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma is the SD for the control group + +If not specified, it will be set to "modelBased" for all def excluding +"hybridExc" and "hybridAdd", for these the default is "hybridSD".} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridPercentile"} + +\item{controlSD}{numeric value specifying the standard deviation of the +control group (used in the hybrid approach). If not specified the SD for the +control group will be estimated as the square root of the residual variance +(assuming variance homogeneity).} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response. "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response. "relative", "extra", and "point" are for count response data. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data + +"relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +continuous and count response data + +"extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +continuous and count response data + +"added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response} + +\item{respTrans}{if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).} + +\item{interval}{character string specifying the type of confidence interval +to use: "delta" (default), "inv", "profile" or "profileGrid" + +"delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method + +"inv" - BMDL is based on inverse regression, that is the dose associated +with the upper limit of the pointwise confidence interval of the +dose-response curve. Currently not available for a transformed response +variable. + +"profile" - A profile confidence interval is computed by reparametrising the +model. Only available for \code{backgType} in ("modelBased", "absolute"), +\code{def} in ("excess", "additional","relative", "extra", "point") and +dose-response models with model functions of types Log-Logistic, Log-Normal +and Weibull 1 and 2. The limits of the confidence interval are searched for +within a grid of size specified by the \code{profileGridSize} argument, +however the values of the confidence interval are not limited to the values +on the grid. + +"profileGrid" - A profile confidence interval is computed by creating a +multi-dimensional grid of parameter values for the model. Then, a confidence +region for the parameters in the model is estimated, and the BMD is +estimated for all combinations of parameter values within the region. The +interval for the BMD is then computed as the minimum and maximum values of +BMD values within the region. Note that for models with several parameters +(3-5), is might take a while to compute the confidence interval using this +method. The number of grid points for each parameter can be specified by the +\code{profileGridSize} argument.} + +\item{sandwich.vcov}{logical. If TRUE BMDL is based on confidence intervals +based on robust standard errors from the sandwich covariance matrix} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} + +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} + +\item{profileGridSize}{integer specifying the number of grid points used for +each parameter, when \code{interval} is either "profile" or +"profileGridSearch". Defaults to 20 if not specified.} + +\item{profileProgressInfo}{logical. If TRUE, progress info is be printed +while computed profile confidence intervals using the \code{profileGrid} +method. Default is TRUE.} } \value{ -A list of four elements: Results contain the estimated BMD and BMDL, bmrScaled is the response value corresponding to the BMD, interval gives the lower (BMDL) and upper (BMDU) end of the confidence interval of BMD, SE gives the standard error of BMD. +A list of four elements: Results contain the estimated BMD and BMDL, +bmrScaled is the response value corresponding to the BMD, interval gives the +lower (BMDL) and upper (BMDU) end of the confidence interval of BMD, SE +gives the standard error of BMD. } -\references{ - Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) - Benchmark Dose Calculation from Epidemiological Data, - \emph{Biometrics} \bold{57}, 698--706. - - Crump, K. (2002) - Critical Issues in Benchmark Calculations from Continuous Data, - \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. -} - -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ +\description{ +Estimation of benchmark doses and benchmark dose lower limit from dose +response model fits } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +Details on the implemented definitions and methods can be found in Crump +(2002) } \examples{ + library(drc) library(drcData) ## Fitting log-logistic two-parameter model to binomial data deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial") -## BMD for 5% additional risk with estimated background risk +## BMD for 5\% additional risk with estimated background risk bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional") -## BMD for 10% additional risk with 2% background risk +## BMD for 10\% additional risk with 2\% background risk bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional") -## BMD for 5% excess risk and background 0 +## BMD for 5\% excess risk and background 0 bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess") -## Dose resulting in 12% risk +## Dose resulting in 12\% risk bmd(deguelin.m1, 0.12, def = "point") ## Benchmark doses for a continuous response ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) -## BMD as the dose resulting in a 5% change relative to the mean background level +## BMD as the dose resulting in a 5\% change relative to the mean background level bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE) ## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE) + +} +\references{ +Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +\bold{57}, 698--706. + +Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bmdBoot.Rd b/man/bmdBoot.Rd index d0490a2..d322185 100644 --- a/man/bmdBoot.Rd +++ b/man/bmdBoot.Rd @@ -1,106 +1,154 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdBoot.R \name{bmdBoot} \alias{bmdBoot} -\title{ -Benchmark dose estimation using bootstrap -} -\description{The function estimates BMD and BMDL using bootstrap based on parametric dose-response models. -} +\title{Benchmark dose estimation using bootstrap} \usage{ -bmdBoot(object, bmr, R = 1000, bootType = "nonparametric", bmdType = "orig", - backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), - backg = NA, controlSD = NA, - def = c("excess", "additional", "relative", "extra", - "added", "hybridExc", "hybridAdd", "point"), - respTrans = c("none", "log", "sqrt"), bootInterval = c("percentile", "BCa"), - display = TRUE, level = 0.95) +bmdBoot( + object, + bmr, + R = 1000, + bootType = "nonparametric", + bmdType = "orig", + backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), + backg = NA, + controlSD = NA, + def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd", + "point"), + respTrans = c("none", "log", "sqrt"), + bootInterval = c("percentile", "BCa"), + display = TRUE, + level = 0.95 +) } \arguments{ - \item{object}{object of class \code{drc}} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{R}{number of bootstrap samples. Default is 1000} - \item{bootType}{character string specifying type of bootstrap used. "nonparametric" (default), "semiparametric" or "parametric". "Semiparametric is only available for continuous data and "nonparametric" is at present the only option for count data. See details below} - \item{bmdType}{Type of estimate for BMD. Default is "orig" the bmd estimate from the original data set. Other choices are "mean" - the mean of the bootstrap estimates, or "median" - the median of the bootstrap estimates} - \item{backgType}{character string specifying how the background level is specified. For binomial and count data the options are "modelBased" and "absolute". For continuous data the options are "modelBased", "absolute", "hybridSD" and "hybridPercentile" - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument: - p0 = backg for binomial response and for the "relative", "extra" and "added" definition for continuous response. - p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), - where phi is the normal distribution function and sigma is the SD for the control group. - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background level for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridpercentile"} - - \item{controlSD}{numeric value specifying the standard deviation of the control group (used in the hybrid approach). If not specified the SD for the control group will be estimated as the square root of the residual variance (assuming variance homogeneity).} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess" , "additional" and "point" are for binomial response whereas "relative", "extra", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response. "relative", "extra", and "point" are for count response data. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response - - "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. - Works for count and continuous response - - "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). - Works for count and continuous response - - "added" - BMR is defined as: BMR= f(BMD) + p0. - Works for count and continuous response - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response} - - \item{respTrans}{if the dose-response model is fitted with a transformed response, specifying this option ensures that the background level for the BMD is computed on the original scale. - Options include "none" (default), "log" (natural logarithm) and "sqrt"(square root).} - - \item{bootInterval}{character string indicating type of bootstrap interval used for estimating BMDL. "Percentile" (default) or "BCa" (Bias corrected and adjusted)} - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} +\item{object}{object of class \code{drc}} -} +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} -\details{ -BMDL is defined as the 5th percentile in the bootstrap distribution. +\item{R}{number of bootstrap samples. Default is 1000} + +\item{bootType}{character string specifying type of bootstrap used. +"nonparametric" (default), "semiparametric" or "parametric". "Semiparametric +is only available for continuous data and "nonparametric" is at present the +only option for count data. See details below} + +\item{bmdType}{Type of estimate for BMD. Default is "orig" the bmd estimate +from the original data set. Other choices are "mean" - the mean of the +bootstrap estimates, or "median" - the median of the bootstrap estimates} + +\item{backgType}{character string specifying how the background level is +specified. For binomial and count data the options are "modelBased" and +"absolute". For continuous data the options are "modelBased", "absolute", +"hybridSD" and "hybridPercentile" + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background level for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"} + +\item{controlSD}{numeric value specifying the standard deviation of the +control group (used in the hybrid approach). If not specified the SD for the +control group will be estimated as the square root of the residual variance +(assuming variance homogeneity).} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess" , "additional" and "point" are for +binomial response whereas "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response. "relative", "extra", and "point" are for count response data. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. -Bootstrapping with the argument boot = "nonparametric" is done by sampling with replacement from the original data set. Bootstrapping with the argument boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming equal variance between groups, in case of continuous data. For binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always produces 0 or 1, respectively. In this case data is sampled from binom(N_i,(Y_i+1/4)/(N_i+1/2)). Bootstrapping with argument boot = "semiparametric" is done by sampling with replacement from the residuals. +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response -All sampling is made within dose groups. +"relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response +"extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +count and continuous response + +"added" - BMR is defined as: BMR= f(BMD) + p0. Works for count and +continuous response + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response} + +\item{respTrans}{if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).} + +\item{bootInterval}{character string indicating type of bootstrap interval +used for estimating BMDL. "Percentile" (default) or "BCa" (Bias corrected +and adjusted)} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} + +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} } \value{ -A list of three elements: Results contain the estimated BMD and BMDL, bootEst is a vector af all of the estimated BMD values from each bootstrap sample, Interval gives BMDL and BMDU, which is identical to the confidence interval for the percentile interval approach. +A list of three elements: Results contain the estimated BMD and +BMDL, bootEst is a vector af all of the estimated BMD values from each +bootstrap sample, Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach. } -\references{ - +\description{ +The function estimates BMD and BMDL using bootstrap based on parametric +dose-response models. } +\details{ +BMDL is defined as the 5th percentile in the bootstrap distribution. -\author{ Signe M. Jensen -} -\note{ -} +Bootstrapping with the argument boot = "nonparametric" is done by sampling +with replacement from the original data set. Bootstrapping with the argument +boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +assuming equal variance between groups, in case of continuous data. For +binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +resampling always produces 0 or 1, respectively. In this case data is +sampled from binom(N_i,(Y_i+1/4)/(N_i+1/2)). Bootstrapping with argument +boot = "semiparametric" is done by sampling with replacement from the +residuals. -\seealso{ +All sampling is made within dose groups. } \examples{ + ## Data on root length in ryegrass after exposure to ferulic acid require(drc) require(drcData) @@ -114,7 +162,9 @@ bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50) ## BMD from the same definitions but using parametric bootstrap bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50) + +} +\author{ +Signe M. Jensen } \keyword{bootstrap} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bmdHetVar.Rd b/man/bmdHetVar.Rd index 8d94fc9..a2b207e 100644 --- a/man/bmdHetVar.Rd +++ b/man/bmdHetVar.Rd @@ -1,82 +1,111 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdHetVar.R \name{bmdHetVar} \alias{bmdHetVar} -\title{ -Benchmark dose estimation with heterogeneous variance -} -\description{Estimation of benchmark doses and benchmark dose lower limit based on the hybrid method from dose response model fits with the option to specify a heterogeneous variance structure, where the variance depends on the dose level and/or the fitted values -} +\title{Benchmark dose estimation with heterogeneous variance} \usage{ -bmdHetVar(object, bmr, backgType = c("absolute", "hybridSD", "hybridPercentile"), - backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), - R = 1000, level = 0.95, bootType = "nonparametric", - progressInfo = TRUE, display = TRUE) +bmdHetVar( + object, + bmr, + backgType = c("absolute", "hybridSD", "hybridPercentile"), + backg = NA, + def = c("hybridExc", "hybridAdd"), + interval = c("boot", "none"), + R = 1000, + level = 0.95, + bootType = "nonparametric", + progressInfo = TRUE, + display = TRUE +) } - \arguments{ - \item{object}{dose-response model with a heterogeneous variance structure of class \code{drcHetVar}} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. The options are "absolute", "hybridSD" and "hybridPercentile". - - "absolute" - the background level is specified by the user through the backg argument: - p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma(0) + f(0)) - f(0))/sigma(0)) = 1 - phi(backg), - where phi is the normal distribution function and sigma(0) is the SD for the control group. - - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(0) is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 2 SD for "hybridSD" background and 0.9 for "hybridPercentile"} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), available. - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(BMD) is the SD at the benchmark dose. - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(BMD) is the SD at the benchmark dose. } - - \item{interval}{character string specifying the type of confidence interval to use: "boot" (default) or "none" - - "boot" - BMDL is based on percentile bootstrapping. - - "none" - no confidence interval is computed.} - - \item{R}{number of bootstrap samples. Ignored if \code{interval = "none"}} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} - - \item{bootType}{character string specifying the type of bootstrap samples. Options are "nonparametric" (observations are drawn without replacement from the original data set), "semi-parametric" (standardised residuals are drawn with replacement and subsequently rescaled according to the model) and "parametric" (new observations are simulated from the distribution given by the fitted model).} - - \item{progressInfo}{logical. If TRUE, progress info is be printed while bootstrap confidence intervals are estimated. Default is TRUE.} - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} -} +\item{object}{dose-response model with a heterogeneous variance structure of +class \code{drcHetVar}} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - REFERENCES TO BE ADDED/WRITTEN +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. The options are "absolute", "hybridSD" and "hybridPercentile". + +"absolute" - the background level is specified by the user through the backg +argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +"hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +distribution function and sigma(0) is the SD for the control group. + +"hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma(0) is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 2 SD +for "hybridSD" background and 0.9 for "hybridPercentile"} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +(additional hybrid), available. + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0)/ (1- p0), where x0 is the level for which the response is considered +adverse, phi is the normal distribution function and sigma(BMD) is the SD at +the benchmark dose. + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0, where x0 is the level for which the response is considered adverse, phi +is the normal distribution function and sigma(BMD) is the SD at the +benchmark dose.} + +\item{interval}{character string specifying the type of confidence interval +to use: "boot" (default) or "none" + +"boot" - BMDL is based on percentile bootstrapping. + +"none" - no confidence interval is computed.} + +\item{R}{number of bootstrap samples. Ignored if \code{interval = "none"}} + +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} + +\item{bootType}{character string specifying the type of bootstrap samples. +Options are "nonparametric" (observations are drawn without replacement from +the original data set), "semi-parametric" (standardised residuals are drawn +with replacement and subsequently rescaled according to the model) and +"parametric" (new observations are simulated from the distribution given by +the fitted model).} + +\item{progressInfo}{logical. If TRUE, progress info is be printed while +bootstrap confidence intervals are estimated. Default is TRUE.} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} } \value{ -A list of five elements: Results contain the estimated BMD and BMDL, bmrScaled is the response value corresponding to the BMD, interval gives the lower (BMDL) and upper (BMDU) end of the confidence interval of BMD -} -\references{ +A list of five elements: Results contain the estimated BMD and BMDL, +bmrScaled is the response value corresponding to the BMD, interval gives the +lower (BMDL) and upper (BMDU) end of the confidence interval of BMD } - -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ +\description{ +Estimation of benchmark doses and benchmark dose lower limit based on the +hybrid method from dose response model fits with the option to specify a +heterogeneous variance structure, where the variance depends on the dose +level and/or the fitted values } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +REFERENCES TO BE ADDED/WRITTEN } \examples{ + library(drc) library(drcData) library(bmd) @@ -115,8 +144,10 @@ plot(GiantKelp.LL.4.hetVarLogSq) bmdHetVar(GiantKelp.LL.4.hetVarLogSq, bmr = 0.1, backgType = "hybridSD", backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) + +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bmdHetVarMA.Rd b/man/bmdHetVarMA.Rd index c31415b..ed9fd05 100644 --- a/man/bmdHetVarMA.Rd +++ b/man/bmdHetVarMA.Rd @@ -1,81 +1,112 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdHetVarMA.R \name{bmdHetVarMA} \alias{bmdHetVarMA} -\title{ -Benchmark dose estimation with heterogeneous variance based on model averaging (MA) -} -\description{Estimation of benchmark doses and benchmark dose lower limit based on the hybrid method from a list of dose response model fits with the option to specify a heterogeneous variance structure, where the variance depends on the dose level and/or the fitted values -} +\title{Benchmark dose estimation with heterogeneous variance based on model +averaging (MA)} \usage{ -bmdHetVarMA(modelList, modelWeights = c("AIC", "BIC"), bmr, - backgType = c("absolute", "hybridSD", "hybridPercentile"), - backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), - R = 1000, level = 0.95, progressInfo = TRUE,display = TRUE) +bmdHetVarMA( + modelList, + modelWeights = c("AIC", "BIC"), + bmr, + backgType = c("absolute", "hybridSD", "hybridPercentile"), + backg = NA, + def = c("hybridExc", "hybridAdd"), + interval = c("boot", "none"), + R = 1000, + level = 0.95, + progressInfo = TRUE, + display = TRUE +) } - \arguments{ - \item{modelList}{a list of dose-response models with a heterogeneous variance structure of class \code{drcHetVar}} - \item{modelWeights}{character string specifying the type of weights used, "AIC" or "BIC", or a numeric vector of the same length as the modelList with user defined weights} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. The options are "absolute", "hybridSD" and "hybridPercentile". - - "absolute" - the background level is specified by the user through the backg argument: - p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma(0) + f(0)) - f(0))/sigma(0)) = 1 - phi(backg), - where phi is the normal distribution function and sigma(0) is the SD for the control group. - - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(0) is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 2 SD for "hybridSD" background and 0.9 for "hybridPercentile"} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), available. - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(BMD) is the SD at the benchmark dose. - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma(BMD) is the SD at the benchmark dose. } - - \item{interval}{character string specifying the type of confidence interval to use: "boot" (default) or "none" - - "boot" - BMDL is based on nonparametric percentile bootstrapping. - - "none" - no confidence interval is computed.} - - \item{R}{number of bootstrap samples. Ignored if \code{interval = "none"}} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} - - \item{progressInfo}{logical. If TRUE, progress info is be printed while bootstrap confidence intervals are estimated. Default is TRUE.} - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} -} +\item{modelList}{a list of dose-response models with a heterogeneous +variance structure of class \code{drcHetVar}} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - REFERENCES TO BE ADDED/WRITTEN +\item{modelWeights}{character string specifying the type of weights used, +"AIC" or "BIC", or a numeric vector of the same length as the modelList with +user defined weights} + +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. The options are "absolute", "hybridSD" and "hybridPercentile". + +"absolute" - the background level is specified by the user through the backg +argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +"hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +distribution function and sigma(0) is the SD for the control group. + +"hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma(0) is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 2 SD +for "hybridSD" background and 0.9 for "hybridPercentile"} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +(additional hybrid), available. + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0)/ (1- p0), where x0 is the level for which the response is considered +adverse, phi is the normal distribution function and sigma(BMD) is the SD at +the benchmark dose. + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0, where x0 is the level for which the response is considered adverse, phi +is the normal distribution function and sigma(BMD) is the SD at the +benchmark dose.} + +\item{interval}{character string specifying the type of confidence interval +to use: "boot" (default) or "none" + +"boot" - BMDL is based on nonparametric percentile bootstrapping. + +"none" - no confidence interval is computed.} + +\item{R}{number of bootstrap samples. Ignored if \code{interval = "none"}} + +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} + +\item{progressInfo}{logical. If TRUE, progress info is be printed while +bootstrap confidence intervals are estimated. Default is TRUE.} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} } \value{ -A list of four elements: Results contain the estimated BMD and BMDL, Boot.samples.used gives the number of boot samples that resulted in succesful estimations and were accordingly used in the estimation of BMDL (and BMDU), Interval gives BMDL and BMDU, which is identical to the confidence interval for the percentile interval approach, and modelWeights includes the estimated weights. -} -\references{ +A list of four elements: Results contain the estimated BMD and BMDL, +Boot.samples.used gives the number of boot samples that resulted in +succesful estimations and were accordingly used in the estimation of BMDL +(and BMDU), Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach, and modelWeights +includes the estimated weights. } - -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ +\description{ +Estimation of benchmark doses and benchmark dose lower limit based on the +hybrid method from a list of dose response model fits with the option to +specify a heterogeneous variance structure, where the variance depends on +the dose level and/or the fitted values } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +REFERENCES TO BE ADDED/WRITTEN } \examples{ + library(drc) library(drcData) library(bmd) @@ -112,8 +143,10 @@ bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) + +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bmdIso.Rd b/man/bmdIso.Rd index 464ed22..cbb311a 100644 --- a/man/bmdIso.Rd +++ b/man/bmdIso.Rd @@ -1,89 +1,115 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdIso.R \name{bmdIso} \alias{bmdIso} -\title{ -Benchmark dose estimation from isotonic regression -} -\description{The function monotonizes the sequence of response values based on the pool-adjacent violators algorithm and based on these use linear interpolating splines to build an isotonic regression model. From this model a benchmark dose is estimated. -} +\title{Benchmark dose estimation from isotonic regression} \usage{ -bmdIso(formula, data, type, bmr, p0, - backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), - backg = NA, def = c("excess", "additional", "relative", - "added", "hybridExc", "hybridAdd", "point"), - display = FALSE) +bmdIso( + formula, + data, + type, + bmr, + p0, + backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), + backg = NA, + def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point"), + display = FALSE +) } \arguments{ - \item{formula}{an object of class "formula" expressing the dose-response relationship. Details of model specification are given under 'Details'} - \item{data}{data frame containing the variables in the model} - \item{type}{character string specifying the type of data used in the model. "continuous", "binomial" or "Poisson"} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{p0}{background probability for hybrid definitions} - \item{backgType}{character string specifying how the background level is specified. For binomial data the options are "modelBased" and "absolute". For continuous data the options are "absolute", "hybridSD" and "hybridPercentile" - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument: - p0 = backg for binomial response and for the "relative" and "added" definition for continuous response. - p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), - where phi is the normal distribution function and sigma is the SD for the control group. - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridpercentile"} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are for binomial response whereas "relative", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response. "relative", "extra", and "point" are for count response data. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response - - "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. - Works for count and continuous response - - "added" - BMR is defined as: BMR= f(BMD) + p0. - Works for continuous response - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response} - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} -} +\item{formula}{an object of class "formula" expressing the dose-response +relationship. Details of model specification are given under 'Details'} -\details{ -Formula should be specified as in the form number/total ~ dose for binomial data. -For details about the use of isotonic regression for BMD estimation see Piegorsch et al. (20014) and Lin et al. (2015). -} -\value{ -A matrix with two columns, one containing BMD and the other containing BMDL. -} -\references{ - Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. (2014). Benchmark dose analysis via nonparametric regression modeling. Risk Analysis, 34(1), 135-151 +\item{data}{data frame containing the variables in the model} - Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric benchmark dose estimation with continuous dose-response data. Scandinavian Journal of Statistics, 42, 713-731 -} +\item{type}{character string specifying the type of data used in the model. +"continuous", "binomial" or "Poisson"} + +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{p0}{background probability for hybrid definitions} + +\item{backgType}{character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "absolute", "hybridSD" and +"hybridPercentile" + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative" and +"added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +"hybridAdd" (additional hybrid), and "point" are for continuous response. +"relative", "extra", and "point" are for count response data. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. -\author{ Signe M. Jensen +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response + +"relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response + +"added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} } -\note{ +\value{ +A matrix with two columns, one containing BMD and the other +containing BMDL. } - -\seealso{ +\description{ +The function monotonizes the sequence of response values based on the +pool-adjacent violators algorithm and based on these use linear +interpolating splines to build an isotonic regression model. From this model +a benchmark dose is estimated. +} +\details{ +Formula should be specified as in the form number/total ~ dose for binomial +data. For details about the use of isotonic regression for BMD estimation +see Piegorsch et al. (20014) and Lin et al. (2015). } \examples{ + ## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014) formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0), tumor.incidence = c(0, 0, 0, 3, 21, 150), @@ -116,8 +142,20 @@ bmdIso(rootl ~ conc, bmr=0.05, backgType = "modelBased", def = "relative") + } -\keyword{nonparametric} -\keyword{isotonic regression} +\references{ +Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +(2014). Benchmark dose analysis via nonparametric regression modeling. Risk +Analysis, 34(1), 135-151 -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file +Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +benchmark dose estimation with continuous dose-response data. Scandinavian +Journal of Statistics, 42, 713-731 +} +\author{ +Signe M. Jensen +} +\keyword{isotonic} +\keyword{nonparametric} +\keyword{regression} diff --git a/man/bmdIsoBoot.Rd b/man/bmdIsoBoot.Rd index 8d9521e..bdc80d0 100644 --- a/man/bmdIsoBoot.Rd +++ b/man/bmdIsoBoot.Rd @@ -1,95 +1,129 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdIsoBoot.R \name{bmdIsoBoot} \alias{bmdIsoBoot} -\title{ -Benchmark dose estimation from isotonic regression -} -\description{The function estimates BMD and BMDL using bootstrap based on isotonic regression. -} +\title{Benchmark dose estimation from isotonic regression} \usage{ -bmdIsoBoot(formula, data, type, bmr, R=1000, boot="resample", - backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), - backg=NA, def = c("excess", "additional", "relative", - "added", "hybridExc", "hybridAdd", "point")) +bmdIsoBoot( + formula, + data, + type, + bmr, + R = 1000, + boot = "resample", + backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), + backg = NA, + def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point") +) } \arguments{ - \item{formula}{an object of class "formula" expressing dose-response relationship. Details of model specification are given under 'Details'} - \item{data}{data frame containing the variables in the model} - \item{type}{character string specifying the type of data used in the model. "continuous" or "binomial" or "Poisson"} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{R}{number of bootstrap samples} - \item{boot}{character string specifying type of bootstrap used. "resample" or "pseudorandom". Only option for count data is "resample"} - \item{backgType}{character string specifying how the background level is specified. For binomial data the options are "modelBased" and "absolute". For continuous data the options are "modelBased", "absolute", "hybridSD" and "hybridPercentile" - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument: - p0 = backg for binomial response and for the "relative" and "added" definition for continuous response. - p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), - where phi is the normal distribution function and sigma is the SD for the control group. - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridpercentile"} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are for binomial response whereas "relative", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response. "relative", "extra", and "point" are for count response data. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response - - "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. - Works for count and continuous response - - "added" - BMR is defined as: BMR= f(BMD) + p0. - Works for continuous response - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response} - -} +\item{formula}{an object of class "formula" expressing dose-response +relationship. Details of model specification are given under 'Details'} -\details{ -BMD and BMDL is defined as the median and the 5th percentile in the bootstrap distribution, respectively. +\item{data}{data frame containing the variables in the model} + +\item{type}{character string specifying the type of data used in the model. +"continuous" or "binomial" or "Poisson"} + +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{R}{number of bootstrap samples} + +\item{boot}{character string specifying type of bootstrap used. "resample" +or "pseudorandom". Only option for count data is "resample"} + +\item{backgType}{character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "modelBased", "absolute", "hybridSD" and +"hybridPercentile" + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative" and +"added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +"hybridAdd" (additional hybrid), and "point" are for continuous response. +"relative", "extra", and "point" are for count response data. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response -Formula should be specified as in the form number/total ~ dose for binomial data. +"relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response -Bootstrapping with the argument boot = "resample" is done by sampling with replacement from the original data set. Bootstrapping with the argument boot = "pseudorandom" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming equal variance between groups, in case of continuous data. For binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always produces 0 or 1, respectively. In this case data is sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)). +"added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response -All sampling is made within dose groups. +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response -For details about the use of isotonic regression for BMD estimation see Piegorsch et al. (20014) and Lin et al. (2015). +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response} } \value{ -A matrix with two columns, one containing BMD and the other containing BMDL. +A matrix with two columns, one containing BMD and the other +containing BMDL. } -\references{ - Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. (2014). Benchmark dose analysis via nonparametric regression modeling. Risk Analysis, 34(1), 135-151 - - Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric benchmark dose estimation with continuous dose-response data. Scandinavian Journal of Statistics, 42, 713-731 +\description{ +The function estimates BMD and BMDL using bootstrap based on isotonic +regression. } +\details{ +BMD and BMDL is defined as the median and the 5th percentile in the +bootstrap distribution, respectively. -\author{ Signe M. Jensen -} -\note{ -} +Formula should be specified as in the form number/total ~ dose for binomial +data. + +Bootstrapping with the argument boot = "resample" is done by sampling with +replacement from the original data set. Bootstrapping with the argument boot += "pseudorandom" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming +equal variance between groups, in case of continuous data. For binomial +data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of +Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always +produces 0 or 1, respectively. In this case data is sampled from +binom(N_i,(Y_i+1/3)/(N_i+1/3)). -\seealso{ +All sampling is made within dose groups. + +For details about the use of isotonic regression for BMD estimation see +Piegorsch et al. (20014) and Lin et al. (2015). } \examples{ + ## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014) formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0), tumor.incidence = c(0, 0, 0, 3, 21, 150), @@ -120,9 +154,21 @@ bmdIsoBoot(rootl ~ conc, bmr=0.05, backgType = "modelBased", def = "relative", R = 100) + } -\keyword{nonparametric} -\keyword{isotonic regression} -\keyword{bootstrap} +\references{ +Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +(2014). Benchmark dose analysis via nonparametric regression modeling. Risk +Analysis, 34(1), 135-151 -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file +Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +benchmark dose estimation with continuous dose-response data. Scandinavian +Journal of Statistics, 42, 713-731 +} +\author{ +Signe M. Jensen +} +\keyword{bootstrap} +\keyword{isotonic} +\keyword{nonparametric} +\keyword{regression} diff --git a/man/bmdMA.Rd b/man/bmdMA.Rd index 8670152..2604e5c 100644 --- a/man/bmdMA.Rd +++ b/man/bmdMA.Rd @@ -1,150 +1,204 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdMA.R \name{bmdMA} \alias{bmdMA} -\title{ -Model-averaged benchmark dose estimation -} -\description{Estimation of benchmark doses and benchmark dose lower limit based on model averaging from a user-defined list of dose response model fits -} +\title{Model-averaged benchmark dose estimation} \usage{ -bmdMA(modelList, modelWeights, bmr, - backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), - backg = NA, def = c("excess", "additional", "relative", "extra", - "added", "hybridExc", "hybridAdd", "point"), - respTrans = c("none", "log", "sqrt"), - interval = c("delta","sandwich","inv", "profile"), - type = c("curve","bootstrap","Kang","Buckland"), - bootstrapType = c("nonparametric", "parametric"), R=1000, - bootInterval = "percentile", level=0.95, stackingSeed, - stackingSplits, display = TRUE, progressInfo = TRUE) +bmdMA( + modelList, + modelWeights, + bmr, + backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), + backg = NA, + def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd", + "point"), + respTrans = c("none", "log", "sqrt"), + interval = c("delta", "sandwich", "inv", "profile"), + type = c("curve", "bootstrap", "Kang", "Buckland"), + bootstrapType = c("nonparametric", "parametric"), + R = 1000, + bootInterval = "percentile", + level = 0.95, + stackingSeed = NULL, + stackingSplits = 2, + display = TRUE, + progressInfo = TRUE +) } \arguments{ - \item{modelList}{list of models of class \code{drc}} - \item{modelWeights}{character string specifying the type of weights used, "AIC", "BIC" or "Stack" (Baalkilde, J. R., Hansen, N. R., and Jensen, S. M., 2025), or a vector of the same length as the modelList with user defined weights} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. For binomial data the options are "modelBased" and "absolute". For continuous data the options are "absolute", "hybridSD" and "hybridPercentile" - - "modelBased" - the background risk is obtained from the model as the risk for dose 0: - p0 = f(0) - - "absolute" - the background risk is specified by the user through the backg argument: - p0 = backg for binomial response and for the "relative", "extra" and "added" definition for continuous response. - p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. - - "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. - p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), - where phi is the normal distribution function and sigma is the SD for the control group. - "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). - p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridpercentile"} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess" , "additional" and "point" are for binomial response whereas "relative", "extra", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for both binomial and continuous response - - "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. - Works for continuous response - - "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). - Works for continuous response - - "added" - BMR is defined as: BMR= f(BMD) + p0. - Works for continuous response - - "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response - - "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, - where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. - Works for continuous response} - - \item{respTrans}{if the dose-response model is fitted with a transformed response, specifying this option ensures that the background level for the BMD is computed on the original scale. - Options include "none" (default), "log" (natural logarithm) and "sqrt"(square root).} - - \item{interval}{character string specifying the type of confidence interval to use for the individual models (no effect when type = "bootstrap" or "curve"): "delta" (default), "sandwich", "inv" or "profile" - - "delta" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method - - "sandwich" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method where the sandwich covariance matrix is used - - "inv" - BMDL is based on inverse regression, that is the dose associated with the upper limit of the point wise confidence interval of the dose-response curve. Not possible if type = "Buckland" - - "profile" - BMDL is based on the lower limit of a profile likelihood confidence interval. Not possible if type = "Buckland"} - - \item{type}{character string specifying how to estimate BMD and BMDL: "curve", "bootstrap", "Kang" or "Buckland" - - "curve" - - - "bootstrap" - - - "Kang" - - - "Buckland" - - } - - \item{bootstrapType}{character string indicating type of bootstrap sampling to be used if type="bootstrap" or "curve". "nonparametric" (default), or "parametric" (see details)} - - \item{bootInterval}{character string indicating how to estimate the bootstrap confidence intervals used to find BMDL type="bootstrap". "percentile" (default) or "BCa" (Bias corrected and adjusted)} - - \item{R}{number of bootstrap samples to use. Default is 1000} - - \item{level}{numeric value specifying the level of the confidence interval underlying BMDL. Default is 0.95. Note that the full CI is also computed. The full CI has level 1-2*(1-level)} - - \item{stackingSeed}{integer or NULL: Random seed to use in the data split in the estimation of the Stacking Weights when \code{modelWeights = "Stack"}. The global seed is reset to the initial value after estimation of the weights, so this option does not interfere with a globally set seed.} - - \item{stackingSplits}{integer or "LOO": When \code{modelWeights = "Stack"}, the Stacking Weights are estimated, which are based on V-fold cross-validation. The stackingSplits argument sets the number V of data splits used in the cross validation. The "LOO" (Leave one out) is a shortcut to setting V equal to the number of observations in the data set. } - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} - - \item{progressInfo}{logical. If TRUE, a progressbar is shown when computing bootstrap confidence intervals.} - -} +\item{modelList}{list of models of class \code{drc}} -\details{ -This package project is still under development. The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response model based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) - - Bootstrapping with the argument boot = "nonparametric" is done by sampling with replacement from the original data set. Bootstrapping with the argument boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming equal variance between groups, in case of continuous data. For binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always produces 0 or 1, respectively. In this case data is sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)). - -All sampling is made within dose groups. +\item{modelWeights}{character string specifying the type of weights used, +"AIC", "BIC" or "Stack" (Baalkilde, J. R., Hansen, N. R., and Jensen, S. M., +2025), or a vector of the same length as the modelList with user defined +weights} + +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "absolute", "hybridSD" and +"hybridPercentile" + +"modelBased" - the background risk is obtained from the model as the risk +for dose 0: p0 = f(0) + +"absolute" - the background risk is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. + +"hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess" , "additional" and "point" are for +binomial response whereas "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for both binomial and continuous +response + +"relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +continuous response + +"extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +continuous response + +"added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response + +"hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response + +"hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response} + +\item{respTrans}{if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).} + +\item{interval}{character string specifying the type of confidence interval +to use for the individual models (no effect when type = "bootstrap" or +"curve"): "delta" (default), "sandwich", "inv" or "profile" + +"delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method + +"sandwich" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method where the sandwich covariance matrix is used + +"inv" - BMDL is based on inverse regression, that is the dose associated +with the upper limit of the point wise confidence interval of the +dose-response curve. Not possible if type = "Buckland" + +"profile" - BMDL is based on the lower limit of a profile likelihood +confidence interval. Not possible if type = "Buckland"} + +\item{type}{character string specifying how to estimate BMD and BMDL: +"curve", "bootstrap", "Kang" or "Buckland" + +"curve" - + +"bootstrap" - + +"Kang" - + +"Buckland" -} + +\item{bootstrapType}{character string indicating type of bootstrap sampling +to be used if type="bootstrap" or "curve". "nonparametric" (default), or +"parametric" (see details)} + +\item{R}{number of bootstrap samples to use. Default is 1000} + +\item{bootInterval}{character string indicating how to estimate the +bootstrap confidence intervals used to find BMDL type="bootstrap". +"percentile" (default) or "BCa" (Bias corrected and adjusted)} + +\item{level}{numeric value specifying the level of the confidence interval +underlying BMDL. Default is 0.95. Note that the full CI is also computed. +The full CI has level 1-2*(1-level)} + +\item{stackingSeed}{integer or NULL: Random seed to use in the data split in +the estimation of the Stacking Weights when \code{modelWeights = "Stack"}. +The global seed is reset to the initial value after estimation of the +weights, so this option does not interfere with a globally set seed.} + +\item{stackingSplits}{integer or "LOO": When \code{modelWeights = "Stack"}, +the Stacking Weights are estimated, which are based on V-fold +cross-validation. The stackingSplits argument sets the number V of data +splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +to setting V equal to the number of observations in the data set.} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} + +\item{progressInfo}{logical. If TRUE, a progressbar is shown when computing +bootstrap confidence intervals.} } \value{ -A list of five elements: Results contain the estimated BMD and BMDL, Boot.samples.used gives the number of boot samples that resulted in succesful estimations and were accordingly used in the estimation of BMDL (and BMDU), Interval gives BMDL and BMDU, which is identical to the confidence interval for the percentile interval approach, SE gives the estimated SE for the "Buckland" method, and modelWeights includes the estimated weights. +A list of five elements: Results contain the estimated BMD and BMDL, +Boot.samples.used gives the number of boot samples that resulted in +succesful estimations and were accordingly used in the estimation of BMDL +(and BMDU), Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach, SE gives the +estimated SE for the "Buckland" method, and modelWeights includes the +estimated weights. } -\references{ - Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) - Benchmark Dose Calculation from Epidemiological Data, - \emph{Biometrics} \bold{57}, 698--706. - - Crump, K. (2002) - Critical Issues in Benchmark Calculations from Continuous Data, - \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. - - Baalkilde, J. R., Hansen, N. R., and Jensen, S. M. (2025) - Stacking Weights and Model Space Selection in Frequentist Model Averaging for Benchmark Dose Estimation, - \emph{Environmetrics} \bold{36(2)}, e70002. +\description{ +Estimation of benchmark doses and benchmark dose lower limit based on model +averaging from a user-defined list of dose response model fits } +\details{ +This package project is still under development. The aim to provide an R +package calculating the benchmark dose (BMD) and the lower limit of the +corresponding 95\% confidence interval (BMDL) for continuous and quantal +dose-response data for a range of dose-response model based on the available +definitions of the benchmark dose concepts. -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ -} +Details on the implemented definitions and methods can be found in Crump +(2002) -\seealso{ +Bootstrapping with the argument boot = "nonparametric" is done by sampling +with replacement from the original data set. Bootstrapping with the argument +boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +assuming equal variance between groups, in case of continuous data. For +binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +resampling always produces 0 or 1, respectively. In this case data is +sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)). + +All sampling is made within dose groups. } \examples{ + library(drc) library(drcData) @@ -155,13 +209,13 @@ deguelin.m3 <- drm(r/n~dose, weights=n, data=deguelin, fct=W2.2(), type="binomia deguelin.m4 <- drm(r/n~dose, weights=n, data=deguelin, fct=LN.2(), type="binomial") -## Model averaged BMD for 5% additional risk with estimated background risk +## Model averaged BMD for 5\% additional risk with estimated background risk ## and BMDL based on Buckland et al. bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, backgType = "modelBased", def = "additional", type = "Buckland") -## Model averaged BMD for 5% additional risk with estimated background risk +## Model averaged BMD for 5\% additional risk with estimated background risk ## and BMDL based on an average of the model curves bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, backgType = "modelBased", def = "additional", @@ -174,7 +228,7 @@ ryegrass.m2<-drm(rootl~conc, data=ryegrass, fct=W1.4()) ryegrass.m3<-drm(rootl~conc, data=ryegrass, fct=W2.4()) ryegrass.m4<-drm(rootl~conc, data=ryegrass, fct=LN.4()) -## Model-averaged BMD and bootstrap BMDL for bmr=5% and using the hybrid approach +## Model-averaged BMD and bootstrap BMDL for bmr=5\% and using the hybrid approach ## to estimate the background risk. bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="AIC", bmr=0.05, backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", @@ -186,9 +240,24 @@ bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="Stack backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", bootstrapType = "nonparametric", bootInterval = "percentile", R = 50) + } -\keyword{model averaging} -\keyword{nonlinear} -\keyword{bootstrap} +\references{ +Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +\bold{57}, 698--706. + +Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. -\concept{BMD BMDL benchmark dose-response model averaging} \ No newline at end of file +Baalkilde, J. R., Hansen, N. R., and Jensen, S. M. (2025) Stacking Weights +and Model Space Selection in Frequentist Model Averaging for Benchmark Dose +Estimation, \emph{Environmetrics} \bold{36(2)}, e70002. +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde +} +\keyword{averaging} +\keyword{bootstrap} +\keyword{model} +\keyword{nonlinear} diff --git a/man/bmdMACurve.Rd b/man/bmdMACurve.Rd index ec58447..62d9e7a 100644 --- a/man/bmdMACurve.Rd +++ b/man/bmdMACurve.Rd @@ -1,5 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdMACurve.R \name{bmdMACurve} \alias{bmdMACurve} -\title{ +\title{Help funtion to bmdMA} +\usage{ +bmdMACurve(modelList, modelWeights, bmrScaled0, searchInterval = "dataBased") +} +\description{ Help funtion to bmdMA } diff --git a/man/bmdOrdinal.Rd b/man/bmdOrdinal.Rd index 328abfe..e9d89c2 100644 --- a/man/bmdOrdinal.Rd +++ b/man/bmdOrdinal.Rd @@ -1,103 +1,126 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdOrdinal.R \name{bmdOrdinal} \alias{bmdOrdinal} -\title{ -Benchmark dose estimation for ordinal dose-response models -} -\description{Estimation of benchmark doses and benchmark dose lower limit from ordinal dose response model fits -} +\title{Benchmark dose estimation for ordinal dose-response models} \usage{ -bmdOrdinal(object, bmr, backgType = c("modelBased", "absolute"), backg = NA, - def = c("excess", "additional", "point"), - interval = c("delta", "sandwich", "profile", "bootstrap"), level = 0.95, - R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical"), - display = TRUE, progressInfo = TRUE) +bmdOrdinal( + object, + bmr, + backgType = c("modelBased", "absolute"), + backg = NA, + def = c("excess", "additional", "point"), + interval = c("delta", "sandwich", "profile", "bootstrap"), + level = 0.95, + R = 500, + bootType = c("nonparametric", "parametric", "model", "hierarchical"), + display = TRUE, + progressInfo = TRUE +) } \arguments{ - \item{object}{object of class \code{drcOrdinal}} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. The options are "modelBased" and "absolute". - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument.} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk.} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are available for ordinal response. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response data.} - - \item{interval}{character string specifying the type of confidence interval to use: "delta" (default), "sandwich", "profile" or "bootstrap" - - "delta" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method - - "sandwich" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method, where the sandwich covariance matrix is used - - "bootstrap" - BMDL is based on bmd estimates on resampled data sets. The type of bootstrap applied can be specified by the "bootType" argument. Default is "nonparametric". - - "none" - No confidence interval is computed.} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} - - \item{R}{integer specifying the number of data sets resampled from the original data set when computing the confidence interval by bootstrap.} - - \item{bootType}{character string specifying the resampling procedure for the data sets used for bootstrap. - - "nonparametric" - Bootstrapping is done by sampling with replacement from the original data set. - - "parametric" - Bootstrapping is done by sampling from a multinomial distribution with probabilites given by the number of observations for each level. If all observations for one group are in the same level, shrinkage is used to avoid that the resampling always produces that particular level. In this case data is sampled from a multinomial distribution with probabilities (1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + 1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the particular group, and |K| is the number of levels. - - "model" - New data sets are resampled from the fitted model. - - "hierarchical" - If the experiment design is hierarchical (i.e. observations are grouped according to a categorical variable, for instance litter), a special resampling procedure is suggested (Blessinger 2020) - - All resampling is done within the dose values. - } - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} - - \item{progressInfo}{logical. If TRUE, a progressbar is displayed when calculating bootstrap confidence intervals} -} +\item{object}{object of class \code{drcOrdinal}} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous, quantal, quantal and ordinal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. The options are "modelBased" and "absolute". + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument.} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk.} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are available +for ordinal response. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data.} + +\item{interval}{character string specifying the type of confidence interval +to use: "delta" (default), "sandwich", "profile" or "bootstrap" + +"delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method + +"sandwich" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method, where the sandwich covariance matrix is used + +"bootstrap" - BMDL is based on bmd estimates on resampled data sets. The +type of bootstrap applied can be specified by the "bootType" argument. +Default is "nonparametric". + +"none" - No confidence interval is computed.} + +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} + +\item{R}{integer specifying the number of data sets resampled from the +original data set when computing the confidence interval by bootstrap.} + +\item{bootType}{character string specifying the resampling procedure for the +data sets used for bootstrap. + +"nonparametric" - Bootstrapping is done by sampling with replacement from +the original data set. + +"parametric" - Bootstrapping is done by sampling from a multinomial +distribution with probabilites given by the number of observations for each +level. If all observations for one group are in the same level, shrinkage is +used to avoid that the resampling always produces that particular level. In +this case data is sampled from a multinomial distribution with probabilities +(1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +particular group, and |K| is the number of levels. + +"model" - New data sets are resampled from the fitted model. + +"hierarchical" - If the experiment design is hierarchical (i.e. observations +are grouped according to a categorical variable, for instance litter), a +special resampling procedure is suggested (Blessinger 2020) + +All resampling is done within the dose values.} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} + +\item{progressInfo}{logical. If TRUE, a progressbar is displayed when +calculating bootstrap confidence intervals} } \value{ -A list of four elements: Results contain the estimated BMD and BMDL, interval gives the lower (BMDL) and upper (BMDU) end of the confidence interval of BMD. -} -\references{ - Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) - Benchmark Dose Calculation from Epidemiological Data, - \emph{Biometrics} \bold{57}, 698--706. - - Crump, K. (2002) - Critical Issues in Benchmark Calculations from Continuous Data, - \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. - - Blessinger, T. D., Euling, S. Y., Wang, L., Hogan, K. A., Cai, C., Klinefelter, G., Saillenfait, A.M. (2020) - \emph{Environment International} \bold{134} -} - -\author{ Signe M. Jensen and Jens Riis Baalkilde +A list of four elements: Results contain the estimated BMD and BMDL, +interval gives the lower (BMDL) and upper (BMDU) end of the confidence +interval of BMD. } -\note{ +\description{ +Estimation of benchmark doses and benchmark dose lower limit from ordinal +dose response model fits } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous, quantal, quantal and ordinal dose-response data for a range of +dose-response models based on the available definitions of the benchmark +dose concepts. -\seealso{ +Details on the implemented definitions and methods can be found in Crump +(2002) } \examples{ + library(drc) library(drcData) data(guthion) @@ -107,8 +130,22 @@ guthionS <- subset(guthion, trt == "S") guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "total", dose = "dose", data = guthionS, fct = LL.2()) bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50) + +} +\references{ +Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +\bold{57}, 698--706. + +Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. + +Blessinger, T. D., Euling, S. Y., Wang, L., Hogan, K. A., Cai, C., +Klinefelter, G., Saillenfait, A.M. (2020) \emph{Environment International} +\bold{134} +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bmdOrdinalMA.Rd b/man/bmdOrdinalMA.Rd index 6a1fe77..9403d2d 100644 --- a/man/bmdOrdinalMA.Rd +++ b/man/bmdOrdinalMA.Rd @@ -1,90 +1,115 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmdOrdinalMA.R \name{bmdOrdinalMA} \alias{bmdOrdinalMA} -\title{ -Benchmark dose estimation for ordinal dose-response models -} -\description{Estimation of benchmark doses and benchmark dose lower limit based on model averaging from a user-defined list of ordinal dose-response model fits -} +\title{Benchmark dose estimation for ordinal dose-response models} \usage{ -bmdOrdinalMA(modelList, modelWeights = c("AIC", "BIC"), bmr, - backgType = c("modelBased", "absolute"), backg = NA, - def=c("excess", "additional", "point"), type = c("bootstrap", "Kang"), - level = 0.95, R = 500, - bootType = c("nonparametric", "parametric"), - display = TRUE, progressInfo = TRUE) +bmdOrdinalMA( + modelList, + modelWeights = c("AIC", "BIC"), + bmr, + backgType = c("modelBased", "absolute"), + backg = NA, + def = c("excess", "additional", "point"), + type = c("bootstrap", "Kang"), + level = 0.95, + R = 500, + bootType = c("nonparametric", "parametric"), + display = TRUE, + progressInfo = TRUE +) } \arguments{ - \item{modelList}{A list of ordinal dose-response models of class \code{drcOrdinal}} - \item{modelWeights}{character string specifying the type of weights used, "AIC" or "BIC", or a numeric vector of the same length as the modelList with user defined weights} - \item{bmr}{numeric value of benchmark response level for which to calculate the benchmark dose} - \item{backgType}{character string specifying how the background level is specified. The options are "modelBased" and "absolute". - - "modelBased" - the background level is obtained from the model as the level for dose 0: - p0 = f(0) - - "absolute" - the background level is specified by the user through the backg argument.} - - \item{backg}{numeric value specifying the background level. Defaults to 0 for "absolute" background risk.} - - \item{def}{character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are available for ordinal response. - - "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). - Works for binomial response. BMR should be between 0 and 1. - - "additional" - BMR is defined as: BMR = f(BMD) - p0. - Works for binomial response. BMR should be between 0 and 1. - - "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response data.} - - \item{type}{specify the model averaging type used for the confidence intervals. Options are "Kang" (confidence intervals computed as weighted averages of individual confidence intervals) and "bootstrap"} - - \item{level}{numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95} - - \item{R}{integer specifying the number of data sets resampled from the original data set when computing the confidence interval by bootstrap.} - - \item{bootType}{character string specifying the resampling procedure for the data sets used for bootstrap. - - "nonparametric" - Bootstrapping is done by sampling with replacement from the original data set. - - "parametric" - Bootstrapping is done by sampling from a multinomial distribution with probabilites given by the number of observations for each level. If all observations for one group are in the same level, shrinkage is used to avoid that the resampling always produces that particular level. In this case data is sampled from a multinomial distribution with probabilities (1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + 1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the particular group, and |K| is the number of levels. - - All resampling is done within the dose values. - } - - \item{display}{logical. If TRUE the results are displayed; otherwise they are not} - - \item{progressInfo}{logical. If TRUE, a progressbar is displayed when calculating bootstrap confidence intervals} -} +\item{modelList}{A list of ordinal dose-response models of class +\code{drcOrdinal}} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous, quantal, quantal and ordinal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) -} -\value{ -A list of four elements: Results contain the estimated BMD and BMDL, interval gives the lower (BMDL) and upper (BMDU) end of the confidence interval of BMD. -} -\references{ - Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) - Benchmark Dose Calculation from Epidemiological Data, - \emph{Biometrics} \bold{57}, 698--706. +\item{modelWeights}{character string specifying the type of weights used, +"AIC" or "BIC", or a numeric vector of the same length as the modelList with +user defined weights} - Crump, K. (2002) - Critical Issues in Benchmark Calculations from Continuous Data, - \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. -} +\item{bmr}{numeric value of benchmark response level for which to calculate +the benchmark dose} + +\item{backgType}{character string specifying how the background level is +specified. The options are "modelBased" and "absolute". + +"modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0) + +"absolute" - the background level is specified by the user through the backg +argument.} + +\item{backg}{numeric value specifying the background level. Defaults to 0 +for "absolute" background risk.} + +\item{def}{character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are available +for ordinal response. + +"excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1. + +"additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1. + +"point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data.} + +\item{type}{specify the model averaging type used for the confidence +intervals. Options are "Kang" (confidence intervals computed as weighted +averages of individual confidence intervals) and "bootstrap"} -\author{ Signe M. Jensen and Jens Riis Baalkilde +\item{level}{numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95} + +\item{R}{integer specifying the number of data sets resampled from the +original data set when computing the confidence interval by bootstrap.} + +\item{bootType}{character string specifying the resampling procedure for the +data sets used for bootstrap. + +"nonparametric" - Bootstrapping is done by sampling with replacement from +the original data set. + +"parametric" - Bootstrapping is done by sampling from a multinomial +distribution with probabilites given by the number of observations for each +level. If all observations for one group are in the same level, shrinkage is +used to avoid that the resampling always produces that particular level. In +this case data is sampled from a multinomial distribution with probabilities +(1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +particular group, and |K| is the number of levels. + +All resampling is done within the dose values.} + +\item{display}{logical. If TRUE the results are displayed; otherwise they +are not} + +\item{progressInfo}{logical. If TRUE, a progressbar is displayed when +calculating bootstrap confidence intervals} +} +\value{ +A list of four elements: Results contain the estimated BMD and BMDL, +interval gives the lower (BMDL) and upper (BMDU) end of the confidence +interval of BMD. } -\note{ +\description{ +Estimation of benchmark doses and benchmark dose lower limit based on model +averaging from a user-defined list of ordinal dose-response model fits } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous, quantal, quantal and ordinal dose-response data for a range of +dose-response models based on the available definitions of the benchmark +dose concepts. -\seealso{ +Details on the implemented definitions and methods can be found in Crump +(2002) } \examples{ + library(drc) library(drcData) data(guthion) @@ -106,8 +131,18 @@ bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), modelWeights = "AIC", bmr = 0.1, backgType = "modelBased", def = "excess", type = "bootstrap", R = 50) + +} +\references{ +Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, \emph{Biometrics} +\bold{57}, 698--706. + +Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, \emph{Critical Reviews in Toxicology} \bold{32}, 133--153. +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/bootDataGen.Rd b/man/bootDataGen.Rd index 155bf2c..b59506c 100644 --- a/man/bootDataGen.Rd +++ b/man/bootDataGen.Rd @@ -1,5 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bootDataGen.R \name{bootDataGen} \alias{bootDataGen} -\title{ +\title{Help funtion to bmdBoot} +\usage{ +bootDataGen(object, R = 1000, bootType = "nonparametric", aggregated = TRUE) +} +\description{ Help funtion to bmdBoot } diff --git a/man/bootDataGenOrdinal.Rd b/man/bootDataGenOrdinal.Rd index f900b14..045fdc3 100644 --- a/man/bootDataGenOrdinal.Rd +++ b/man/bootDataGenOrdinal.Rd @@ -1,5 +1,15 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bootDataGenOrdinal.R \name{bootDataGenOrdinal} \alias{bootDataGenOrdinal} -\title{ +\title{Help funtion to bmdOrdinal and bmdOrdinalMA} +\usage{ +bootDataGenOrdinal( + object, + R = 500, + bootType = c("nonparametric", "parametric", "model", "hierarchical") +) +} +\description{ Help funtion to bmdOrdinal and bmdOrdinalMA } diff --git a/man/coef.drcHetVar.Rd b/man/coef.drcHetVar.Rd new file mode 100644 index 0000000..bb32d40 --- /dev/null +++ b/man/coef.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/coef.drcHetVar.R +\name{coef.drcHetVar} +\alias{coef.drcHetVar} +\title{S3 method} +\usage{ +\method{coef}{drcHetVar}(object, ...) +} +\description{ +S3 method +} diff --git a/man/drmHetVar.Rd b/man/drmHetVar.Rd index cb99bc9..d1a42b3 100644 --- a/man/drmHetVar.Rd +++ b/man/drmHetVar.Rd @@ -1,48 +1,55 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/drmHetVar.R \name{drmHetVar} \alias{drmHetVar} -\title{ -Dose response modeling with heterogeneous variance -} -\description{Fit a dose-response model with heterogeneous variance dependending on dose level. -} +\title{Dose response modeling with heterogeneous variance} \usage{ drmHetVar(formula, var.formula, data, fct, curveStart = NULL) } - \arguments{ - \item{formula}{formula for the dose-response relationship} - \item{var.formula}{one-sided formula specifying the dependance of the dose values and/or the fitted values on the point-wise standard error} - \item{data}{data.frame containing the observations} - \item{fct}{a list with three or more elements specifying the non-linear function, the accompanying self starter function, the names of the parameter in the non-linear function and, optionally, the first and second derivatives as well as information used for calculation of ED values. Currently available functions include, among others, the four- and five-parameter log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use drc::getMeanFunctions for a full list.} - \item{curveStart}{numerical of length equal to the number of parameters for the curve. Starting values for the curve parameters (optional).} -} +\item{formula}{formula for the dose-response relationship} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - REFERENCES TO BE ADDED/WRITTEN -} -\value{ -dose-response model with a heterogeneous variance structure of class \code{drcHetVar}. +\item{var.formula}{one-sided formula specifying the dependance of the dose +values and/or the fitted values on the point-wise standard error} -The primary objective is to use this model for benchmark dose estimation based on the hybrid method with a heterogeneous variance structure. This can be done using the \code{bmdHetVar} function. +\item{data}{data.frame containing the observations} -A plot method is available, which can be useful for assessing the fit of the variance structure. -} -\references{ +\item{fct}{a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well as information used for calculation of ED values. Currently +available functions include, among others, the four- and five-parameter +log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +drc::getMeanFunctions for a full list.} + +\item{curveStart}{numerical of length equal to the number of parameters for +the curve. Starting values for the curve parameters (optional).} } +\value{ +dose-response model with a heterogeneous variance structure of class +\code{drcHetVar}. -\author{ Signe M. Jensen and Jens Riis Baalkilde +The primary objective is to use this model for benchmark dose estimation +based on the hybrid method with a heterogeneous variance structure. This can +be done using the \code{bmdHetVar} function. + +A plot method is available, which can be useful for assessing the fit of the +variance structure. } -\note{ +\description{ +Fit a dose-response model with heterogeneous variance dependending on dose +level. } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +REFERENCES TO BE ADDED/WRITTEN } \examples{ + library(drc) library(drcData) library(bmd) @@ -76,8 +83,10 @@ plot(GiantKelp.LL.4.hetVarLogSq) + +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/drmMMRE.Rd b/man/drmMMRE.Rd index b17f1b2..13ed4eb 100644 --- a/man/drmMMRE.Rd +++ b/man/drmMMRE.Rd @@ -1,49 +1,58 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/drmMMRE.R \name{drmMMRE} \alias{drmMMRE} -\title{ -Dose response modeling with hierarchical variance structure -} -\description{Fits a meta-analytic hierarchical dose-response model. -} +\title{Dose response modeling with hierarchical variance structure} \usage{ drmMMRE(formula, exp_id, data, fct, type = c("continuous", "binomial")) } - \arguments{ - \item{formula}{a symbolic description of the model to be fit of the form 'response ~ dose'} - \item{exp_id}{the name of the column in the data set that specifies the hierarchical structure of the data} - \item{data}{a data frame containing the variables in the model.} - \item{fct}{a list with three or more elements specifying the non-linear function, the accompanying self starter function, the names of the parameter in the non-linear function and, optionally, the first and second derivatives as well as information used for calculation of ED values. Currently available functions include, among others, the four- and five-parameter log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use drc::getMeanFunctions for a full list.} - \item{type}{a character string specifying the distribution of the data. The default is "continuous", corresponding to assuming a normal distribution. "binary" imply a binomial distribution.} -} +\item{formula}{a symbolic description of the model to be fit of the form +'response ~ dose'} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Fitting the meta-analytic model relies on a multivariate meta-analytic model provided by the function \code{rma.mv} in the "metafor" package, which can be installed by running - \code{remotes::install_github("wviechtb/metafor")} - - Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. doi:10.18637/jss.v036.i03 +\item{exp_id}{the name of the column in the data set that specifies the +hierarchical structure of the data} + +\item{data}{a data frame containing the variables in the model.} + +\item{fct}{a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well as information used for calculation of ED values. Currently +available functions include, among others, the four- and five-parameter +log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +drc::getMeanFunctions for a full list.} + +\item{type}{a character string specifying the distribution of the data. The +default is "continuous", corresponding to assuming a normal distribution. +"binary" imply a binomial distribution.} } \value{ -meta-analytic dose-response model with a hierarchical variance structure of class \code{drcMMRE}. +meta-analytic dose-response model with a hierarchical variance +structure of class \code{drcMMRE}. -The primary objective is to use this model for benchmark dose estimation based on dose-response data with a heterogeneous variance structure. +The primary objective is to use this model for benchmark dose estimation +based on dose-response data with a heterogeneous variance structure. } -\references{ +\description{ +Fits a meta-analytic hierarchical dose-response model. } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ -} +Fitting the meta-analytic model relies on a multivariate meta-analytic model +provided by the function \code{rma.mv} in the "metafor" package, which can +be installed by running \code{remotes::install_github("wviechtb/metafor")} -\seealso{ +Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor +package. Journal of Statistical Software, 36(3), 1-48. +doi:10.18637/jss.v036.i03 } \examples{ + library(drc) library(drcData) library(metafor) @@ -59,8 +68,10 @@ data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2), modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4()) bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative") + +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/drmOrdinal.Rd b/man/drmOrdinal.Rd index e87207e..d892340 100644 --- a/man/drmOrdinal.Rd +++ b/man/drmOrdinal.Rd @@ -1,52 +1,53 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/drmOrdinal.R \name{drmOrdinal} \alias{drmOrdinal} -\title{ -Fitting ordinal dose-response models -} -\description{A model fitting function for analysis of ordinal dose-response data. -} +\title{Fitting ordinal dose-response models} \usage{ drmOrdinal(levels, dose, weights, blocks, data, fct, p.epsilon = 1e-16) } \arguments{ - \item{levels}{a character vector of the levels of the response variable in increasing order, as they appear in the supplied data set} - - \item{dose}{a character string specifying the column with the dose values in the supplied data set} - - \item{weights}{a character string specifying the column containing the number of observations pr. group} - - \item{blocks}{a character string specifying the column containing the blocks of the experiment, if available (optional)} - - \item{data}{a dataframe containing the observations} - - \item{fct}{a list with three or more elements specifying the non-linear - function, the accompanying self starter function, the names of the parameter in the non-linear function and, - optionally, the first and second derivatives as well, for the individual fitted curves. For more information see the help page for the "drm" function in the "drc" package. - Currently available functions for ordinal dose-response models include, among others, the log-logistic models - \code{\link[drc]{LL.4}}, the log-normal model \code{\link[drc]{LN.4}} and the two Weibull models \code{\link[drc]{W1.4}} and \code{\link[drc]{W2.4}}. Use - \code{\link[drc]{getMeanFunctions}} for a full list.} +\item{levels}{a character vector of the levels of the response variable in +increasing order, as they appear in the supplied data set} - \item{p.epsilon}{numeric value specifying the lower bound for the probabilites for each level returned by the function pFun created when fitting the model. Default value is 10^(-16)} -} +\item{dose}{a character string specifying the column with the dose values in +the supplied data set} -\details{ - This functions fits a dose-response model for ordinal dose-response data by fitting a series of binomial dose-response models. +\item{weights}{a character string specifying the column containing the +number of observations pr. group} + +\item{blocks}{a character string specifying the column containing the blocks +of the experiment, if available (optional)} + +\item{data}{a dataframe containing the observations} + +\item{fct}{a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well, for the individual fitted curves. For more information see the help +page for the "drm" function in the "drc" package. Currently available +functions for ordinal dose-response models include, among others, the +log-logistic models \code{\link[drc]{LL.4}}, the log-normal model +\code{\link[drc]{LN.4}} and the two Weibull models \code{\link[drc]{W1.4}} +and \code{\link[drc]{W2.4}}. Use \code{\link[drc]{getMeanFunctions}} for a +full list.} + +\item{p.epsilon}{numeric value specifying the lower bound for the +probabilites for each level returned by the function pFun created when +fitting the model. Default value is 10^(-16)} } \value{ - An object of (S3) class 'drcOrdinal'. -} -\references{ - # ADD REFERENCES +An object of (S3) class 'drcOrdinal'. } - -\author{ Signe M. Jensen and Jens Riis Baalkilde -} -\note{ +\description{ +A model fitting function for analysis of ordinal dose-response data. } - -\seealso{ +\details{ +This functions fits a dose-response model for ordinal dose-response data by +fitting a series of binomial dose-response models. } \examples{ + library(drc) library(drcData) data(guthion) @@ -57,8 +58,13 @@ guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "to plot(guthionS.LL, xlim = c(15,55)) # uses ggplot + +} +\references{ +# ADD REFERENCES +} +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/expandBinomial.Rd b/man/expandBinomial.Rd index d268302..6829a8c 100644 --- a/man/expandBinomial.Rd +++ b/man/expandBinomial.Rd @@ -1,46 +1,46 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/expandBinomial.R \name{expandBinomial} \alias{expandBinomial} -\title{ -Utility function -} -\description{Utility function for expanding binomial data -} +\title{Utility function} \usage{ expandBinomial(data, number, total, dose, curveid = character(0)) } - \arguments{ - \item{data}{a data.frame} - \item{number}{the name of the column in the data set containing the number of affected individuals per dose level} - \item{total}{the name of the column in the data set containing the total number of individuals per dose level} - \item{dose}{the name of the column in the data set containing the dose values} - \item{curveid}{the name of the column in the data set specifying the curveid (if available)} -} +\item{data}{a data.frame} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. +\item{number}{the name of the column in the data set containing the number +of affected individuals per dose level} + +\item{total}{the name of the column in the data set containing the total +number of individuals per dose level} + +\item{dose}{the name of the column in the data set containing the dose +values} +\item{curveid}{the name of the column in the data set specifying the curveid +(if available)} } \value{ data.frame } -\references{ +\description{ +Utility function for expanding binomial data } - -\author{ Signe M. Jensen and Jens Riis Baalkilde +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. } -\note{ +\examples{ +\dontrun{ } + -\seealso{ } - -\examples{ +\author{ +Signe M. Jensen and Jens Riis Baalkilde } \keyword{models} \keyword{nonlinear} - -\concept{BMD BMDL benchmark dose-response} \ No newline at end of file diff --git a/man/getStackingWeights.Rd b/man/getStackingWeights.Rd index 516ad61..c7ee814 100644 --- a/man/getStackingWeights.Rd +++ b/man/getStackingWeights.Rd @@ -1,40 +1,35 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/getStackingWeights.R \name{getStackingWeights} \alias{getStackingWeights} -\title{ -Model-average dose-response curves -} -\description{Computing stacking weights. -} +\title{Model-average dose-response curves} \usage{ getStackingWeights(modelList, nSplits = 2) } \arguments{ - \item{modelList}{list of models of class \code{drc}} - \item{nSplits}{integer. The Stacking Weights are based on V-fold cross-validation. The nSplits argument sets the number V of data splits used in the cross validation.} -} +\item{modelList}{list of models of class \code{drc}} -\details{ -The aim to provide an R package - calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) - for continuous and quantal dose-response data for a range of dose-response models based on the available - definitions of the benchmark dose concepts. - - Details on the implemented definitions and methods can be found in Crump (2002) +\item{nSplits}{integer. The Stacking Weights are based on V-fold +cross-validation. The nSplits argument sets the number V of data splits used +in the cross validation.} } \value{ numeric } -\references{ -} - -\author{ Jens Riis Baalkilde -} -\note{ +\description{ +Computing stacking weights. } +\details{ +The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95\% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts. -\seealso{ +Details on the implemented definitions and methods can be found in Crump +(2002) } \examples{ + library(bmd) library(drc) library(drcData) @@ -51,9 +46,12 @@ getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, aconiazide.W1.3, aconiazide.W2.3), nSplits = 7) + +} +\author{ +Jens Riis Baalkilde } +\keyword{averaging} +\keyword{model} \keyword{models} \keyword{nonlinear} -\keyword{model averaging} - -\concept{dose-response, MA, Model Averaging} diff --git a/man/invBmd.Rd b/man/invBmd.Rd index c825536..720363e 100644 --- a/man/invBmd.Rd +++ b/man/invBmd.Rd @@ -1,5 +1,23 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/invBmd.R \name{invBmd} \alias{invBmd} -\title{ +\title{Help funtion to bmd} +\usage{ +invBmd( + object, + bmr, + level = 0.9, + slope, + backgType = "modelBased", + backg = NA, + catLev = NA, + extFactor = 10, + def, + useSD = useSD, + sandwich.vcov = FALSE +) +} +\description{ Help funtion to bmd } diff --git a/man/logLik.drcHetVar.Rd b/man/logLik.drcHetVar.Rd new file mode 100644 index 0000000..6adb0a7 --- /dev/null +++ b/man/logLik.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/logLik.drcHetVar.R +\name{logLik.drcHetVar} +\alias{logLik.drcHetVar} +\title{S3 method} +\usage{ +\method{logLik}{drcHetVar}(object, ...) +} +\description{ +S3 method +} diff --git a/man/logLik.drcOrdinal.Rd b/man/logLik.drcOrdinal.Rd new file mode 100644 index 0000000..caba8ae --- /dev/null +++ b/man/logLik.drcOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/logLik.drcOrdinal.R +\name{logLik.drcOrdinal} +\alias{logLik.drcOrdinal} +\title{S3 method} +\usage{ +\method{logLik}{drcOrdinal}(object, ...) +} +\description{ +S3 method +} diff --git a/man/monotonicityTest.Rd b/man/monotonicityTest.Rd index ab2c915..f6f8feb 100644 --- a/man/monotonicityTest.Rd +++ b/man/monotonicityTest.Rd @@ -1,35 +1,58 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/monotonicityTest.R \name{monotonicityTest} \alias{monotonicityTest} \title{Test for Monotonicity of Relationship Between Two Variables} -\description{ - Conducts a test for monotonicity between a numeric independent variable \code{x} and a numeric dependent variable \code{y} using specified statistical tests. -} \usage{ -monotonicityTest(x, y, data, test = c("jonckheere", "bartholomew"), level = 0.05, ...) +monotonicityTest( + x, + y, + data, + test = c("jonckheere", "bartholomew"), + level = 0.05, + ... +) } \arguments{ - \item{x}{A numeric vector or the name of the independent variable (if \code{data} is provided).} - \item{y}{A numeric vector or the name of the dependent variable (if \code{data} is provided).} - \item{data}{An optional data frame containing the variables \code{x} and \code{y}. If provided, \code{x} and \code{y} should be column names in \code{data}.} - \item{test}{A character string specifying the test to use. Must be one of \code{"jonckheere"} (default) or \code{"bartholomew"}.} - \item{level}{Significance level for the test. Defaults to 0.05.} - \item{...}{Additional arguments passed to the underlying test functions.} -} -\details{ - The function tests the monotonicity of the relationship between \code{x} and \code{y} based on the specified test: - \itemize{ - \item \code{"jonckheere"}: Uses the Jonckheere-Terpstra test to assess monotonic trends. - \item \code{"bartholomew"}: Uses Bartholomew's test to assess monotonicity. - } +\item{x}{A numeric vector or the name of the independent variable (if +\code{data} is provided).} + +\item{y}{A numeric vector or the name of the dependent variable (if +\code{data} is provided).} + +\item{data}{An optional data frame containing the variables \code{x} and +\code{y}. If provided, \code{x} and \code{y} should be column names in +\code{data}.} - The direction of the monotonicity (increasing or decreasing) is determined by the sign of the coefficient from a simple linear model \code{lm(y ~ x)}. +\item{test}{A character string specifying the test to use. Must be one of +\code{"jonckheere"} (default) or \code{"bartholomew"}.} + +\item{level}{Significance level for the test. Defaults to 0.05.} + +\item{...}{Additional arguments passed to the underlying test functions.} } \value{ - A list with the following components: - \item{p.value}{The p-value of the test.} - \item{acceptMonotonicity}{A logical value indicating whether monotonicity is accepted (\code{TRUE}) or rejected (\code{FALSE}) based on the specified significance level.} +A list with the following components: \item{p.value}{The p-value of +the test.} \item{acceptMonotonicity}{A logical value indicating whether +monotonicity is accepted (\code{TRUE}) or rejected (\code{FALSE}) based on +the specified significance level.} +} +\description{ +Conducts a test for monotonicity between a numeric independent variable +\code{x} and a numeric dependent variable \code{y} using specified +statistical tests. +} +\details{ +The function tests the monotonicity of the relationship between \code{x} and +\code{y} based on the specified test: \itemize{ \item \code{"jonckheere"}: +Uses the Jonckheere-Terpstra test to assess monotonic trends. \item +\code{"bartholomew"}: Uses Bartholomew's test to assess monotonicity. } + +The direction of the monotonicity (increasing or decreasing) is determined +by the sign of the coefficient from a simple linear model \code{lm(y ~ x)}. } \examples{ + # Example with custom data x <- c(1, 2, 3, 4, 5) y <- c(2, 4, 6, 8, 10) @@ -39,17 +62,19 @@ print(result) data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew") print(result) -} - -\author{Jens Riis Baalkilde} -\seealso{ - \code{.jonckheereTest}, \code{.bartholomewTest} } - \references{ - A. R. Jonckheere (1954). "A Distribution-Free k-Sample Test Against Ordered Alternatives." - D. J. Bartholomew (1961). "Ordered tests in the analysis of variance." - OECD (2006). Rapport No. 54, Annexes. +A. R. Jonckheere (1954). "A Distribution-Free k-Sample Test +Against Ordered Alternatives." D. J. Bartholomew (1961). "Ordered tests in +the analysis of variance." OECD (2006). Rapport No. 54, Annexes. +} +\seealso{ +\code{.jonckheereTest}, \code{.bartholomewTest} +} +\author{ +Jens Riis Baalkilde } -\keyword{monotonicity, trend test} +\keyword{monotonicity,} +\keyword{test} +\keyword{trend} diff --git a/man/plot.bmd.Rd b/man/plot.bmd.Rd index 74367fd..41b2edb 100644 --- a/man/plot.bmd.Rd +++ b/man/plot.bmd.Rd @@ -1,44 +1,35 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/plot.bmd.R \name{plot.bmd} \alias{plot.bmd} \alias{\method{plot}{bmd}} - \title{Plotting benchmark doses} - -\description{ - \code{plot.bmd} displays benchmark dose values with options to plot confidence intervals as well. -} - \usage{ - \method{plot}{bmd}(x, ..., interval = c("BMDL", "twosided", "none")) +\method{plot}{bmd}(x, ..., interval = c("BMDL", "twosided", "none")) } - \arguments{ - \item{x}{an object of class 'bmd'.} - \item{...}{arguments to be passed on to \code{plot.drc}, if \code{add = FALSE}} - \item{interval}{option to plot only the lower limit of the confidence interval for the benchmark dose ("BMDL", default), both limit - of the confidence interval ("twosided"), or no confidence interval ("none").} -} +\item{x}{an object of class 'bmd'.} -\details{ - This function is a simple function to plot benchmark dose values along with the fitted curve. -} +\item{...}{arguments to be passed on to \code{plot.drc}, if \code{add = +FALSE}} +\item{interval}{option to plot only the lower limit of the confidence +interval for the benchmark dose ("BMDL", default), both limit of the +confidence interval ("twosided"), or no confidence interval ("none").} +} \value{ - Creates a plot. No value returned. +Creates a plot. No value returned. } - -\author{ - Jens Riis Baalkilde. +\description{ +\code{plot.bmd} displays benchmark dose values with options to plot +confidence intervals as well. +} +\details{ +This function is a simple function to plot benchmark dose values along with +the fitted curve. } - -%\references{ -%} - -%\note{ ~~further notes~~ } - -%\seealso{\code{\link{plotraw}} plots the observations only.} - \examples{ + library(drc) library(drcData) @@ -56,5 +47,9 @@ plot(bmd0, interval = "twosided") plot(bmd0, type = "confidence") + +} +\author{ +Jens Riis Baalkilde. } -\keyword{ggplot} \ No newline at end of file +\keyword{ggplot} diff --git a/man/plot.drcHetVar.Rd b/man/plot.drcHetVar.Rd new file mode 100644 index 0000000..94a4ef2 --- /dev/null +++ b/man/plot.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/plot.drcHetVar.R +\name{plot.drcHetVar} +\alias{plot.drcHetVar} +\title{S3 method} +\usage{ +\method{plot}{drcHetVar}(x, ...) +} +\description{ +S3 method +} diff --git a/man/plot.drcOrdinal.Rd b/man/plot.drcOrdinal.Rd new file mode 100644 index 0000000..4721bc4 --- /dev/null +++ b/man/plot.drcOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/plot.drcOrdinal.R +\name{plot.drcOrdinal} +\alias{plot.drcOrdinal} +\title{S3 method} +\usage{ +\method{plot}{drcOrdinal}(x, ...) +} +\description{ +S3 method +} diff --git a/man/print.bmdOrdinal.Rd b/man/print.bmdOrdinal.Rd new file mode 100644 index 0000000..7f79e87 --- /dev/null +++ b/man/print.bmdOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.bmdOrdinal.R +\name{print.bmdOrdinal} +\alias{print.bmdOrdinal} +\title{S3 method} +\usage{ +\method{print}{bmdOrdinal}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\description{ +S3 method +} diff --git a/man/print.drcHetVar.Rd b/man/print.drcHetVar.Rd new file mode 100644 index 0000000..ef0dc4f --- /dev/null +++ b/man/print.drcHetVar.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.drcHetVar.R +\name{print.drcHetVar} +\alias{print.drcHetVar} +\title{S3 method} +\usage{ +\method{print}{drcHetVar}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\description{ +S3 method +} diff --git a/man/print.drcMMRE.Rd b/man/print.drcMMRE.Rd new file mode 100644 index 0000000..a9583e1 --- /dev/null +++ b/man/print.drcMMRE.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.drcMMRE.R +\name{print.drcMMRE} +\alias{print.drcMMRE} +\title{S3 method} +\usage{ +\method{print}{drcMMRE}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\description{ +S3 method +} diff --git a/man/print.drcOrdinal.Rd b/man/print.drcOrdinal.Rd new file mode 100644 index 0000000..b80e518 --- /dev/null +++ b/man/print.drcOrdinal.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.drcOrdinal.R +\name{print.drcOrdinal} +\alias{print.drcOrdinal} +\title{S3 method} +\usage{ +\method{print}{drcOrdinal}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\description{ +S3 method +} diff --git a/man/qplotBmd.Rd b/man/qplotBmd.Rd index b8189a1..b66880b 100644 --- a/man/qplotBmd.Rd +++ b/man/qplotBmd.Rd @@ -1,46 +1,46 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/qplotBmd.R \name{qplotBmd} - \alias{qplotBmd} - \title{Plotting benchmark doses using ggplot2} - -\description{ - \code{qplotBmd} displays benchmark dose values with options to plot confidence intervals as well using \code{ggplot2}. -} - \usage{ - qplotBmd(x, ..., interval = c("BMDL", "twosided", "none"), col = FALSE, add = FALSE) +qplotBmd( + x, + ..., + interval = c("BMDL", "twosided", "none"), + col = FALSE, + add = FALSE +) } - \arguments{ - \item{x}{an object of class 'bmd'.} - \item{...}{arguments to be passed on to qplotDrc, if \code{add = FALSE}} - \item{interval}{option to plot only the lower limit of the confidence interval for the benchmark dose ("BMDL", default), both limit - of the confidence interval ("twosided"), or no confidence interval ("none").} - \item{col}{logical. If TRUE then multiple curves specified by "curveid" in the dose-response model are distinguised by colours rather than point shapes and line types} - \item{add}{logical. If TRUE then the functions returns a list of plot layers to be added to an already existing ggplot.} -} +\item{x}{an object of class 'bmd'.} -\details{ - This function is a simple function to plot benchmark dose values -} +\item{...}{arguments to be passed on to qplotDrc, if \code{add = FALSE}} +\item{interval}{option to plot only the lower limit of the confidence +interval for the benchmark dose ("BMDL", default), both limit of the +confidence interval ("twosided"), or no confidence interval ("none").} + +\item{col}{logical. If TRUE then multiple curves specified by "curveid" in +the dose-response model are distinguised by colours rather than point shapes +and line types} + +\item{add}{logical. If TRUE then the functions returns a list of plot layers +to be added to an already existing ggplot.} +} \value{ - A \code{ggplot} object. If the option \code{add} is used, a list of \code{ggplot} layers is returned. +A \code{ggplot} object. If the option \code{add} is used, a list of +\code{ggplot} layers is returned. } - -\author{ - Jens Riis Baalkilde. +\description{ +\code{qplotBmd} displays benchmark dose values with options to plot +confidence intervals as well using \code{ggplot2}. +} +\details{ +This function is a simple function to plot benchmark dose values } - -%\references{ -%} - -%\note{ ~~further notes~~ } - -%\seealso{\code{\link{plotraw}} plots the observations only.} - \examples{ + library(drc) library(drcData) @@ -57,5 +57,9 @@ qplotDrc(model,type="confidence") + qplotBmd(bmd0, interval = "twosided", add = FALSE) + +} +\author{ +Jens Riis Baalkilde. } -\keyword{ggplot} \ No newline at end of file +\keyword{ggplot} diff --git a/man/qplotDrc.Rd b/man/qplotDrc.Rd index 3692671..09e0feb 100644 --- a/man/qplotDrc.Rd +++ b/man/qplotDrc.Rd @@ -1,91 +1,110 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/qplotDrc.R \name{qplotDrc} - \alias{qplotDrc} - \title{Plotting fitted dose-response curves using ggplot2} - -\description{ - \code{qplotDrc} displays fitted curves and observations in the same plot window, - distinguishing between curves by different plot symbols and line types or colours using \code{ggplot2}. -} - \usage{ - - qplotDrc(x, add = FALSE, level = NULL, - type = c("average", "all", "bars", "none", "obs", "confidence"), - gridsize = 250, xtrans = "pseudo_log", xlab, xlim, - ytrans = NULL, ylab, ylim, col = FALSE, - normal = FALSE, normRef = 1, confidence.level = 0.95) +qplotDrc( + x, + add = FALSE, + level = NULL, + type = c("average", "all", "bars", "none", "obs", "confidence"), + gridsize = 250, + xtrans = "pseudo_log", + xlab, + xlim, + ytrans = NULL, + ylab, + ylim, + col = FALSE, + normal = FALSE, + normRef = 1, + confidence.level = 0.95 +) } - \arguments{ - \item{x}{an object of class 'drc'.} - \item{add}{logical. If TRUE then the functions returns a list of plot layers to be added to an already existing ggplot.} - \item{level}{vector of curve levels to plot. To plot only the curves specified by their names.} - \item{type}{a character string specifying how to plot the data. There are currently - 5 options: "average" (averages and fitted curve(s); default), - "none" (only the fitted curve(s)), "obs" (only the data points), - "all" (all data points and fitted curve(s)), - "bars" (averages and fitted curve(s) with model-based standard errors (see Details)), and - "confidence" (confidence bands for fitted curve(s)).} - \item{gridsize}{numeric. Number of points in the grid used for plotting the fitted curves.} - \item{xtrans}{Transformation to use on the x-axis. The default is "pesudo_log", which is a logarithmic - transformation with a smooth transition to 0. Other options include (among others) "log" and "identity". Can be overridden - by adding a scale using the \code{scale_x_continuous} function.} - \item{xlab}{an optional label for the x axis.} - \item{xlim}{a numeric vector of length two, containing the lower and upper limit for the x axis.} - \item{ytrans}{Transformation to use on the y-axis. The default is no transformation. Other options include (among others) "pseudo_log" and "log" and. Can be overridden - by adding a scale using the \code{scale_y_continuous} function.} - \item{ylab}{an optional label for the y axis.} - \item{ylim}{a numeric vector of length two, containing the lower and upper limit for the y axis.} - \item{col}{logical. If TRUE default ggplot colours are used, can be overridden by \code{scale_color_manual}. - If FALSE (default) no colours are used.} - \item{normal}{logical. If TRUE the plot of the normalized data and fitted curves are shown - (for details see Weimer et al. (2012) for details).} - \item{normRef}{numeric specifying the reference for the normalization (default is 1).} - \item{confidence.level}{confidence level for error bars and confidence bands. Defaults to 0.95.} -} +\item{x}{an object of class 'drc'.} -\details{ - This function largely seeks to mimic the behaviour of the \code{plot} method for the \code{drc} package using - the \code{ggplot2} package for plotting. - - The use of \code{xlim} allows changing the range of the x axis, extrapolating the fitted dose-response curves. - Note that changing the range on the x axis may also entail a change of the range on the y axis. - - See \code{\link{colors}} for the available colours. - - Suitable labels are automatically provided. - - The model-based standard errors used for the error bars are calculated - as the fitted value plus/minus the estimated error times the - 1-(alpha/2) quantile in the t distribution with degrees of freedom - equal to the residual degrees of freedom for the model (or using a - standard normal distribution in case of binomial and poisson data), - where alpha=1-confidence.level. The standard errors are obtained using - the predict method with the arguments interval = "confidence" - and level=confidence.level. -} +\item{add}{logical. If TRUE then the functions returns a list of plot layers +to be added to an already existing ggplot.} + +\item{level}{vector of curve levels to plot. To plot only the curves +specified by their names.} + +\item{type}{a character string specifying how to plot the data. There are +currently 5 options: "average" (averages and fitted curve(s); default), +"none" (only the fitted curve(s)), "obs" (only the data points), "all" (all +data points and fitted curve(s)), "bars" (averages and fitted curve(s) with +model-based standard errors (see Details)), and "confidence" (confidence +bands for fitted curve(s)).} + +\item{gridsize}{numeric. Number of points in the grid used for plotting the +fitted curves.} + +\item{xtrans}{Transformation to use on the x-axis. The default is +"pesudo_log", which is a logarithmic transformation with a smooth transition +to 0. Other options include (among others) "log" and "identity". Can be +overridden by adding a scale using the \code{scale_x_continuous} function.} + +\item{xlab}{an optional label for the x axis.} + +\item{xlim}{a numeric vector of length two, containing the lower and upper +limit for the x axis.} + +\item{ytrans}{Transformation to use on the y-axis. The default is no +transformation. Other options include (among others) "pseudo_log" and "log" +and. Can be overridden by adding a scale using the \code{scale_y_continuous} +function.} + +\item{ylab}{an optional label for the y axis.} +\item{ylim}{a numeric vector of length two, containing the lower and upper +limit for the y axis.} + +\item{col}{logical. If TRUE default ggplot colours are used, can be +overridden by \code{scale_color_manual}. If FALSE (default) no colours are +used.} + +\item{normal}{logical. If TRUE the plot of the normalized data and fitted +curves are shown (for details see Weimer et al. (2012) for details).} + +\item{normRef}{numeric specifying the reference for the normalization +(default is 1).} + +\item{confidence.level}{confidence level for error bars and confidence +bands. Defaults to 0.95.} +} \value{ - A \code{ggplot} object. If the option \code{add} is used, a list of \code{ggplot} layers is returned. +A \code{ggplot} object. If the option \code{add} is used, a list of +\code{ggplot} layers is returned. } - -\author{ - Jens Riis Baalkilde. Based on \code{plot.drc} by Christian Ritz and Jens C. Streibig with Contributions from Xiaoyan Wang and Greg Warnes. +\description{ +\code{qplotDrc} displays fitted curves and observations in the same plot +window, distinguishing between curves by different plot symbols and line +types or colours using \code{ggplot2}. } +\details{ +This function largely seeks to mimic the behaviour of the \code{plot} method +for the \code{drc} package using the \code{ggplot2} package for plotting. -\references{ - Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., Kopp-Schneider, A. (2012) - The impact of data transformations on concentration-response modeling. - \emph{Toxicology Letters}, \bold{213}, 292--298. -} +The use of \code{xlim} allows changing the range of the x axis, +extrapolating the fitted dose-response curves. Note that changing the range +on the x axis may also entail a change of the range on the y axis. -%\note{ ~~further notes~~ } +See \code{\link{colors}} for the available colours. -%\seealso{\code{\link{plotraw}} plots the observations only.} +Suitable labels are automatically provided. +The model-based standard errors used for the error bars are calculated as +the fitted value plus/minus the estimated error times the 1-(alpha/2) +quantile in the t distribution with degrees of freedom equal to the residual +degrees of freedom for the model (or using a standard normal distribution in +case of binomial and poisson data), where alpha=1-confidence.level. The +standard errors are obtained using the predict method with the arguments +interval = "confidence" and level=confidence.level. +} \examples{ + library(drc) library(drcData) library(ggplot2) @@ -135,5 +154,16 @@ qplotDrc(spinach.m1, col = TRUE, type = "confidence") + scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1))) + +} +\references{ +Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., +Kopp-Schneider, A. (2012) The impact of data transformations on +concentration-response modeling. \emph{Toxicology Letters}, \bold{213}, +292--298. +} +\author{ +Jens Riis Baalkilde. Based on \code{plot.drc} by Christian Ritz and +Jens C. Streibig with Contributions from Xiaoyan Wang and Greg Warnes. } -\keyword{ggplot} \ No newline at end of file +\keyword{ggplot} diff --git a/man/trendTest.Rd b/man/trendTest.Rd index 172bf5e..2e6dba7 100644 --- a/man/trendTest.Rd +++ b/man/trendTest.Rd @@ -1,36 +1,52 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/trendTest.R \name{trendTest} \alias{trendTest} \title{Test for Trend in Relationship Between Two Variables} -\description{ - Conducts a test for trends between a numeric independent variable \code{x} and a numeric dependent variable \code{y} using specified statistical tests. -} \usage{ trendTest(x, y, data, test = c("william", "shirley", "tukey"), level = 0.05) } \arguments{ - \item{x}{A numeric vector or the name of the independent variable (if \code{data} is provided).} - \item{y}{A numeric vector or the name of the dependent variable (if \code{data} is provided).} - \item{data}{An optional data frame containing the variables \code{x} and \code{y}. If provided, \code{x} and \code{y} should be column names in \code{data}.} - \item{test}{A character string specifying the test to use. Must be one of \code{"william"}, \code{"shirley"}, or \code{"tukey"} (default).} - \item{level}{Significance level for the test. Defaults to 0.05.} -} -\details{ - The function tests for a trend in the relationship between \code{x} and \code{y} based on the specified test: - \itemize{ - \item \code{"william"}: Applies Williams' test to assess trend significance. - \item \code{"shirley"}: Uses Shirley's test for trend analysis with ordered alternatives. - \item \code{"tukey"}: Implements the Tukey trend test using multiple marginal models. - } +\item{x}{A numeric vector or the name of the independent variable (if +\code{data} is provided).} + +\item{y}{A numeric vector or the name of the dependent variable (if +\code{data} is provided).} - The direction of the trend (increasing or decreasing) is determined by the slope of the linear model \code{lm(y ~ x)}. +\item{data}{An optional data frame containing the variables \code{x} and +\code{y}. If provided, \code{x} and \code{y} should be column names in +\code{data}.} + +\item{test}{A character string specifying the test to use. Must be one of +\code{"william"}, \code{"shirley"}, or \code{"tukey"} (default).} + +\item{level}{Significance level for the test. Defaults to 0.05.} } \value{ - A list with the following components: - \item{p.values}{A numeric vector of p-values for the tests (if applicable).} - \item{decisions}{A character vector indicating whether the trend is \code{"accept"} or \code{"reject"} based on the test results.} - \item{acceptTrend}{A logical value indicating whether a trend is accepted (\code{TRUE}) or rejected (\code{FALSE}) based on the specified significance level.} +A list with the following components: \item{p.values}{A numeric +vector of p-values for the tests (if applicable).} \item{decisions}{A +character vector indicating whether the trend is \code{"accept"} or +\code{"reject"} based on the test results.} \item{acceptTrend}{A logical +value indicating whether a trend is accepted (\code{TRUE}) or rejected +(\code{FALSE}) based on the specified significance level.} +} +\description{ +Conducts a test for trends between a numeric independent variable \code{x} +and a numeric dependent variable \code{y} using specified statistical tests. +} +\details{ +The function tests for a trend in the relationship between \code{x} and +\code{y} based on the specified test: \itemize{ \item \code{"william"}: +Applies Williams' test to assess trend significance. \item +\code{"shirley"}: Uses Shirley's test for trend analysis with ordered +alternatives. \item \code{"tukey"}: Implements the Tukey trend test using +multiple marginal models. } + +The direction of the trend (increasing or decreasing) is determined by the +slope of the linear model \code{lm(y ~ x)}. } \examples{ + # Example with custom data x <- c(1, 2, 3, 4, 5) y <- c(2, 4, 6, 8, 10) @@ -41,16 +57,23 @@ print(result) data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) result <- trendTest("x", "y", data = data, test = "shirley") print(result) -} -\seealso{ - \code{.williamsTest}, \code{.shirleyTest}, \code{.tukeytrendfit} + } \references{ - Williams, D. A. (1971). "A test for differences between treatment means when several dose levels are compared with a zero dose control." Biometrics, 27(1), 103-117. - Shirley, E. (1977). "A non-parametric equivalent of Williams' test for contrasting increasing dose levels of a treatment." Biometrics, 33(2), 386-389. - Schaarschmidt, F. et al. (2021). "The Tukey trend test: Multiplicity adjustment using multiple marginal models" Biometrics, 78(2), 789-797. +Williams, D. A. (1971). "A test for differences between +treatment means when several dose levels are compared with a zero dose +control." Biometrics, 27(1), 103-117. Shirley, E. (1977). "A non-parametric +equivalent of Williams' test for contrasting increasing dose levels of a +treatment." Biometrics, 33(2), 386-389. Schaarschmidt, F. et al. (2021). +"The Tukey trend test: Multiplicity adjustment using multiple marginal +models" Biometrics, 78(2), 789-797. +} +\seealso{ +\code{.williamsTest}, \code{.shirleyTest}, \code{.tukeytrendfit} } \author{ - Jens Riis Baalkilde +Jens Riis Baalkilde } -\keyword{trend, statistical test} +\keyword{statistical} +\keyword{test} +\keyword{trend,} diff --git a/man/vcov.drcMMRE.Rd b/man/vcov.drcMMRE.Rd new file mode 100644 index 0000000..5dd8b63 --- /dev/null +++ b/man/vcov.drcMMRE.Rd @@ -0,0 +1,11 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/drmMMRE.R +\name{vcov.drcMMRE} +\alias{vcov.drcMMRE} +\title{S3 method} +\usage{ +\method{vcov}{drcMMRE}(object, ...) +} +\description{ +S3 method +} diff --git a/tests/testthat.R b/tests/testthat.R index b00de44..01d0433 100644 --- a/tests/testthat.R +++ b/tests/testthat.R @@ -8,5 +8,5 @@ library(testthat) library(bmd) - +library(drc) test_check("bmd") diff --git a/tests/testthat/test-bmd.R b/tests/testthat/test-bmd.R index 5a30a68..dd9ade0 100644 --- a/tests/testthat/test-bmd.R +++ b/tests/testthat/test-bmd.R @@ -30,7 +30,7 @@ # - correct bmd estimate (point, extra, hybridExc) # - delta # - Meta analytic model (drmMMRE) - +library(drc) # Arguments and structure ------------------------------------------------- diff --git a/vignettes/.gitignore b/vignettes/.gitignore new file mode 100644 index 0000000..097b241 --- /dev/null +++ b/vignettes/.gitignore @@ -0,0 +1,2 @@ +*.html +*.R diff --git a/vignettes/bmd_Package.Rmd b/vignettes/bmd_Package.Rmd new file mode 100644 index 0000000..9e14681 --- /dev/null +++ b/vignettes/bmd_Package.Rmd @@ -0,0 +1,107 @@ +--- +title: "bmd Package" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{bmd_Package} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(drcData) +library(drc) +library(bmd) +``` + + +## Package Summary + +This R package focuses on Benchmark Dose (BMD) modeling, which is commonly used in toxicology and risk assessment to determine the dose of a substance that corresponds to a specific level of response or risk. The package provides a comprehensive range of functionalities. It supports various model types, confidence interval methods, and model averaging approaches. + +### Core Functionalities + +1. **Dose-Response Modeling**: + - Fits various dose-response models including logistic, log-normal, Weibull, and fractional polynomial models + - Supports continuous, binomial, Poisson, and negative binomial response types + - Handles both single and multiple curves/groups + +2. **BMD Estimation**: + - Calculates benchmark doses (BMDs) and their lower confidence limits (BMDLs) + - Implements multiple BMD definitions: excess, additional, relative, extra, added, hybrid excess, hybrid additional, and point + - Provides various background types: model-based, absolute, hybridSD, and hybridPercentile + +3. **Confidence Interval Methods**: + - Delta method + - Profile likelihood + - Bootstrap (parametric, nonparametric) + - Sandwich estimator + - Inverse regression + +4. **Model Averaging**: + - Implements model averaging for BMD estimation via `bmdMA()` + - Supports various weighting schemes: AIC, BIC, and stacking (cross-validation) + - Implements different averaging approaches: Kang, Buckland, curve, and bootstrap + +5. **Special Model Types**: + - Ordinal response models (`drcOrdinal`) + - Heterogeneous variance models (`drcHetVar`) + - Mixed models with random effects (`drcMMRE`) + +6. **Trend Testing**: + - Implements monotonicity tests (Jonckheere-Terpstra, Bartholomew) + - Provides trend tests (Williams, Shirley, Tukey) + +7. **Visualization**: + - Plot methods for BMD objects + - ggplot2-based plotting functions (`qplotDrc`, `qplotBmd`) + +## Usage of the Package + +The package follows a workflow typically seen in dose-response analysis: + +1. **Fit dose-response models** using functions like `drm()`, `drcOrdinal()`, `drcHetVar()`, or `drcMMRE()` +2. **Estimate BMDs** using `bmd()` or specialized functions like `bmdOrdinal()`, `bmdHetVar()` +3. **Apply model averaging** with `bmdMA()` if multiple models are considered +4. **Visualize results** using plot methods or specialized plotting functions +5. **Test for trends** using `trendTest()` or `monotonicityTest()` + +### Example usage: + +```{r} +# Fit dose-response model + +data("secalonic") +model <- drm(rootl ~ dose, data = secalonic, fct = LL.4()) +## model <- drm(response ~ dose, data = mydata, fct = LL.4()) + +# Calculate BMD +bmd_result <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative", interval = "profile") + +# Plot result +plot(bmd_result) +## note that ggplot2 style plot can be generated using qplot function +## qplotBmd(bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative", display = FALSE)) # display = FALSE hides output from bmd function +``` + +#### Fit multiple models for model averaging + +```{r} +# Fit multiple models for model averaging + +# Apply model averaging (if multiple models are fitted) +model1 <- model +model2 <- drm(rootl ~ dose, data = secalonic, fct = LN.3()) +model3 <- drm(rootl ~ dose, data = secalonic, fct = LN.4()) +model_list <- list(model1, model2, model3) +bmd_ma <- bmdMA(model_list, modelWeights = "AIC", backgType = "modelBased", bmr = 0.1, + def = "relative" , type = "bootstrap") +print(bmd_ma) +``` + From ec20a9440f8c3e787dabe5e50ea69d3ca5d1a142 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Thu, 3 Jul 2025 19:01:15 +0200 Subject: [PATCH 02/17] updated NAMESPACE --- NAMESPACE | 54 ++++++++++++++++++++++++++++++++++++++++++++ R/BCa.R | 2 +- R/PAV.R | 1 + R/bmd-package.R | 18 +++++++++++++++ R/bmd.R | 1 + R/bmdBoot.R | 2 +- R/bmdHetVar.R | 2 +- R/bmdHetVarMA.R | 2 +- R/bmdIso.R | 2 +- R/bmdIsoBoot.R | 1 + R/bmdMA.R | 1 + R/bmdMACurve.R | 2 +- R/bootDataGen.R | 1 - R/drmOrdinal.R | 2 +- R/monotonicityTest.R | 1 + R/plot.bmd.R | 1 + R/qplotBmd.R | 2 +- R/qplotDrc.R | 2 +- R/trendTest.R | 1 + man/bmd-package.Rd | 10 ++++++++ man/bmdBoot.Rd | 1 - man/bmdHetVar.Rd | 1 - man/bmdHetVarMA.Rd | 1 - man/bmdIso.Rd | 1 - man/drmOrdinal.Rd | 1 - man/qplotBmd.Rd | 1 - man/qplotDrc.Rd | 1 - 27 files changed, 98 insertions(+), 17 deletions(-) create mode 100644 R/bmd-package.R create mode 100644 man/bmd-package.Rd diff --git a/NAMESPACE b/NAMESPACE index f785f83..5661794 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -7,6 +7,7 @@ S3method(BIC,drcOrdinal) S3method(coef,drcHetVar) S3method(logLik,drcHetVar) S3method(logLik,drcOrdinal) +S3method(plot,bmd) S3method(plot,drcHetVar) S3method(plot,drcOrdinal) S3method(print,bmdOrdinal) @@ -14,3 +15,56 @@ S3method(print,drcHetVar) S3method(print,drcMMRE) S3method(print,drcOrdinal) S3method(vcov,drcMMRE) +export(BCa) +export(PAV) +export(bmd) +export(bmdBoot) +export(bmdHetVar) +export(bmdHetVarMA) +export(bmdIso) +export(bmdIsoBoot) +export(bmdMA) +export(bmdMACurve) +export(drmOrdinal) +export(monotonicityTest) +export(qplotBmd) +export(qplotDrc) +export(trendTest) +import(dplyr) +import(drc) +import(ggplot2) +importFrom(graphics,lines) +importFrom(stats,AIC) +importFrom(stats,BIC) +importFrom(stats,aggregate) +importFrom(stats,approx) +importFrom(stats,as.formula) +importFrom(stats,coef) +importFrom(stats,complete.cases) +importFrom(stats,confint) +importFrom(stats,constrOptim) +importFrom(stats,df.residual) +importFrom(stats,dnorm) +importFrom(stats,fitted) +importFrom(stats,lm) +importFrom(stats,logLik) +importFrom(stats,model.frame) +importFrom(stats,model.matrix) +importFrom(stats,optim) +importFrom(stats,pnorm) +importFrom(stats,predict) +importFrom(stats,qchisq) +importFrom(stats,qnorm) +importFrom(stats,qt) +importFrom(stats,quantile) +importFrom(stats,rbinom) +importFrom(stats,resid) +importFrom(stats,residuals) +importFrom(stats,rnorm) +importFrom(stats,sd) +importFrom(stats,uniroot) +importFrom(stats,update) +importFrom(stats,var) +importFrom(stats,vcov) +importFrom(utils,setTxtProgressBar) +importFrom(utils,txtProgressBar) diff --git a/R/BCa.R b/R/BCa.R index ce6e380..c069272 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,7 +1,7 @@ #' Help funtion to bmdBoot #' #' -#' +#' @export BCa <- function(obs, data, bootSample, bootjack, level){ R <- length(bootSample) b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) diff --git a/R/PAV.R b/R/PAV.R index 4e30bae..0020dbf 100644 --- a/R/PAV.R +++ b/R/PAV.R @@ -20,6 +20,7 @@ #' inference: order, inequality, and shape constraints. New York: John Wiley & #' Sons. #' @keywords nonparametric isotonic regression +#' @export PAV<-function(formula,data,type){ object <- formula if( identical(type,"binomial")){ diff --git a/R/bmd-package.R b/R/bmd-package.R new file mode 100644 index 0000000..7c7c46a --- /dev/null +++ b/R/bmd-package.R @@ -0,0 +1,18 @@ +#' BMD: Benchmark Dose Modeling +#' +#' A package for benchmark dose modeling in toxicology and risk assessment +#' +#' @import drc +#' @import ggplot2 +#' @import dplyr +#' @importFrom graphics lines +#' @importFrom stats aggregate approx as.formula coef complete.cases +#' @importFrom stats confint constrOptim df.residual dnorm fitted +#' @importFrom stats lm model.frame model.matrix optim pnorm predict +#' @importFrom stats qchisq qnorm qt quantile rbinom resid residuals +#' @importFrom stats rnorm sd uniroot update var vcov AIC BIC logLik +#' @importFrom utils setTxtProgressBar txtProgressBar +#' +#' @name bmd-package +#' @aliases bmd +"_PACKAGE" \ No newline at end of file diff --git a/R/bmd.R b/R/bmd.R index e031311..24805f1 100644 --- a/R/bmd.R +++ b/R/bmd.R @@ -170,6 +170,7 @@ #' bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE) #' #' +#' @export bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg=NA, controlSD=NA, def = c("excess", "additional", diff --git a/R/bmdBoot.R b/R/bmdBoot.R index e97fdd7..dc4568b 100644 --- a/R/bmdBoot.R +++ b/R/bmdBoot.R @@ -125,7 +125,7 @@ #' ## BMD from the same definitions but using parametric bootstrap #' bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50) #' -#' +#' @export bmdBoot <- function(object, bmr, R=1000, bootType="nonparametric", bmdType = "orig", backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg=NA, diff --git a/R/bmdHetVar.R b/R/bmdHetVar.R index c3dd32c..5b75288 100644 --- a/R/bmdHetVar.R +++ b/R/bmdHetVar.R @@ -112,7 +112,7 @@ #' bmdHetVar(GiantKelp.LL.4.hetVarLogSq, bmr = 0.1, backgType = "hybridSD", backg = 1, #' def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) #' -#' +#' @export bmdHetVar <- function(object, bmr, backgType = c("absolute", "hybridSD", "hybridPercentile"), backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), R = 1000, level = 0.95, bootType = "nonparametric", progressInfo = TRUE, display = TRUE){ ### Assertions ### # object diff --git a/R/bmdHetVarMA.R b/R/bmdHetVarMA.R index 8a6da69..22a1fa0 100644 --- a/R/bmdHetVarMA.R +++ b/R/bmdHetVarMA.R @@ -111,7 +111,7 @@ #' backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, #' display = TRUE) #' -#' +#' @export bmdHetVarMA <- function(modelList, modelWeights = c("AIC", "BIC"), bmr, backgType = c("absolute", "hybridSD", "hybridPercentile"), backg = NA, def = c("hybridExc", "hybridAdd"), interval = c("boot", "none"), R = 1000, level = 0.95, progressInfo = TRUE, display = TRUE){ ### Assertions ### # modelList diff --git a/R/bmdIso.R b/R/bmdIso.R index e084b57..ee855e9 100644 --- a/R/bmdIso.R +++ b/R/bmdIso.R @@ -121,7 +121,7 @@ #' bmr=0.05, #' backgType = "modelBased", #' def = "relative") -#' +#' @export bmdIso <- function(formula, data, type, bmr, p0, backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), backg=NA, def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point"), display=FALSE){ object <- formula PAV.p <- PAV(object, data, type) diff --git a/R/bmdIsoBoot.R b/R/bmdIsoBoot.R index 7c40973..8b33f7e 100644 --- a/R/bmdIsoBoot.R +++ b/R/bmdIsoBoot.R @@ -101,6 +101,7 @@ #' benchmark dose estimation with continuous dose-response data. Scandinavian #' Journal of Statistics, 42, 713-731 #' @keywords nonparametric isotonic regression bootstrap +#' @export #' @examples #' #' ## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014) diff --git a/R/bmdMA.R b/R/bmdMA.R index beddc13..5c7a45f 100644 --- a/R/bmdMA.R +++ b/R/bmdMA.R @@ -162,6 +162,7 @@ #' and Model Space Selection in Frequentist Model Averaging for Benchmark Dose #' Estimation, \emph{Environmetrics} \bold{36(2)}, e70002. #' @keywords model averaging nonlinear bootstrap +#' @export #' @examples #' #' library(drc) diff --git a/R/bmdMACurve.R b/R/bmdMACurve.R index ea372e3..3bda697 100644 --- a/R/bmdMACurve.R +++ b/R/bmdMACurve.R @@ -1,7 +1,7 @@ #' Help funtion to bmdMA #' #' -#' +#' @export bmdMACurve<-function(modelList,modelWeights,bmrScaled0, searchInterval="dataBased"){ nCurves <- ncol(modelList[[1]]$parmMat) diff --git a/R/bootDataGen.R b/R/bootDataGen.R index a16581b..9489d55 100644 --- a/R/bootDataGen.R +++ b/R/bootDataGen.R @@ -1,7 +1,6 @@ #' Help funtion to bmdBoot #' #' -#' bootDataGen <- function(object, R=1000, bootType="nonparametric",aggregated=TRUE){ if(bootType=="nonparametric"){ if(object$type=="binomial"){ diff --git a/R/drmOrdinal.R b/R/drmOrdinal.R index 1b1b946..71540a7 100644 --- a/R/drmOrdinal.R +++ b/R/drmOrdinal.R @@ -43,7 +43,7 @@ #' #' plot(guthionS.LL, xlim = c(15,55)) # uses ggplot #' -#' +#' @export drmOrdinal <- function(levels, dose, weights, blocks, data, fct, p.epsilon = 1e-16){ if(missing(blocks)){ blocks = NULL diff --git a/R/monotonicityTest.R b/R/monotonicityTest.R index 0d9891b..9b69989 100644 --- a/R/monotonicityTest.R +++ b/R/monotonicityTest.R @@ -45,6 +45,7 @@ #' result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew") #' print(result) #' +#' @export monotonicityTest <- function(x, y, data, test = c("jonckheere", "bartholomew"), level = 0.05, ...){ # , "drc", "quad" if(!missing(data)){ x <- data[[x]] diff --git a/R/plot.bmd.R b/R/plot.bmd.R index b93962a..69b1d86 100644 --- a/R/plot.bmd.R +++ b/R/plot.bmd.R @@ -16,6 +16,7 @@ #' @return Creates a plot. No value returned. #' @author Jens Riis Baalkilde. #' @keywords ggplot +#' @export #' @examples #' #' library(drc) diff --git a/R/qplotBmd.R b/R/qplotBmd.R index 1ea0cc8..270467b 100644 --- a/R/qplotBmd.R +++ b/R/qplotBmd.R @@ -37,7 +37,7 @@ #' qplotBmd(bmd0, interval = "twosided", add = FALSE) #' #' -#' +#' @export qplotBmd <- function(x, ..., interval = c("BMDL", "twosided", "none"), col = FALSE, add = FALSE){ object <- x diff --git a/R/qplotDrc.R b/R/qplotDrc.R index 494c131..396e2ed 100644 --- a/R/qplotDrc.R +++ b/R/qplotDrc.R @@ -119,7 +119,7 @@ #' scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1))) #' #' -#' +#' @export qplotDrc <- function(x, add = FALSE, level = NULL, type = c("average", "all", "bars", "none", "obs", "confidence"), gridsize = 250, xtrans = "pseudo_log", xlab, xlim, ytrans = NULL, ylab, ylim, col = FALSE, diff --git a/R/trendTest.R b/R/trendTest.R index 5903093..86990ae 100644 --- a/R/trendTest.R +++ b/R/trendTest.R @@ -52,6 +52,7 @@ #' result <- trendTest("x", "y", data = data, test = "shirley") #' print(result) #' +#' @export trendTest <- function(x, y, data, test = c("william", "shirley", "tukey"), level = 0.05){ if(!missing(data)){ x <- data[[x]] diff --git a/man/bmd-package.Rd b/man/bmd-package.Rd new file mode 100644 index 0000000..ca769fc --- /dev/null +++ b/man/bmd-package.Rd @@ -0,0 +1,10 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/bmd-package.R +\docType{package} +\name{bmd-package} +\alias{bmd-package} +\alias{bmd} +\title{BMD: Benchmark Dose Modeling} +\description{ +A package for benchmark dose modeling in toxicology and risk assessment +} diff --git a/man/bmdBoot.Rd b/man/bmdBoot.Rd index d322185..a55df1f 100644 --- a/man/bmdBoot.Rd +++ b/man/bmdBoot.Rd @@ -162,7 +162,6 @@ bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50) ## BMD from the same definitions but using parametric bootstrap bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50) - } \author{ Signe M. Jensen diff --git a/man/bmdHetVar.Rd b/man/bmdHetVar.Rd index a2b207e..e5b50b3 100644 --- a/man/bmdHetVar.Rd +++ b/man/bmdHetVar.Rd @@ -144,7 +144,6 @@ plot(GiantKelp.LL.4.hetVarLogSq) bmdHetVar(GiantKelp.LL.4.hetVarLogSq, bmr = 0.1, backgType = "hybridSD", backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) - } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/bmdHetVarMA.Rd b/man/bmdHetVarMA.Rd index ed9fd05..b53eacd 100644 --- a/man/bmdHetVarMA.Rd +++ b/man/bmdHetVarMA.Rd @@ -143,7 +143,6 @@ bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) - } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/bmdIso.Rd b/man/bmdIso.Rd index cbb311a..8bbf8c2 100644 --- a/man/bmdIso.Rd +++ b/man/bmdIso.Rd @@ -142,7 +142,6 @@ bmdIso(rootl ~ conc, bmr=0.05, backgType = "modelBased", def = "relative") - } \references{ Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. diff --git a/man/drmOrdinal.Rd b/man/drmOrdinal.Rd index d892340..5339e71 100644 --- a/man/drmOrdinal.Rd +++ b/man/drmOrdinal.Rd @@ -58,7 +58,6 @@ guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "to plot(guthionS.LL, xlim = c(15,55)) # uses ggplot - } \references{ # ADD REFERENCES diff --git a/man/qplotBmd.Rd b/man/qplotBmd.Rd index b66880b..24e8a24 100644 --- a/man/qplotBmd.Rd +++ b/man/qplotBmd.Rd @@ -57,7 +57,6 @@ qplotDrc(model,type="confidence") + qplotBmd(bmd0, interval = "twosided", add = FALSE) - } \author{ Jens Riis Baalkilde. diff --git a/man/qplotDrc.Rd b/man/qplotDrc.Rd index 09e0feb..9602f51 100644 --- a/man/qplotDrc.Rd +++ b/man/qplotDrc.Rd @@ -154,7 +154,6 @@ qplotDrc(spinach.m1, col = TRUE, type = "confidence") + scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1))) - } \references{ Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., From cfec8053a4daf0b381016da88ddb7304d26fc673 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Fri, 4 Jul 2025 11:03:19 +0200 Subject: [PATCH 03/17] added vignettes skeleton --- .gitignore | 1 + NAMESPACE | 6 + R/MACurve.R | 2 +- R/bmdOrdinal.R | 1 + R/bmdOrdinalMA.R | 2 +- R/drmHetVar.R | 2 +- R/drmMMRE.R | 2 +- R/getStackingWeights.R | 2 +- man/MACurve.Rd | 1 - man/bmdOrdinalMA.Rd | 1 - man/drmHetVar.Rd | 1 - man/drmMMRE.Rd | 1 - man/getStackingWeights.Rd | 1 - vignettes/basic-bmd-functions.Rmd | 120 ++++++++++++ vignettes/model-averaging.Rmd | 191 +++++++++++++++++++ vignettes/specialized-models.Rmd | 306 ++++++++++++++++++++++++++++++ vignettes/statistical-tests.Rmd | 82 ++++++++ vignettes/utilities.Rmd | 21 ++ vignettes/visualization.Rmd | 21 ++ 19 files changed, 754 insertions(+), 10 deletions(-) create mode 100644 vignettes/basic-bmd-functions.Rmd create mode 100644 vignettes/model-averaging.Rmd create mode 100644 vignettes/specialized-models.Rmd create mode 100644 vignettes/statistical-tests.Rmd create mode 100644 vignettes/utilities.Rmd create mode 100644 vignettes/visualization.Rmd diff --git a/.gitignore b/.gitignore index 0b05f50..f10dacb 100644 --- a/.gitignore +++ b/.gitignore @@ -5,3 +5,4 @@ cache/ bmd.Rproj inst/doc +example_extracts/ \ No newline at end of file diff --git a/NAMESPACE b/NAMESPACE index 5661794..fbb6e16 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -16,6 +16,7 @@ S3method(print,drcMMRE) S3method(print,drcOrdinal) S3method(vcov,drcMMRE) export(BCa) +export(MACurve) export(PAV) export(bmd) export(bmdBoot) @@ -25,7 +26,12 @@ export(bmdIso) export(bmdIsoBoot) export(bmdMA) export(bmdMACurve) +export(bmdOrdinal) +export(bmdOrdinalMA) +export(drmHetVar) +export(drmMMRE) export(drmOrdinal) +export(getStackingWeights) export(monotonicityTest) export(qplotBmd) export(qplotDrc) diff --git a/R/MACurve.R b/R/MACurve.R index b3d7244..f71b383 100644 --- a/R/MACurve.R +++ b/R/MACurve.R @@ -57,7 +57,7 @@ #' modelWeights = "AIC") #' }) #' -#' +#' @export MACurve <- function(x, modelList, modelWeights, stackingSeed = 1, stackingSplits = 2){ diff --git a/R/bmdOrdinal.R b/R/bmdOrdinal.R index d48bf70..0a379b1 100644 --- a/R/bmdOrdinal.R +++ b/R/bmdOrdinal.R @@ -109,6 +109,7 @@ #' weights = "total", dose = "dose", data = guthionS, fct = LL.2()) #' bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50) #' +#' @export bmdOrdinal <- function(object, bmr, backgType = c("modelBased", "absolute"), backg = NA, def=c("excess", "additional", "point"), interval = c("delta", "sandwich", "profile", "bootstrap"), level = 0.95, R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical"), display = TRUE, progressInfo = TRUE){ interval <- match.arg(interval) diff --git a/R/bmdOrdinalMA.R b/R/bmdOrdinalMA.R index 0e5a4e1..5c277bb 100644 --- a/R/bmdOrdinalMA.R +++ b/R/bmdOrdinalMA.R @@ -103,7 +103,7 @@ #' bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), #' modelWeights = "AIC", bmr = 0.1, #' backgType = "modelBased", def = "excess", type = "bootstrap", R = 50) -#' +#' @export bmdOrdinalMA <- function(modelList, modelWeights = c("AIC", "BIC"), bmr, backgType = c("modelBased", "absolute"), backg = NA, def = c("excess", "additional", "point"), type = c("bootstrap", "Kang"), level = 0.95, R = 500, bootType = c("nonparametric", "parametric"), display = TRUE, progressInfo = TRUE){ # assertions if(!all(sapply(modelList, function(object) inherits(object, "drcOrdinal")))){ diff --git a/R/drmHetVar.R b/R/drmHetVar.R index 23602a5..28605a7 100644 --- a/R/drmHetVar.R +++ b/R/drmHetVar.R @@ -69,7 +69,7 @@ #' #' #' -#' +#' @export drmHetVar <- function(formula, var.formula, data, fct, curveStart = NULL) { call <- match.call() diff --git a/R/drmMMRE.R b/R/drmMMRE.R index 0c87143..4e19f5d 100644 --- a/R/drmMMRE.R +++ b/R/drmMMRE.R @@ -54,7 +54,7 @@ #' modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4()) #' bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative") #' -#' +#' @export drmMMRE <- function(formula, exp_id, data, fct, type = c("continuous", "binomial")){ call_expr <- match.call() diff --git a/R/getStackingWeights.R b/R/getStackingWeights.R index c3e6b0d..41eb0f3 100644 --- a/R/getStackingWeights.R +++ b/R/getStackingWeights.R @@ -239,7 +239,7 @@ getDataSplits <- function(object, nSplits){ #' aconiazide.W1.3, aconiazide.W2.3), #' nSplits = 7) #' -#' +#' @export getStackingWeights <- function(modelList, nSplits = 2){ if(!requireNamespace("CVXR")){ stop('package "CVXR" must be installed to estimate stacking weights') diff --git a/man/MACurve.Rd b/man/MACurve.Rd index 6766f25..38621d3 100644 --- a/man/MACurve.Rd +++ b/man/MACurve.Rd @@ -71,7 +71,6 @@ qplotDrc(aconiazide.LL.3, type = "obs") + modelWeights = "AIC") }) - } \author{ Jens Riis Baalkilde diff --git a/man/bmdOrdinalMA.Rd b/man/bmdOrdinalMA.Rd index 9403d2d..4cec746 100644 --- a/man/bmdOrdinalMA.Rd +++ b/man/bmdOrdinalMA.Rd @@ -131,7 +131,6 @@ bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), modelWeights = "AIC", bmr = 0.1, backgType = "modelBased", def = "excess", type = "bootstrap", R = 50) - } \references{ Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) diff --git a/man/drmHetVar.Rd b/man/drmHetVar.Rd index d1a42b3..364446e 100644 --- a/man/drmHetVar.Rd +++ b/man/drmHetVar.Rd @@ -83,7 +83,6 @@ plot(GiantKelp.LL.4.hetVarLogSq) - } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/drmMMRE.Rd b/man/drmMMRE.Rd index 13ed4eb..4f7875f 100644 --- a/man/drmMMRE.Rd +++ b/man/drmMMRE.Rd @@ -68,7 +68,6 @@ data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2), modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4()) bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative") - } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/getStackingWeights.Rd b/man/getStackingWeights.Rd index c7ee814..2ee0ade 100644 --- a/man/getStackingWeights.Rd +++ b/man/getStackingWeights.Rd @@ -46,7 +46,6 @@ getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, aconiazide.W1.3, aconiazide.W2.3), nSplits = 7) - } \author{ Jens Riis Baalkilde diff --git a/vignettes/basic-bmd-functions.Rmd b/vignettes/basic-bmd-functions.Rmd new file mode 100644 index 0000000..cebb5aa --- /dev/null +++ b/vignettes/basic-bmd-functions.Rmd @@ -0,0 +1,120 @@ +--- +title: "basic-bmd-functions" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{basic-bmd-functions} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + +# Basic BMD Functions Examples + +This vignette demonstrates the usage of functions related to +basic bmd functions +. +```r + + + + +library(drc) + +library(drcData) + + + +## Fitting log-logistic two-parameter model to binomial data + +deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial") + + + +## BMD for 5% additional risk with estimated background risk + +bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional") + + + +## BMD for 10% additional risk with 2% background risk + +bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional") + + + +## BMD for 5% excess risk and background 0 + +bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess") + + + +## Dose resulting in 12% risk + +bmd(deguelin.m1, 0.12, def = "point") + + + +## Benchmark doses for a continuous response + +ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) + + + +## BMD as the dose resulting in a 5% change relative to the mean background level + +bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE) + + + +## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk + +bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE) + + +``` + + + + +## Bootstrapping Methods + +```r + +## Data on root length in ryegrass after exposure to ferulic acid + +require(drc) + +require(drcData) + +data(ryegrass) + + + +ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) + + + +## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk + +bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50) + + + +## BMD from the same definitions but using parametric bootstrap + +bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50) + + + +``` + diff --git a/vignettes/model-averaging.Rmd b/vignettes/model-averaging.Rmd new file mode 100644 index 0000000..ba34e26 --- /dev/null +++ b/vignettes/model-averaging.Rmd @@ -0,0 +1,191 @@ +--- +title: "model-averaging" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{model-averaging} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + + +## Example for `bmdMA` function + +```r + + + + +library(drc) + +library(drcData) + + + +## Fitting 4 different two-parameter models to binomial data + +deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial") + +deguelin.m2 <- drm(r/n~dose, weights=n, data=deguelin, fct=W1.2(), type="binomial") + +deguelin.m3 <- drm(r/n~dose, weights=n, data=deguelin, fct=W2.2(), type="binomial") + +deguelin.m4 <- drm(r/n~dose, weights=n, data=deguelin, fct=LN.2(), type="binomial") + + + + + +## Model averaged BMD for 5% additional risk with estimated background risk + +## and BMDL based on Buckland et al. + +bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, + + backgType = "modelBased", def = "additional", + + type = "Buckland") + + + +## Model averaged BMD for 5% additional risk with estimated background risk + +## and BMDL based on an average of the model curves + +bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, + + backgType = "modelBased", def = "additional", + + type = "curve", bootstrapType = "parametric", bootInterval = "percentile", R=50) + + + + + +## Fitting 4 different two-parameter models to binomial data + +ryegrass.m1<-drm(rootl~conc, data=ryegrass, fct=LL.4()) + +ryegrass.m2<-drm(rootl~conc, data=ryegrass, fct=W1.4()) + +ryegrass.m3<-drm(rootl~conc, data=ryegrass, fct=W2.4()) + +ryegrass.m4<-drm(rootl~conc, data=ryegrass, fct=LN.4()) + + + +## Model-averaged BMD and bootstrap BMDL for bmr=5% and using the hybrid approach + +## to estimate the background risk. + +bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="AIC", bmr=0.05, + + backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", + + bootstrapType = "nonparametric", bootInterval = "percentile", R = 50) + + + + + +## Model-averaged BMD using the Stacking Weights + +bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="Stack", bmr=0.05, + + backgType = "hybridSD", def = "hybridAdd", type = "bootstrap", + + bootstrapType = "nonparametric", bootInterval = "percentile", R = 50) + + + + + +``` + +## bmd MA curve + +```r + + + + +library(bmd) + +library(drc) + +library(drcData) + +library(ggplot2) + + + +# fit models to aconiazide data + +aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3()) + +aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3()) + +aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3()) + +aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3()) + + + +# plot the MA curve + +plot(aconiazide.LL.3, type = "obs") + +curve( + + MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,aconiazide.W1.3, aconiazide.W2.3), + + modelWeights = "AIC"), + + add = TRUE) + + + +# or plot using ggplot2 + +qplotDrc(aconiazide.LL.3, type = "obs") + + + geom_function(fun = function(x){ + + MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3, + + aconiazide.W1.3, aconiazide.W2.3), + + modelWeights = "AIC") + + ) + + + +``` + +## get stacking weights + +```r +getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, + + aconiazide.W1.3, aconiazide.W2.3)) + +getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3, + + aconiazide.W1.3, aconiazide.W2.3), + + nSplits = 7) + + + +``` \ No newline at end of file diff --git a/vignettes/specialized-models.Rmd b/vignettes/specialized-models.Rmd new file mode 100644 index 0000000..f514071 --- /dev/null +++ b/vignettes/specialized-models.Rmd @@ -0,0 +1,306 @@ +--- +title: "specialized-models" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{specialized-models} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + + +## Oridnal + +```{r} + + + + +library(drc) + +library(drcData) + +data(guthion) + +guthionS <- subset(guthion, trt == "S") + + + +guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "total", + + dose = "dose", data = guthionS, fct = LL.2()) + + + +plot(guthionS.LL, xlim = c(15,55)) # uses ggplot + + +bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50) + + +``` + + +### MA + +```r + + + + +library(drc) + +library(drcData) + +data(guthion) + + + +guthionS <- subset(guthion, trt == "S") + + + +guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), + + weights = "total", dose = "dose", data = guthionS, fct = LL.2()) + +guthionS.LN <- drmOrdinal(levels = c("alive", "moribund", "dead"), + + weights = "total", dose = "dose", data = guthionS, fct = LN.2()) + +guthionS.W1 <- drmOrdinal(levels = c("alive", "moribund", "dead"), + + weights = "total", dose = "dose", data = guthionS, fct = W1.2()) + +guthionS.W2 <- drmOrdinal(levels = c("alive", "moribund", "dead"), + + weights = "total", dose = "dose", data = guthionS, fct = W2.2()) + + + +bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), + + modelWeights = "AIC", bmr = 0.1, + + backgType = "modelBased", def = "excess", type = "Kang") + +bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), + + modelWeights = "AIC", bmr = 0.1, + + backgType = "modelBased", def = "excess", type = "bootstrap", R = 50) + +``` + + + +## Heterogenous Variance Models + + +```r + + + + +library(drc) + +library(drcData) + +library(bmd) + +# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT. + + + +# ryegrass data + +set.seed(123) + +ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), + + data = ryegrass, fct = LL.4()) + +plot(ryegrass.LL.4.hetVar) + +bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, + + def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) + +bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, + + def = "hybridExc", R = 50, level = 0.95, + + bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap + + + +# barley data + +set.seed(123) + +barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4()) + +plot(barley.LL.4.hetVar) + + + +# GiantKelp data + +set.seed(123) + +GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), + + data = GiantKelp, fct = LL.4()) + +plot(GiantKelp.LL.4.hetVarSq) + + + +GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), + + data = GiantKelp, fct = LL.4()) + +plot(GiantKelp.LL.4.hetVarLogSq) + + + + + + + +``` + + + +```{r} + + + + +library(drc) + +library(drcData) + +library(bmd) + +# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT. + + + +# ryegrass data + +set.seed(123) + +ryegrass.hetVar.list <- list( + + drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LL.4()), + + drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LN.4()), + + drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W1.4()), + + drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W2.4())) + +bmdHetVarMA(ryegrass.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridPercentile", + + backg = 0.1, def = "hybridExc", R = 100, level = 0.95) + +bmdHetVarMA(ryegrass.hetVar.list, modelWeights = c(0.4, 0.2, 0.1, 0.3), bmr = 0.1, + + backgType = "hybridPercentile", backg = 0.1, + + def = "hybridExc", R = 50, level = 0.95) # user-defined weights + + + +# barley data + +set.seed(123) + +barley.hetVar.list <- list(drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), + + data = barley, fct = LL.4()), + + drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), + + data = barley, fct = W2.4())) + +bmdHetVarMA(barley.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", backg = 2, + + def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE) + + + +# GiantKelp data + +set.seed(123) + +GiantKelp.hetVar.list <- list( + + drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), data = GiantKelp, fct = LL.4()), + + drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), data = GiantKelp, fct = LL.4())) + +bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", + + backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, + + display = TRUE) + + + +``` + +## Mixed Models + +```{r} + + + + + +library(drc) + +library(drcData) + +library(metafor) + +library(bmd) + + + +set.seed(1) + +data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2), + + y = rep(drcData::ryegrass$rootl, 2) + + + c(rnorm(n = nrow(drcData::ryegrass), mean = 2, sd = 0.5), + + rnorm(n = nrow(drcData::ryegrass), mean = 2.7, sd = 0.7)), + + EXP_ID = rep(as.character(1:2), each = nrow(drcData::ryegrass))) + + + +modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4()) + +bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative") + + + +``` + + + + diff --git a/vignettes/statistical-tests.Rmd b/vignettes/statistical-tests.Rmd new file mode 100644 index 0000000..31f1f73 --- /dev/null +++ b/vignettes/statistical-tests.Rmd @@ -0,0 +1,82 @@ +--- +title: "statistical-tests" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{statistical-tests} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + +# Statistical Tests Examples + +This vignette demonstrates the usage of functions related to +statistical tests. + +## Monotonicity Test + +```{r} + + + + +# Example with custom data + +x <- c(1, 2, 3, 4, 5) + +y <- c(2, 4, 6, 8, 10) + +result <- monotonicityTest(x, y, test = "jonckheere") + +print(result) + + + +data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) + +result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew") + +print(result) + + + + +``` + + + +## Trend Test + +```{r} + +# Example with custom data + +x <- c(1, 2, 3, 4, 5) + +y <- c(2, 4, 6, 8, 10) + +result <- trendTest(x, y, test = "tukey") + +print(result) + + + +# Example with a data frame + +data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6)) + +result <- trendTest("x", "y", data = data, test = "shirley") + +print(result) +``` + diff --git a/vignettes/utilities.Rmd b/vignettes/utilities.Rmd new file mode 100644 index 0000000..f32e985 --- /dev/null +++ b/vignettes/utilities.Rmd @@ -0,0 +1,21 @@ +--- +title: "utilities" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{utilities} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + +Utility functions included in the package `bmd` are: "PAV", "expandBinomial", "bootDataGen", "BCa" \ No newline at end of file diff --git a/vignettes/visualization.Rmd b/vignettes/visualization.Rmd new file mode 100644 index 0000000..a371e53 --- /dev/null +++ b/vignettes/visualization.Rmd @@ -0,0 +1,21 @@ +--- +title: "visualization" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{visualization} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(bmd) +``` + +Visualization functions included in the `bmd` package are: "qplotDrc", "qplotBmd", "plot.bmd". 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+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) {year}  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    {project}  Copyright (C) {year}  {fullname}
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+
+ +
+ + + +
+ + + +
+

Developed by Signe M. Jensen.

+
+ +
+

Site built with pkgdown 2.1.0.

+
+ +
+ + + + + + + + diff --git a/docs/articles/basic-bmd-functions.html b/docs/articles/basic-bmd-functions.html new file mode 100644 index 0000000..f6a3931 --- /dev/null +++ b/docs/articles/basic-bmd-functions.html @@ -0,0 +1,221 @@ + + + + + + + +basic-bmd-functions • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

basic-bmd-functions

+ + + + + +
+ + + +
+library(bmd)
+
+

Basic BMD Functions Examples +

+

This vignette demonstrates the usage of functions related to basic +bmd functions .

+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+
+
+## Fitting log-logistic two-parameter model to binomial data
+
+deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial")
+
+
+
+## BMD for 5% additional risk with estimated background risk
+
+bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional")
+
+
+
+## BMD for 10% additional risk with 2% background risk
+
+bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional")
+
+
+
+## BMD for 5% excess risk and background 0
+
+bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess")
+
+
+
+## Dose resulting in 12% risk
+
+bmd(deguelin.m1, 0.12, def = "point")
+
+
+
+## Benchmark doses for a continuous response
+
+ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+
+
+
+## BMD as the dose resulting in a 5% change relative to the mean background level
+
+bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE)
+
+
+
+## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk
+
+bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE)
+
+

Bootstrapping Methods +

+
+
+## Data on root length in ryegrass after exposure to ferulic acid
+
+require(drc)
+
+require(drcData)
+
+data(ryegrass)
+
+
+
+ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+
+
+
+## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk
+
+bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50)
+
+
+
+## BMD from the same definitions but using parametric bootstrap
+
+bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50)
+
+
+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
+ + + + + + + + diff --git a/docs/articles/bmd_Package.html b/docs/articles/bmd_Package.html new file mode 100644 index 0000000..4503bbc --- /dev/null +++ b/docs/articles/bmd_Package.html @@ -0,0 +1,317 @@ + + + + + + + +bmd Package • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

bmd Package

+ + + + + +
+ + + +
+library(drcData)
+library(drc)
+#> Warning: package 'drc' was built under R version 4.4.2
+#> Loading required package: MASS
+#> 
+#> 'drc' has been loaded.
+#> Please cite R and 'drc' if used for a publication,
+#> for references type 'citation()' and 'citation('drc')'.
+#> 
+#> Attaching package: 'drc'
+#> The following objects are masked from 'package:drcData':
+#> 
+#>     auxins, nasturtium
+#> The following objects are masked from 'package:stats':
+#> 
+#>     gaussian, getInitial
+library(bmd)
+
+

Package Summary +

+

This R package focuses on Benchmark Dose (BMD) modeling, which is +commonly used in toxicology and risk assessment to determine the dose of +a substance that corresponds to a specific level of response or risk. +The package provides a comprehensive range of functionalities. It +supports various model types, confidence interval methods, and model +averaging approaches.

+
+

Core Functionalities +

+
    +
  1. +Dose-Response Modeling: +
      +
    • Fits various dose-response models including logistic, log-normal, +Weibull, and fractional polynomial models
      • +
    • Supports continuous, binomial, Poisson, and negative binomial +response types
      • +
    • Handles both single and multiple curves/groups
      • +
    +
    2. +
  2. +BMD Estimation: +
      +
    • Calculates benchmark doses (BMDs) and their lower confidence limits +(BMDLs)
      • +
    • Implements multiple BMD definitions: excess, additional, relative, +extra, added, hybrid excess, hybrid additional, and point
      • +
    • Provides various background types: model-based, absolute, hybridSD, +and hybridPercentile
      • +
    +
    3. +
  3. +Confidence Interval Methods: +
      +
    • Delta method
      • +
    • Profile likelihood
      • +
    • Bootstrap (parametric, nonparametric)
      • +
    • Sandwich estimator
      • +
    • Inverse regression
      • +
    +
    4. +
  4. +Model Averaging: +
      +
    • Implements model averaging for BMD estimation via +bmdMA() +
      • +
    • Supports various weighting schemes: AIC, BIC, and stacking +(cross-validation)
      • +
    • Implements different averaging approaches: Kang, Buckland, curve, +and bootstrap
      • +
    +
    5. +
  5. +Special Model Types: +
      +
    • Ordinal response models (drcOrdinal)
      • +
    • Heterogeneous variance models (drcHetVar)
      • +
    • Mixed models with random effects (drcMMRE)
      • +
    +
    6. +
  6. +Trend Testing: +
      +
    • Implements monotonicity tests (Jonckheere-Terpstra, +Bartholomew)
      • +
    • Provides trend tests (Williams, Shirley, Tukey)
      • +
    +
    7. +
  7. +Visualization: +
      +
    • Plot methods for BMD objects
      • +
    • ggplot2-based plotting functions (qplotDrc, +qplotBmd)
      • +
    +
    8. +
+
+
+
+

Usage of the Package +

+

The package follows a workflow typically seen in dose-response +analysis:

+
    +
  1. +Fit dose-response models using functions like +drm(), drcOrdinal(), drcHetVar(), +or drcMMRE() +
    2. +
  2. +Estimate BMDs using bmd() or +specialized functions like bmdOrdinal(), +bmdHetVar() +
    3. +
  3. +Apply model averaging with bmdMA() if +multiple models are considered
    4. +
  4. +Visualize results using plot methods or specialized +plotting functions
    5. +
  5. +Test for trends using trendTest() or +monotonicityTest() +
    6. +
+
+

Example usage: +

+
+# Fit dose-response model
+
+data("secalonic")
+model <- drm(rootl ~ dose, data = secalonic, fct = LL.4())
+## model <- drm(response ~ dose, data = mydata, fct = LL.4())
+
+# Calculate BMD
+bmd_result <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative", interval = "profile")
+#>       BMD       BMDL
+#>  0.035362 0.02619523
+
+# Plot result
+plot(bmd_result)
+

+
+## note that ggplot2 style plot can be generated using qplot function
+## qplotBmd(bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative", display = FALSE)) # display = FALSE hides output from bmd function
+
+

Fit multiple models for model averaging +

+
+# Fit multiple models for model averaging
+
+# Apply model averaging (if multiple models are fitted)
+model1 <- model
+model2 <- drm(rootl ~ dose, data = secalonic, fct = LN.3())
+model3 <- drm(rootl ~ dose, data = secalonic, fct = LN.4())
+model_list <- list(model1, model2, model3)
+bmd_ma <- bmdMA(model_list, modelWeights = "AIC", backgType = "modelBased", bmr = 0.1, 
+                def =  "relative" , type = "bootstrap")
+#> Performing bootstrap
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+#>      BMD_MA    BMDL_MA
+#>  0.03492014 0.02809378
+print(bmd_ma)
+#> $Results
+#>      BMD_MA    BMDL_MA
+#>  0.03492014 0.02809378
+#> 
+#> $Boot.samples.used
+#> [1] 1000
+#> 
+#> $interval
+#>     BMDL_MA    BMDU_MA
+#>  0.02809378 0.03730574
+#> 
+#> $SE
+#>  SE
+#>  NA
+#> 
+#> $modelWeights
+#> [1] 0.3117292 0.4709065 0.2173643
+#> 
+#> attr(,"class")
+#> [1] "bmd"
+
+
+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
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+
+ + + +
+
+
+

Articles

+
+ +
+

All vignettes

+

+ +
basic-bmd-functions
+
+
bmd Package
+
+
model-averaging
+
+
specialized-models
+
+
statistical-tests
+
+
utilities
+
+
visualization
+
+
+
+
+ + +
+

Developed by Signe M. Jensen.

+
+ +
+

Site built with pkgdown 2.1.0.

+
+ +
+ + + + + + + + diff --git a/docs/articles/model-averaging.html b/docs/articles/model-averaging.html new file mode 100644 index 0000000..97c28ff --- /dev/null +++ b/docs/articles/model-averaging.html @@ -0,0 +1,294 @@ + + + + + + + +model-averaging • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

model-averaging

+ + + + + +
+ + + +
+library(bmd)
+
+

Example for bmdMA function +

+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+
+
+## Fitting 4 different two-parameter models to binomial data
+
+deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial")
+
+deguelin.m2 <- drm(r/n~dose, weights=n, data=deguelin, fct=W1.2(), type="binomial")
+
+deguelin.m3 <- drm(r/n~dose, weights=n, data=deguelin, fct=W2.2(), type="binomial")
+
+deguelin.m4 <- drm(r/n~dose, weights=n, data=deguelin, fct=LN.2(), type="binomial")
+
+
+
+
+
+## Model averaged BMD for 5% additional risk with estimated background risk 
+
+## and BMDL based on Buckland et al.
+
+bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, 
+
+      backgType = "modelBased", def = "additional",
+
+      type = "Buckland")
+
+
+
+## Model averaged BMD for 5% additional risk with estimated background risk
+
+## and BMDL based on an average of the model curves
+
+bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, 
+
+      backgType = "modelBased", def = "additional",
+
+      type = "curve", bootstrapType = "parametric", bootInterval = "percentile", R=50)
+
+
+
+
+
+## Fitting 4 different two-parameter models to binomial data
+
+ryegrass.m1<-drm(rootl~conc, data=ryegrass, fct=LL.4())
+
+ryegrass.m2<-drm(rootl~conc, data=ryegrass, fct=W1.4())
+
+ryegrass.m3<-drm(rootl~conc, data=ryegrass, fct=W2.4())
+
+ryegrass.m4<-drm(rootl~conc, data=ryegrass, fct=LN.4())
+
+
+
+## Model-averaged BMD and bootstrap BMDL for bmr=5% and using the hybrid approach
+
+## to estimate the background risk.  
+
+bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="AIC", bmr=0.05, 
+
+      backgType = "hybridSD", def = "hybridAdd", type = "bootstrap",
+
+      bootstrapType = "nonparametric", bootInterval = "percentile", R = 50)
+
+
+
+
+
+## Model-averaged BMD using the Stacking Weights
+
+bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="Stack", bmr=0.05, 
+
+      backgType = "hybridSD", def = "hybridAdd", type = "bootstrap",
+
+      bootstrapType = "nonparametric", bootInterval = "percentile", R = 50)
+
+
+
+
+
+

bmd MA curve +

+

+
+
+
+library(bmd)
+
+library(drc)
+
+library(drcData)
+
+library(ggplot2)
+
+
+
+# fit models to aconiazide data
+
+aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3())
+
+aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3())
+
+aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3())
+
+aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3())
+
+
+
+# plot the MA curve
+
+plot(aconiazide.LL.3, type = "obs")
+
+curve(
+
+  MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,aconiazide.W1.3, aconiazide.W2.3),
+
+          modelWeights = "AIC"),
+
+  add = TRUE)
+
+
+
+# or plot using ggplot2
+
+qplotDrc(aconiazide.LL.3, type = "obs") +
+
+ geom_function(fun = function(x){ 
+
+                MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+
+                                            aconiazide.W1.3, aconiazide.W2.3), 
+
+                        modelWeights = "AIC")
+
+                )
+
+
+
+
+

get stacking weights +

+
+getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+
+                                  aconiazide.W1.3, aconiazide.W2.3))
+
+getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+
+                                  aconiazide.W1.3, aconiazide.W2.3),
+
+                  nSplits = 7)
+
+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
+ + + + + + + + diff --git a/docs/articles/specialized-models.html b/docs/articles/specialized-models.html new file mode 100644 index 0000000..de817cb --- /dev/null +++ b/docs/articles/specialized-models.html @@ -0,0 +1,439 @@ + + + + + + + +specialized-models • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

specialized-models

+ + + + + +
+ + + +
+library(bmd)
+
+

Oridnal +

+
+
+
+
+
+library(drc)
+#> Warning: package 'drc' was built under R version 4.4.2
+#> Loading required package: MASS
+#> 
+#> 'drc' has been loaded.
+#> Please cite R and 'drc' if used for a publication,
+#> for references type 'citation()' and 'citation('drc')'.
+#> 
+#> Attaching package: 'drc'
+#> The following objects are masked from 'package:stats':
+#> 
+#>     gaussian, getInitial
+
+library(drcData)
+#> 
+#> Attaching package: 'drcData'
+#> The following objects are masked from 'package:drc':
+#> 
+#>     auxins, nasturtium
+
+data(guthion)
+
+guthionS <- subset(guthion, trt == "S")
+
+
+
+guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "total",
+
+                          dose = "dose", data = guthionS, fct = LL.2())
+
+
+
+plot(guthionS.LL, xlim = c(15,55)) # uses ggplot
+

+
+
+
+bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50)
+#>                    BMD     BMDL
+#> moribund+dead 20.50104 17.11484
+#> dead          20.59249 16.69573
+
+

MA +

+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+data(guthion)
+
+
+
+guthionS <- subset(guthion, trt == "S")
+
+
+
+guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), 
+
+                          weights = "total", dose = "dose", data = guthionS, fct = LL.2())
+
+guthionS.LN <- drmOrdinal(levels = c("alive", "moribund", "dead"), 
+
+                          weights = "total", dose = "dose", data = guthionS, fct = LN.2())
+
+guthionS.W1 <- drmOrdinal(levels = c("alive", "moribund", "dead"),
+
+                          weights = "total", dose = "dose", data = guthionS, fct = W1.2())
+
+guthionS.W2 <- drmOrdinal(levels = c("alive", "moribund", "dead"),
+
+                          weights = "total", dose = "dose", data = guthionS, fct = W2.2())
+
+
+
+bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), 
+
+             modelWeights = "AIC", bmr = 0.1, 
+
+             backgType = "modelBased", def = "excess", type = "Kang")
+
+bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), 
+
+             modelWeights = "AIC", bmr = 0.1, 
+
+             backgType = "modelBased", def = "excess", type = "bootstrap", R = 50)
+
+
+
+

Heterogenous Variance Models +

+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+library(bmd)
+
+# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT.
+
+
+
+# ryegrass data
+
+set.seed(123)
+
+ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2),
+
+                                  data = ryegrass, fct = LL.4())
+
+plot(ryegrass.LL.4.hetVar)
+
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1,
+
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, 
+
+          def = "hybridExc", R = 50, level = 0.95, 
+
+          bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap
+
+
+
+# barley data
+
+set.seed(123)
+
+barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4())
+
+plot(barley.LL.4.hetVar)
+
+
+
+# GiantKelp data
+
+set.seed(123)
+
+GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), 
+
+                                     data = GiantKelp, fct = LL.4())
+
+plot(GiantKelp.LL.4.hetVarSq)
+
+
+
+GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), 
+
+                                        data = GiantKelp, fct = LL.4())
+
+plot(GiantKelp.LL.4.hetVarLogSq)
+
+
+
+
+
+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+library(bmd)
+
+# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT.
+
+
+
+# ryegrass data
+
+set.seed(123)
+
+ryegrass.hetVar.list <- list(
+
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LL.4()),
+
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LN.4()),
+
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W1.4()),
+
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W2.4()))
+
+bmdHetVarMA(ryegrass.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridPercentile",
+
+            backg = 0.1, def = "hybridExc", R = 100, level = 0.95)
+#> Performing bootstrap
+#>   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   5%  |                                              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+#>        BMD_MA   BMDL_MA
+#> [1,] 1.093996 0.7095869
+
+bmdHetVarMA(ryegrass.hetVar.list, modelWeights = c(0.4, 0.2, 0.1, 0.3), bmr = 0.1, 
+
+            backgType = "hybridPercentile", backg = 0.1, 
+
+            def = "hybridExc", R = 50, level = 0.95) # user-defined weights
+#> Performing bootstrap
+#>   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   2%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   6%  |                                                                              |======                                                                |   8%  |                                                                              |=======                                                               |  10%  |                                              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+#>        BMD_MA   BMDL_MA
+#> [1,] 0.964126 0.7893021
+
+
+
+# barley data
+
+set.seed(123)
+
+barley.hetVar.list <- list(drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), 
+
+                                     data = barley, fct = LL.4()),
+
+                           drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), 
+
+                                     data = barley, fct = W2.4()))
+
+bmdHetVarMA(barley.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", backg = 2,
+
+            def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#>   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   2%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   6%  |                                                                              |======                                                                |   8%  |                                                                              |=======                                                               |  10%  |                                              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+#>        BMD_MA  BMDL_MA
+#> [1,] 218.9167 151.2401
+
+
+
+# GiantKelp data
+
+set.seed(123)
+
+GiantKelp.hetVar.list <- list(
+
+  drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), data = GiantKelp, fct = LL.4()),
+
+  drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), data = GiantKelp, fct = LL.4()))
+
+bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD",
+
+            backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, 
+
+            display = TRUE)
+#> Performing bootstrap
+#>   |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   2%  |                                                                              |===                                                                   |   4%  |                                                                              |====                                                                  |   6%  |                                                                              |======                                                                |   8%  |                                                                              |=======                                                               |  10%  |                                              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+#>        BMD_MA   BMDL_MA
+#> [1,] 4.073336 0.6266271
+
+
+

Mixed Models +

+
+
+
+
+
+
+library(drc)
+
+library(drcData)
+
+library(metafor)
+#> Warning: package 'metafor' was built under R version 4.4.2
+#> Loading required package: Matrix
+#> Loading required package: metadat
+#> Warning: package 'metadat' was built under R version 4.4.2
+#> Loading required package: numDeriv
+#> 
+#> Loading the 'metafor' package (version 4.6-0). For an
+#> introduction to the package please type: help(metafor)
+
+library(bmd)
+
+
+
+set.seed(1)
+
+data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2),
+
+                    y = rep(drcData::ryegrass$rootl, 2) +
+
+                      c(rnorm(n = nrow(drcData::ryegrass), mean = 2, sd = 0.5),
+
+                        rnorm(n = nrow(drcData::ryegrass), mean = 2.7, sd = 0.7)),
+
+                    EXP_ID = rep(as.character(1:2), each = nrow(drcData::ryegrass)))
+
+
+
+modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4())
+
+bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative")
+#>       BMD     BMDL
+#>  1.669136 1.316628
+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
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z>d<*R4ymND>lO{dsvsXcen~N^{oeG2Tm>D#4cOgQT-WrYajy}|qTlzQ89ZRXE;hs1 zA-Op@9dqlP9w3y2bNBYhdVAM^2BJr&Cm$Cf>$f??>FMeE?9-8+n&PYSvxQSmoJEya z#8M<`*hn$r^8`~0jlSNWGlAjGA}0*#=pjd@dGEo47cj@gG&jOxR8#L!OeCsuzx}3E z1(J*yH}U~^OANOa0S*GrD2|hfO+-_0+}35jyt5C`t3J^FB=Vq5%xOa~aw;OZbd{IU zOcDA + + + + + + +statistical-tests • bmd + + + + + + + + + + + +

+
+ + + + +
+
+
+

statistical-tests

+ + + + + +
+ + + +
+library(bmd)
+
+

Statistical Tests Examples +

+

This vignette demonstrates the usage of functions related to +statistical tests.

+
+

Monotonicity Test +

+
+
+
+
+
+# Example with custom data
+
+x <- c(1, 2, 3, 4, 5)
+
+y <- c(2, 4, 6, 8, 10)
+
+result <- monotonicityTest(x, y, test = "jonckheere")
+
+print(result)
+#> $p.value
+#> [1] 0.007152939
+#> 
+#> $acceptMonotonicity
+#> [1] TRUE
+
+
+
+data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6))
+
+result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew")
+#> Loading required namespace: isotone
+
+print(result)
+#> $p.value
+#> [1] 0
+#> 
+#> $acceptMonotonicity
+#> [1] TRUE
+
+
+

Trend Test +

+
+
+# Example with custom data
+
+x <- c(1, 2, 3, 4, 5)
+
+y <- c(2, 4, 6, 8, 10)
+
+result <- trendTest(x, y, test = "tukey")
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(x): essentially perfect fit: summary may be unreliable
+#> Warning in summary.lm(x): essentially perfect fit: summary may be unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(object, ...): essentially perfect fit: summary may be
+#> unreliable
+#> Warning in summary.lm(model): essentially perfect fit: summary may be
+#> unreliable
+
+print(result)
+#> $p.values
+#>       xari: xari       xord: xord xarilog: xarilog 
+#>     0.000000e+00     0.000000e+00     2.093881e-13 
+#> 
+#> $decisions
+#>       xari: xari       xord: xord xarilog: xarilog 
+#>         "accept"         "accept"         "accept" 
+#> 
+#> $acceptTrend
+#> [1] TRUE
+
+
+
+# Example with a data frame
+
+data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6))
+
+result <- trendTest("x", "y", data = data, test = "shirley")
+
+print(result)
+#> $p.values
+#> NULL
+#> 
+#> $decisions
+#>     ctr     
+#> mu1 "reject"
+#> mu2 "reject"
+#> mu3 "reject"
+#> mu4 "accept"
+#> 
+#> $acceptTrend
+#> [1] TRUE
+
+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
+ + + + + + + + diff --git a/docs/articles/utilities.html b/docs/articles/utilities.html new file mode 100644 index 0000000..e573c30 --- /dev/null +++ b/docs/articles/utilities.html @@ -0,0 +1,131 @@ + + + + + + + +utilities • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

utilities

+ + + + + +
+ + + +
+library(bmd)
+

Utility functions included in the package bmd are: +“PAV”, “expandBinomial”, “bootDataGen”, “BCa”

+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
+ + + + + + + + diff --git a/docs/articles/visualization.html b/docs/articles/visualization.html new file mode 100644 index 0000000..37d6df0 --- /dev/null +++ b/docs/articles/visualization.html @@ -0,0 +1,6521 @@ + + + + + + + +visualization • bmd + + + + + + + + + + + +
+
+ + + + +
+
+
+

visualization

+ + + + + +
+ + + +
+library(bmd)
+

Visualization functions included in the bmd package are: +“qplotDrc”, “qplotBmd”, “plot.bmd”.

+
+library(drc)
+#> Warning: package 'drc' was built under R version 4.4.2
+#> Loading required package: MASS
+#> 
+#> 'drc' has been loaded.
+#> Please cite R and 'drc' if used for a publication,
+#> for references type 'citation()' and 'citation('drc')'.
+#> 
+#> Attaching package: 'drc'
+#> The following objects are masked from 'package:stats':
+#> 
+#>     gaussian, getInitial
+
+library(drcData)
+#> 
+#> Attaching package: 'drcData'
+#> The following objects are masked from 'package:drc':
+#> 
+#>     auxins, nasturtium
+
+
+
+## Fitting model and calculating BMD. 
+
+model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+
+bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative")
+#>       BMD     BMDL
+#>  1.499026 1.169727
+
+
+
+## Plotting
+
+plot(bmd0)
+

+
+
+
+
+# Plot both limits of confidence interval
+
+plot(bmd0, interval = "twosided")
+

+
+
+
+
+# Pass argument to plot.bmd to plot confidence band around curve
+
+plot(bmd0, type = "confidence")
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+

+
+# Plot
+
+qplotBmd(bmd0, interval = "twosided", add = FALSE)
+

+
+
+
+
+qplotDrc(model,type="confidence") +
+
+  qplotBmd(bmd0, interval = "twosided", add = TRUE)
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+

+
+
+
+
+qplotBmd(bmd0, interval = "twosided", add = FALSE)
+

+
+

qplotDrc +

+
+
+library(drc)
+
+library(drcData)
+
+library(ggplot2)
+
+
+
+## Fitting models to be plotted below
+
+ryegrass.m1 <- drm(rootl~conc, data = ryegrass, fct = LL.4())
+
+ryegrass.m2 <- drm(rootl~conc, data = ryegrass, fct = LL.3())  # lower limit fixed at 0
+
+
+
+## Plotting observations and fitted curve for the first model
+
+p <- qplotDrc(ryegrass.m1) 
+
+p
+

+
+
+
+
+## Add confidence region for the first model.
+
+p + qplotDrc(ryegrass.m1, type="confidence", add = TRUE)$confBandLayer 
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+

+
+
+
+
+## Plot both models
+
+p + qplotDrc(ryegrass.m2, add = TRUE)$curveLayer
+

+
+
+
+
+## Fitting model to be plotted below
+
+spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4())
+
+
+
+## Plot with no colours
+
+qplotDrc(spinach.m1)
+

+
+
+
+
+## Plot with default colours
+
+qplotDrc(spinach.m1, col = TRUE)
+

+
+
+
+
+## Plot with specified colours
+
+qplotDrc(spinach.m1, col = TRUE) + 
+
+  scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+
+                                "darkslategray4", "plum4"))
+

+
+
+
+
+## Plot of curves 1 and 2 only
+
+qplotDrc(spinach.m1, level = c(1,4))
+

+
+
+
+
+## Plot with confidence regions
+
+qplotDrc(spinach.m1, col = TRUE, type = "confidence")
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+

+
+
+
+
+## Plot points and add confidence regions. Confidence regions are coloured by the "fill" aesthetic.
+
+## Customising the x scale by adding a new scale.
+
+qplotDrc(spinach.m1, col = TRUE, type = "confidence") +
+
+  qplotDrc(spinach.m1, col = TRUE, type = "average", add = TRUE)$obsLayer + 
+
+  scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+
+                                "darkslategray4", "plum4"))+ 
+
+  scale_fill_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+
+                               "darkslategray4", "plum4")) +
+
+  scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1)))
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning in (tquan * sqrt(varVal + sumObjRV)) * c(-1, 1): Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Scale for x is already present.
+#> Adding another scale for x, which will replace the existing scale.
+

+
+
+ + + +
+ + + +
+

+

Developed by Signe M. Jensen.

+
+ +
+

+

Site built with pkgdown 2.1.0.

+
+ +
+
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/dev/null +++ b/docs/bootstrap-toc.css @@ -0,0 +1,60 @@ +/*! + * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) + * Copyright 2015 Aidan Feldman + * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ + +/* modified from https://github.com/twbs/bootstrap/blob/94b4076dd2efba9af71f0b18d4ee4b163aa9e0dd/docs/assets/css/src/docs.css#L548-L601 */ + +/* All levels of nav */ +nav[data-toggle='toc'] .nav > li > a { + display: block; + padding: 4px 20px; + font-size: 13px; + font-weight: 500; + color: #767676; +} +nav[data-toggle='toc'] .nav > li > a:hover, +nav[data-toggle='toc'] .nav > li > a:focus { + padding-left: 19px; + color: #563d7c; + text-decoration: none; + background-color: transparent; + border-left: 1px solid #563d7c; +} +nav[data-toggle='toc'] .nav > .active > a, +nav[data-toggle='toc'] .nav > .active:hover > a, +nav[data-toggle='toc'] .nav > .active:focus > a { + padding-left: 18px; + font-weight: bold; + color: #563d7c; + background-color: transparent; + border-left: 2px solid #563d7c; +} + +/* Nav: second level (shown on .active) */ +nav[data-toggle='toc'] .nav .nav { + display: none; /* Hide by default, but at >768px, show it */ + padding-bottom: 10px; +} +nav[data-toggle='toc'] .nav .nav > li > a { + padding-top: 1px; + padding-bottom: 1px; + padding-left: 30px; + font-size: 12px; + font-weight: normal; +} +nav[data-toggle='toc'] .nav .nav > li > a:hover, +nav[data-toggle='toc'] .nav .nav > li > a:focus { + padding-left: 29px; +} +nav[data-toggle='toc'] .nav .nav > .active > a, +nav[data-toggle='toc'] .nav .nav > .active:hover > a, +nav[data-toggle='toc'] .nav .nav > .active:focus > a { + padding-left: 28px; + font-weight: 500; +} + +/* from https://github.com/twbs/bootstrap/blob/e38f066d8c203c3e032da0ff23cd2d6098ee2dd6/docs/assets/css/src/docs.css#L631-L634 */ +nav[data-toggle='toc'] .nav > .active > ul { + display: block; +} diff --git a/docs/bootstrap-toc.js b/docs/bootstrap-toc.js new file mode 100644 index 0000000..1cdd573 --- /dev/null +++ b/docs/bootstrap-toc.js @@ -0,0 +1,159 @@ +/*! + * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) + * Copyright 2015 Aidan Feldman + * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ +(function() { + 'use strict'; + + window.Toc = { + helpers: { + // return all matching elements in the set, or their descendants + findOrFilter: function($el, selector) { + // http://danielnouri.org/notes/2011/03/14/a-jquery-find-that-also-finds-the-root-element/ + // http://stackoverflow.com/a/12731439/358804 + var $descendants = $el.find(selector); + return $el.filter(selector).add($descendants).filter(':not([data-toc-skip])'); + }, + + generateUniqueIdBase: function(el) { + var text = $(el).text(); + var anchor = text.trim().toLowerCase().replace(/[^A-Za-z0-9]+/g, '-'); + return anchor || el.tagName.toLowerCase(); + }, + + generateUniqueId: function(el) { + var anchorBase = this.generateUniqueIdBase(el); + for (var i = 0; ; i++) { + var anchor = anchorBase; + if (i > 0) { + // add suffix + anchor += '-' + i; + } + // check if ID already exists + if (!document.getElementById(anchor)) { + return anchor; + } + } + }, + + generateAnchor: function(el) { + if (el.id) { + return el.id; + } else { + var anchor = this.generateUniqueId(el); + el.id = anchor; + return anchor; + } + }, + + createNavList: function() { + return $('
    '); + }, + + createChildNavList: function($parent) { + var $childList = this.createNavList(); + $parent.append($childList); + return $childList; + }, + + generateNavEl: function(anchor, text) { + var $a = $(''); + $a.attr('href', '#' + anchor); + $a.text(text); + var $li = $('
  • '); + $li.append($a); + return $li; + }, + + generateNavItem: function(headingEl) { + var anchor = this.generateAnchor(headingEl); + var $heading = $(headingEl); + var text = $heading.data('toc-text') || $heading.text(); + return this.generateNavEl(anchor, text); + }, + + // Find the first heading level (`

    `, then `

    `, etc.) that has more than one element. Defaults to 1 (for `

    `). + getTopLevel: function($scope) { + for (var i = 1; i <= 6; i++) { + var $headings = this.findOrFilter($scope, 'h' + i); + if ($headings.length > 1) { + return i; + } + } + + return 1; + }, + + // returns the elements for the top level, and the next below it + getHeadings: function($scope, topLevel) { + var topSelector = 'h' + topLevel; + + var secondaryLevel = topLevel + 1; + var secondarySelector = 'h' + secondaryLevel; + + return this.findOrFilter($scope, topSelector + ',' + secondarySelector); + }, + + getNavLevel: function(el) { + return parseInt(el.tagName.charAt(1), 10); + }, + + populateNav: function($topContext, topLevel, $headings) { + var $context = $topContext; + var $prevNav; + + var helpers = this; + $headings.each(function(i, el) { + var $newNav = helpers.generateNavItem(el); + var navLevel = helpers.getNavLevel(el); + + // determine the proper $context + if (navLevel === topLevel) { + // use top level + $context = $topContext; + } else if ($prevNav && $context === $topContext) { + // create a new level of the tree and switch to it + $context = helpers.createChildNavList($prevNav); + } // else use the current $context + + $context.append($newNav); + + $prevNav = $newNav; + }); + }, + + parseOps: function(arg) { + var opts; + if (arg.jquery) { + opts = { + $nav: arg + }; + } else { + opts = arg; + } + opts.$scope = opts.$scope || $(document.body); + return opts; + } + }, + + // accepts a jQuery object, or an options object + init: function(opts) { + opts = this.helpers.parseOps(opts); + + // ensure that the data attribute is in place for styling + opts.$nav.attr('data-toggle', 'toc'); + + var $topContext = this.helpers.createChildNavList(opts.$nav); + var topLevel = this.helpers.getTopLevel(opts.$scope); + var $headings = this.helpers.getHeadings(opts.$scope, topLevel); + this.helpers.populateNav($topContext, topLevel, $headings); + } + }; + + $(function() { + $('nav[data-toggle="toc"]').each(function(i, el) { + var $nav = $(el); + Toc.init($nav); + }); + }); +})(); diff --git a/docs/docsearch.css b/docs/docsearch.css new file mode 100644 index 0000000..e5f1fe1 --- /dev/null +++ b/docs/docsearch.css @@ -0,0 +1,148 @@ +/* Docsearch -------------------------------------------------------------- */ +/* + Source: https://github.com/algolia/docsearch/ + License: MIT +*/ + +.algolia-autocomplete { + display: block; + -webkit-box-flex: 1; + -ms-flex: 1; + flex: 1 +} + +.algolia-autocomplete .ds-dropdown-menu { + width: 100%; + min-width: none; + max-width: none; + padding: .75rem 0; + background-color: #fff; + background-clip: padding-box; + border: 1px solid rgba(0, 0, 0, .1); + box-shadow: 0 .5rem 1rem rgba(0, 0, 0, .175); +} + +@media (min-width:768px) { + .algolia-autocomplete .ds-dropdown-menu { + width: 175% + } +} + +.algolia-autocomplete .ds-dropdown-menu::before { + display: none +} + +.algolia-autocomplete .ds-dropdown-menu [class^=ds-dataset-] { + padding: 0; + background-color: rgb(255,255,255); + border: 0; + max-height: 80vh; +} + +.algolia-autocomplete .ds-dropdown-menu .ds-suggestions { + margin-top: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion { + padding: 0; + overflow: visible +} + +.algolia-autocomplete .algolia-docsearch-suggestion--category-header { + padding: .125rem 1rem; + margin-top: 0; + font-size: 1.3em; + font-weight: 500; + color: #00008B; + border-bottom: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--wrapper { + float: none; + padding-top: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--subcategory-column { + float: none; + width: auto; + padding: 0; + text-align: left +} + +.algolia-autocomplete .algolia-docsearch-suggestion--content { + float: none; + width: auto; + padding: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--content::before { + display: none +} + +.algolia-autocomplete .ds-suggestion:not(:first-child) .algolia-docsearch-suggestion--category-header { + padding-top: .75rem; + margin-top: .75rem; + border-top: 1px solid rgba(0, 0, 0, .1) +} + +.algolia-autocomplete .ds-suggestion .algolia-docsearch-suggestion--subcategory-column { + display: block; + padding: .1rem 1rem; + margin-bottom: 0.1; + font-size: 1.0em; + font-weight: 400 + /* display: none */ +} + +.algolia-autocomplete .algolia-docsearch-suggestion--title { + display: block; + padding: .25rem 1rem; + margin-bottom: 0; + font-size: 0.9em; + font-weight: 400 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--text { + padding: 0 1rem .5rem; + margin-top: -.25rem; + font-size: 0.8em; + font-weight: 400; + line-height: 1.25 +} + +.algolia-autocomplete .algolia-docsearch-footer { + width: 110px; + height: 20px; + z-index: 3; + margin-top: 10.66667px; + float: right; + font-size: 0; + line-height: 0; +} + +.algolia-autocomplete .algolia-docsearch-footer--logo { + background-image: url("data:image/svg+xml;utf8,"); + background-repeat: no-repeat; + background-position: 50%; + background-size: 100%; + overflow: hidden; + text-indent: -9000px; + width: 100%; + height: 100%; + display: block; + transform: translate(-8px); +} + +.algolia-autocomplete .algolia-docsearch-suggestion--highlight { + color: #FF8C00; + background: rgba(232, 189, 54, 0.1) +} + + +.algolia-autocomplete .algolia-docsearch-suggestion--text .algolia-docsearch-suggestion--highlight { + box-shadow: inset 0 -2px 0 0 rgba(105, 105, 105, .5) +} + +.algolia-autocomplete .ds-suggestion.ds-cursor .algolia-docsearch-suggestion--content { + background-color: rgba(192, 192, 192, .15) +} diff --git a/docs/docsearch.js b/docs/docsearch.js new file mode 100644 index 0000000..b35504c --- /dev/null +++ b/docs/docsearch.js @@ -0,0 +1,85 @@ +$(function() { + + // register a handler to move the focus to the search bar + // upon pressing shift + "/" (i.e. "?") + $(document).on('keydown', function(e) { + if (e.shiftKey && e.keyCode == 191) { + e.preventDefault(); + $("#search-input").focus(); + } + }); + + $(document).ready(function() { + // do keyword highlighting + /* modified from https://jsfiddle.net/julmot/bL6bb5oo/ */ + var mark = function() { + + var referrer = document.URL ; + var paramKey = "q" ; + + if (referrer.indexOf("?") !== -1) { + var qs = referrer.substr(referrer.indexOf('?') + 1); + var qs_noanchor = qs.split('#')[0]; + var qsa = qs_noanchor.split('&'); + var keyword = ""; + + for (var i = 0; i < qsa.length; i++) { + var currentParam = qsa[i].split('='); + + if (currentParam.length !== 2) { + continue; + } + + if (currentParam[0] == paramKey) { + keyword = decodeURIComponent(currentParam[1].replace(/\+/g, "%20")); + } + } + + if (keyword !== "") { + $(".contents").unmark({ + done: function() { + $(".contents").mark(keyword); + } + }); + } + } + }; + + mark(); + }); +}); + +/* Search term highlighting ------------------------------*/ + +function matchedWords(hit) { + var words = []; + + var hierarchy = hit._highlightResult.hierarchy; + // loop to fetch from lvl0, lvl1, etc. + for (var idx in hierarchy) { + words = words.concat(hierarchy[idx].matchedWords); + } + + var content = hit._highlightResult.content; + if (content) { + words = words.concat(content.matchedWords); + } + + // return unique words + var words_uniq = [...new Set(words)]; + return words_uniq; +} + +function updateHitURL(hit) { + + var words = matchedWords(hit); + var url = ""; + + if (hit.anchor) { + url = hit.url_without_anchor + '?q=' + escape(words.join(" ")) + '#' + hit.anchor; + } else { + url = hit.url + '?q=' + escape(words.join(" ")); + } + + return url; +} diff --git a/docs/index.html b/docs/index.html new file mode 100644 index 0000000..8432f66 --- /dev/null +++ b/docs/index.html @@ -0,0 +1,330 @@ + + + + + + + +Benchmark dose estimation for dose-response data • bmd + + + + + + + + + + + + +
    +
    + + + + +
    +
    +
    +

    bmd +

    +

    This is an R package for benchmark dose (BMD) estimation, which expands upon the functionality of the drc package.

    +

    This package is currently maintained by Jens Riis Baalkilde and Signe Marie Jensen, Department of Plant and Environmental Sciences, University of Copenhagen.

    +
    +

    Installation +

    +

    Install the bmd package from GitHub. The bmd package works best with the drc package installed from GitHub as well.

    +
    +install.packages("devtools")
+devtools::install_github("DoseResponse/drcData")
+devtools::install_github("DoseResponse/drc")
+devtools::install_github("DoseResponse/bmd")
    +
    +
    +

    Key features +

    +

    The bmd package is a natural extension of the drc package. Key features of the bmd package includes:

    +
      +
    • Benchmark dose (BMD) estimation for quantal, continuous, count and ordinal data for a wide range of definitions of BMD. +
        +
      • A range of confidence intervals for BMD estimates, including Wald, Profile and Bootstrap intervals.
        • +
      • BMD estimation based on model averaging.
        • +
      • BMD estimation for multiple dose-response curves.
        • +
      +
      • +
    • Utility functions for plotting dose-response curves and BMD estimates.
      • +
    +
    +
    +

    Example usage +

    +

    In the following it is demonstrated how to use the functions in the bmd package on two data sets with a continuous response variable and one data set with a quantal response.

    +
    +

    Example 1 (secalonic) +

    +

    First, the data set from the drcData package is loaded, and a dose-response model is fitted.

    +
    +data("secalonic")
+secalonic.LL.4 <- drm(rootl ~ dose, data = secalonic, fct = LL.4())
    +

    Users familiar with the drc package already know how straight-forward it is to plot dose-response models using the plot() function. The qplotDrc() function in the bmd package mimics the same functionality based on ggplot2.

    +
    +plot(secalonic.LL.4, main = "Secalonic model plotted by basic R plotting")
    +

    +
    +qplotDrc(secalonic.LL.4) + ggplot2::labs(title = "Secalonic model plotted by ggplot2")
    +

    +

    Similar to the old method of plotting dose-response curves, qplotDrc() features several options for customisation.

    +
    +qplotDrc(secalonic.LL.4, type = "all")
    +

    +
    +qplotDrc(secalonic.LL.4, type = "obs")
    +

    +
    +qplotDrc(secalonic.LL.4, type = "bars")
    +

    +
    +qplotDrc(secalonic.LL.4, type = "confidence")
    +

    +
    +

    Example 1: BMD estimation +

    +

    A wide range of BMD definitions are implemented in the bmd package. In the following, the BMD and BMDL based on the “relative risk” definition recommended by EFSA, with a BMR = 10% are computed.

    +
    +bmd(secalonic.LL.4, bmr = 0.1, backgType = "modelBased", def = "relative")
    +
    ##       BMD       BMDL
+##  0.035362 0.01579886
    +

    The default interval is a Wald type confidence interval. If a profile likelihood confidence interval is preferred, this can be specified by the “interval” argument.

    +
    +bmd(secalonic.LL.4, bmr = 0.1, backgType = "modelBased", def = "relative", interval = "profile")
    +
    ##       BMD       BMDL
+##  0.035362 0.02619532
    +

    The current state-of-the-art definition of the BMD is the hybrid definition. In the following, the BMD and BMDL based on the “excess risk” definition based on the hybrid method with BMR = 10%, and adverse background level set to the estimated background level minus 1SD is calculated.

    +
    +bmd(secalonic.LL.4, bmr = 0.1, backgType = "hybridSD", backg = 1, def = "hybridExc")
    +
    ##         BMD         BMDL
+##  0.01720857 2.344327e-05
    +

    For technical reasons, profile intervals for BMD estimates based on the hybrid method, are not currently available.

    +
    +
    +

    Example 1: BMD plotting +

    +

    The qplotBmd() function ca be used to plot BMD along with the dose-response curve.

    +
    +qplotBmd(bmd(secalonic.LL.4, bmr = 0.1, backgType = "modelBased", def = "relative", display = FALSE)) # display = FALSE hides output from bmd function
    +

    +
    +
    +

    Example 1: BMD estimation using MA +

    +

    An additional set of dose-response models are fitted.

    +
    +secalonic.LL.3 <- drm(rootl ~ dose, data = secalonic, fct = LL.3())
+secalonic.LN.3 <- drm(rootl ~ dose, data = secalonic, fct = LN.3())
+secalonic.LN.4 <- drm(rootl ~ dose, data = secalonic, fct = LN.4())
+secalonic.W1.3 <- drm(rootl ~ dose, data = secalonic, fct = W1.3())
+secalonic.W1.4 <- drm(rootl ~ dose, data = secalonic, fct = W1.4())
+secalonic.W2.3 <- drm(rootl ~ dose, data = secalonic, fct = W2.3())
+secalonic.W2.4 <- drm(rootl ~ dose, data = secalonic, fct = W2.4())
+
+secalonic.modelList <- list(secalonic.LL.3, secalonic.LL.4, secalonic.LN.3, secalonic.LN.4,
+                            secalonic.W1.3, secalonic.W1.4, secalonic.W2.3, secalonic.W2.4)
    +

    BMD can now be estimated by MA by using the function bmdMA. Type of model weights need to be specified as well as MA type.

    +
    +bmdMA(secalonic.modelList, modelWeights = "AIC", type = "Buckland", bmr = 0.1, backgType = "modelBased", def = "relative")
    +
    ##     BMD_MA    BMDL_MA
+##  0.0317763 0.02391615
    +
    +set.seed(123)
+bmdMA(secalonic.modelList, modelWeights = "AIC", type = "bootstrap", bmr = 0.1, backgType = "modelBased", def = "relative", R = 500, progressInfo = FALSE)
    +
    ##     BMD_MA    BMDL_MA
+##  0.0317763 0.02821126
    +
    +bmdMA(secalonic.modelList, modelWeights = "AIC", type = "Buckland", bmr = 0.1, backgType = "hybridSD", def = "hybridExc", backg = 1)
    +
    ##      BMD_MA     BMDL_MA
+##  0.01007999 0.004875864
    +
    +
    +
    +

    Example 2 (S.alba.comp, two dose-response curves) +

    +

    An experiment was conducted where some pots were treated with the herbicide Bentazone, and other pots were treated with Glyphosate. A model with separate curves for each herbicide is fitted as follows.

    +
    +data("S.alba.comp")
+S.alba.comp.LL.4 <- drm(drymatter ~ dose, curveid = herbicide, data = S.alba.comp, fct = LL.4())
    +

    To plot the function, qplotDrc can be used:

    +
    +qplotDrc(S.alba.comp.LL.4)
    +

    +
    +qplotDrc(S.alba.comp.LL.4, col = TRUE, type = "confidence") +
+  qplotDrc(S.alba.comp.LL.4, col = TRUE, type = "obs", add = TRUE)$obsLayer
    +

    +

    This also illustrates how qplotDrc() can be layered to produce custom plots, by using the argument “add = TRUE”, and choosing either the layer of observations (“obsLayer”), the layer with the dose-response curve (“curveLayer”), or the layer with the confidence band around the curves (“confBandLayer”).

    +
    +

    Example 2: BMD estimation. +

    +

    BMD and BMDL can be estimated for the individual curves:

    +
    +bmd(S.alba.comp.LL.4, bmr = 0.1, backgType = "modelBased", def = "relative")
    +
    ##                 BMD      BMDL
+## bentazone  13.57966 10.862398
+## glyphosate 14.16426  7.480309
    +
    +bmd(S.alba.comp.LL.4, bmr = 0.1, backgType = "hybridSD", backg = 1, def = "hybridExc")
    +
    ##                  BMD     BMDL
+## bentazone  10.664119 7.252415
+## glyphosate  7.425644 2.321537
    +
    +
    +
    +

    Example 3 (acute.inh, binomial response) +

    +

    20 animals were exposed to 4 doses of an unknown substance, 5 animals per dose. The number of dead animals for each dose were recorded. In the following, the data is loaded, and a 2-parameter is fitted to the data. Subsequently, a plot of the resulting dose-response curve is created using qplotDrc().

    +
    +data("acute.inh")
+acute.inh.LL.2 <- drm(num.dead/total ~ dose, weights = total, data = acute.inh, fct = LL.2(), type = "binomial")
+
+qplotDrc(acute.inh.LL.2)
    +

    +
    +

    Example 3: BMD Estimation +

    +

    For binomial response data, the “excess” and “additional” BMD definitions are available. When the background response is 00, they are identical:

    +
    +bmd(acute.inh.LL.2, bmr = 0.1, backgType = "modelBased", def = "additional")
    +
    ##       BMD     BMDL
+##  678.6335 481.0896
    +
    +bmd(acute.inh.LL.2, bmr = 0.1, backgType = "modelBased", def = "excess")
    +
    ##       BMD     BMDL
+##  678.6335 481.0896
    +
    +qplotBmd(bmd(acute.inh.LL.2, bmr = 0.1, backgType = "modelBased", def = "additional", display = FALSE)) +
+  ggplot2::scale_x_continuous(limits = c(0,2100), trans = scales::transform_pseudo_log(2000))
    +
    ## Scale for x is already present.
+## Adding another scale for x, which will replace the existing scale.
    +

    +
    +
    +
    +
    +
    + + +
    + + +
    +

    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    +

    Site built with pkgdown 2.1.0.

    +
    + +
    +
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    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+AIC(object, ..., k = 2)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/AIC.drcOrdinal.html b/docs/reference/AIC.drcOrdinal.html new file mode 100644 index 0000000..bfe661e --- /dev/null +++ b/docs/reference/AIC.drcOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — AIC.drcOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcOrdinal'
+AIC(object, ..., k = 2)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/BCa.html b/docs/reference/BCa.html new file mode 100644 index 0000000..d59b6b1 --- /dev/null +++ b/docs/reference/BCa.html @@ -0,0 +1,102 @@ + +Help funtion to bmdBoot — BCa • bmd + + +
    +
    + + + +
    +
    +
    +

    Help funtion to bmdBoot

    + + +
    + +
    +

    Help funtion to bmdBoot

    +
    + +
    + 
    BCa(obs, data, bootSample, bootjack, level)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/BIC.drcHetVar.html b/docs/reference/BIC.drcHetVar.html new file mode 100644 index 0000000..755ef83 --- /dev/null +++ b/docs/reference/BIC.drcHetVar.html @@ -0,0 +1,103 @@ + +S3 method — BIC.drcHetVar • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+BIC(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/BIC.drcOrdinal.html b/docs/reference/BIC.drcOrdinal.html new file mode 100644 index 0000000..1d47925 --- /dev/null +++ b/docs/reference/BIC.drcOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — BIC.drcOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcOrdinal'
+BIC(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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    NzleK2q?Dt#Qz5T1 z<%4z1oR>dyP(QJgX16VcSHdfYt|6rtFj&$shCWk2>{oiv4w_Cfp!Q_HsMKt$=}X7R zfE}-%8rsn2akyIu2 z_LhoZCnDmqqsQ0gUMlf{?W6(~_V3ZS&$^Fu>9oBO;kw>kM1b=>D<035+!qq8?r3BNC?@ zXnFAPOC0FP6vq@(!fM^NX)-wVV9{Ux;x0)sBjF71ywhA*7F__3Aoe=FsTIIMp;i(u z5*8Oy_00l4lbP<)<|r%z==n6Pg9;FZsx&T{vLc>%%kyh80RvIWAf!XQ{ zaFOsU;Go?VV4(>*n#c1SbDSq|P5VXQSoT+7AqpC`1Kt4?3@mp|6Amx{&*Hsf_IaBH zXel&k*8}KeLSQEi7aZ)|DZjww>GEu1FPV5z*g33 z;G7F+OB`@uE&o3oD6_vr8pw?R=X;=|i5SKsWyo*9)V})9XzpdMed3EOxCiLz>gTe~ HDWM4fj13aK literal 0 HcmV?d00001 diff --git a/docs/reference/MACurve.html b/docs/reference/MACurve.html new file mode 100644 index 0000000..7e649d5 --- /dev/null +++ b/docs/reference/MACurve.html @@ -0,0 +1,188 @@ + +Model-average dose-response curves — MACurve • bmd + + +

    +
    + + + +
    +
    +
    +

    Model-average dose-response curves

    + + +
    + +
    +

    Computing weighted average response estimates across multiple dose-response +curves.

    +
    + +
    + 
    MACurve(x, modelList, modelWeights, stackingSeed = 1, stackingSplits = 2)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    a vector of dose values for which the weighted average of response +estimates are to be computed

    + + +
    modelList
    +

    list of models of class drc

    + + +
    modelWeights
    +

    character string specifying the type of weights used, +"AIC", "BIC" or "Stack", or a vector of the same length as the modelList +with user defined weights

    + + +
    stackingSeed
    +

    integer or NULL: Random seed to use in the data split in +the estimation of the Stacking Weights, when modelWeights = "Stack". +The global seed is reset to the initial value after estimation of the +weights, so this option does not interfere with a globally set seed.

    + + +
    stackingSplits
    +

    integer or "LOO": When modelWeights = "Stack", +the Stacking Weights are estimated, which are based on V-fold +cross-validation. The stackingSplits argument sets the number V of data +splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +to setting V equal to the number of observations in the data set.

    + +
    +
    +

    Value

    +

    numeric

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(bmd)
+library(drc)
+library(drcData)
+library(ggplot2)
+
+# fit models to aconiazide data
+aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3())
+aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3())
+aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3())
+aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3())
+
+# plot the MA curve
+plot(aconiazide.LL.3, type = "obs")
+curve(
+  MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,aconiazide.W1.3, aconiazide.W2.3),
+          modelWeights = "AIC"),
+  add = TRUE)
+
+
+# or plot using ggplot2
+qplotDrc(aconiazide.LL.3, type = "obs") +
+ geom_function(fun = function(x){ 
+                MACurve(x, modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+                                            aconiazide.W1.3, aconiazide.W2.3), 
+                        modelWeights = "AIC")
+                })
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/PAV.html b/docs/reference/PAV.html new file mode 100644 index 0000000..d570693 --- /dev/null +++ b/docs/reference/PAV.html @@ -0,0 +1,143 @@ + +Pool-adjacent-violators monotonizing — PAV • bmd + + +
    +
    + + + +
    +
    +
    +

    Pool-adjacent-violators monotonizing

    + + +
    + +
    +

    The function monotonizes a sequence of probabilities or means based on the +pool-adjacent-violators algorithm.

    +
    + +
    + 
    PAV(formula, data, type)
    +
    + +
    +

    Arguments

    + + +
    formula
    +

    an object of class "formula" expressing dose-response +relationship. Details of model specification are given under 'Details'

    + + +
    data
    +

    data frame containing the variables in the formula

    + + +
    type
    +

    character string specifying the type of data used in the model, +"continuous" or "binomial" or "Poisson"

    + +
    +
    +

    Value

    +

    A vector containing the monotonized sequence.

    +
    +
    +

    Details

    +

    For details on how the pool-adjacent-violators algorithm is defined see +Silvapulle and Sen (2004).

    +

    Formula should be specified as in the form number/total ~ dose for binomial +data and response ~ for continuous data.

    +
    +
    +

    References

    +

    Silvapulle, M. J. and Sen, P. K. (2004). Constrained statistical +inference: order, inequality, and shape constraints. New York: John Wiley & +Sons.

    +
    +
    +

    Author

    +

    Signe M. Jensen

    +
    + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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zh~Vghq9P-khk^y(l7@Y6R0K*i|K!~*}LHq(=Ukw1T|H=Zbp&W)ik_Y(%TKeJ^H9v{=! z*4F;}?e)Vvq`a&QEmGXk*Ec3S9D#w6@#m>KIZiZip~9*vl%Gau@$vCIyu3d*Hi+Wl z;-H{XQ&Xj>l0S{y-?wShV9en<5nw3CjW)!zv~YzCY~PqxR`#3JZ(UtsFf%h-Iyi(= z$b90)<>BWa=+B9hNY$Ds1_rpvePzl z22DJi$Y&1^?ww1X{%w{ngY$6yr(a7;CLSKRlEvuJ(a|i~QyF=A!>_MGdHMMZ%Yfzk zNGxJ#Xb9<~BzvTK$D*7^8wDeRRzQP1K0Yp#g9}IMH}FtcND2mn`ykgMNfc_Dnqo;5 zP@mP+7sKNVYBX#Nd`OGVO#vY#R#x%|2!t$JOZfQ-E-fz$KX*<%Jn(|;J-p4U7ml`E z`B>T6gOzCDdN)5p(a>(MrGL-3B$P{`u24h%_8H2)m4GT4X@7tJ@bq*DAc%Q+c~DSE z6otLL#Qwd+<>lpgAW#Uy1k`KT-RUVKJ^?|qZE%D?B5VdtI1>|7!SZq8!jY1)^0%j_ zr>@}%-EO=)JiWb z5h3AXr8?Oo*(-9^KLyf*#zaTA3WSyu2TGj2`;WTe^@)p%;~PQ!zYo3%FUs8=X9eGR QK>-gL2?g<5QKO*$15tu2VgLXD literal 0 HcmV?d00001 diff --git a/docs/reference/bmd-package.html b/docs/reference/bmd-package.html new file mode 100644 index 0000000..70b38b6 --- /dev/null +++ b/docs/reference/bmd-package.html @@ -0,0 +1,99 @@ + +BMD: Benchmark Dose Modeling — bmd-package • bmd + + + + + + + + + + + diff --git a/docs/reference/bmd.html b/docs/reference/bmd.html new file mode 100644 index 0000000..0c69822 --- /dev/null +++ b/docs/reference/bmd.html @@ -0,0 +1,351 @@ + +Benchmark dose estimation — bmd • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit from dose +response model fits

    +
    + +
    + 
    bmd(
+  object,
+  bmr,
+  backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  controlSD = NA,
+  def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd",
+    "point"),
+  respTrans = c("none", "log", "sqrt"),
+  interval = c("delta", "sandwich", "inv", "profile", "profileGrid"),
+  sandwich.vcov = FALSE,
+  display = TRUE,
+  level = 0.95,
+  profileGridSize = NA,
+  profileProgressInfo = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    object
    +

    object of class drc

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "modelBased","absolute", "hybridSD" and +"hybridPercentile". For count data (Poisson, negbin1 or negbin2) the options +are "modelBased" and "absolute".

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous or count response data. p0 = 1 - +phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group.

    +

    "hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma is the SD for the control group

    +

    If not specified, it will be set to "modelBased" for all def excluding +"hybridExc" and "hybridAdd", for these the default is "hybridSD".

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridPercentile"

    + + +
    controlSD
    +

    numeric value specifying the standard deviation of the +control group (used in the hybrid approach). If not specified the SD for the +control group will be estimated as the square root of the residual variance +(assuming variance homogeneity).

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response. "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response. "relative", "extra", and "point" are for count response data.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data

    +

    "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +continuous and count response data

    +

    "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +continuous and count response data

    +

    "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response

    + + +
    respTrans
    +

    if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).

    + + +
    interval
    +

    character string specifying the type of confidence interval +to use: "delta" (default), "inv", "profile" or "profileGrid"

    +

    "delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method

    +

    "inv" - BMDL is based on inverse regression, that is the dose associated +with the upper limit of the pointwise confidence interval of the +dose-response curve. Currently not available for a transformed response +variable.

    +

    "profile" - A profile confidence interval is computed by reparametrising the +model. Only available for backgType in ("modelBased", "absolute"), +def in ("excess", "additional","relative", "extra", "point") and +dose-response models with model functions of types Log-Logistic, Log-Normal +and Weibull 1 and 2. The limits of the confidence interval are searched for +within a grid of size specified by the profileGridSize argument, +however the values of the confidence interval are not limited to the values +on the grid.

    +

    "profileGrid" - A profile confidence interval is computed by creating a +multi-dimensional grid of parameter values for the model. Then, a confidence +region for the parameters in the model is estimated, and the BMD is +estimated for all combinations of parameter values within the region. The +interval for the BMD is then computed as the minimum and maximum values of +BMD values within the region. Note that for models with several parameters +(3-5), is might take a while to compute the confidence interval using this +method. The number of grid points for each parameter can be specified by the +profileGridSize argument.

    + + +
    sandwich.vcov
    +

    logical. If TRUE BMDL is based on confidence intervals +based on robust standard errors from the sandwich covariance matrix

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + + +
    profileGridSize
    +

    integer specifying the number of grid points used for +each parameter, when interval is either "profile" or +"profileGridSearch". Defaults to 20 if not specified.

    + + +
    profileProgressInfo
    +

    logical. If TRUE, progress info is be printed +while computed profile confidence intervals using the profileGrid +method. Default is TRUE.

    + +
    +
    +

    Value

    +

    A list of four elements: Results contain the estimated BMD and BMDL, +bmrScaled is the response value corresponding to the BMD, interval gives the +lower (BMDL) and upper (BMDU) end of the confidence interval of BMD, SE +gives the standard error of BMD.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +
    +
    +

    References

    +

    Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, Biometrics +57, 698–706.

    +

    Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, Critical Reviews in Toxicology 32, 133–153.

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+#> Warning: package 'drc' was built under R version 4.4.2
+#> Loading required package: MASS
+#> 
+#> 'drc' has been loaded.
+#> Please cite R and 'drc' if used for a publication,
+#> for references type 'citation()' and 'citation('drc')'.
+#> 
+#> Attaching package: 'drc'
+#> The following objects are masked from 'package:stats':
+#> 
+#>     gaussian, getInitial
+library(drcData)
+#> 
+#> Attaching package: 'drcData'
+#> The following objects are masked from 'package:drc':
+#> 
+#>     auxins, nasturtium
+
+## Fitting log-logistic two-parameter model to binomial data
+deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial")
+
+## BMD for 5% additional risk with estimated background risk
+bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional")
+#>       BMD     BMDL
+#>  2.176587 1.353876
+
+## BMD for 10% additional risk with 2% background risk
+bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional")
+#>       BMD     BMDL
+#>  3.558084 2.515197
+
+## BMD for 5% excess risk and background 0
+bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess")
+#>       BMD     BMDL
+#>  2.176587 1.353876
+
+## Dose resulting in 12% risk
+bmd(deguelin.m1, 0.12, def = "point")
+#>       BMD     BMDL
+#>  3.558084 2.515197
+
+## Benchmark doses for a continuous response
+ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+
+## BMD as the dose resulting in a 5% change relative to the mean background level
+bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE)
+#>       BMD      BMDL
+#>  1.165279 0.8372753
+
+## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk
+bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE)
+#>       BMD      BMDL
+#>  1.041279 0.7106359
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdBoot.html b/docs/reference/bmdBoot.html new file mode 100644 index 0000000..e602100 --- /dev/null +++ b/docs/reference/bmdBoot.html @@ -0,0 +1,285 @@ + +Benchmark dose estimation using bootstrap — bmdBoot • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation using bootstrap

    + + +
    + +
    +

    The function estimates BMD and BMDL using bootstrap based on parametric +dose-response models.

    +
    + +
    + 
    bmdBoot(
+  object,
+  bmr,
+  R = 1000,
+  bootType = "nonparametric",
+  bmdType = "orig",
+  backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  controlSD = NA,
+  def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd",
+    "point"),
+  respTrans = c("none", "log", "sqrt"),
+  bootInterval = c("percentile", "BCa"),
+  display = TRUE,
+  level = 0.95
+)
    +
    + +
    +

    Arguments

    + + +
    object
    +

    object of class drc

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    R
    +

    number of bootstrap samples. Default is 1000

    + + +
    bootType
    +

    character string specifying type of bootstrap used. +"nonparametric" (default), "semiparametric" or "parametric". "Semiparametric +is only available for continuous data and "nonparametric" is at present the +only option for count data. See details below

    + + +
    bmdType
    +

    Type of estimate for BMD. Default is "orig" the bmd estimate +from the original data set. Other choices are "mean" - the mean of the +bootstrap estimates, or "median" - the median of the bootstrap estimates

    + + +
    backgType
    +

    character string specifying how the background level is +specified. For binomial and count data the options are "modelBased" and +"absolute". For continuous data the options are "modelBased", "absolute", +"hybridSD" and "hybridPercentile"

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background level for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"

    + + +
    controlSD
    +

    numeric value specifying the standard deviation of the +control group (used in the hybrid approach). If not specified the SD for the +control group will be estimated as the square root of the residual variance +(assuming variance homogeneity).

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess" , "additional" and "point" are for +binomial response whereas "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response. "relative", "extra", and "point" are for count response data.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response

    +

    "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response

    +

    "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +count and continuous response

    +

    "added" - BMR is defined as: BMR= f(BMD) + p0. Works for count and +continuous response

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response

    + + +
    respTrans
    +

    if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).

    + + +
    bootInterval
    +

    character string indicating type of bootstrap interval +used for estimating BMDL. "Percentile" (default) or "BCa" (Bias corrected +and adjusted)

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + +
    +
    +

    Value

    +

    A list of three elements: Results contain the estimated BMD and +BMDL, bootEst is a vector af all of the estimated BMD values from each +bootstrap sample, Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach.

    +
    +
    +

    Details

    +

    BMDL is defined as the 5th percentile in the bootstrap distribution.

    +

    Bootstrapping with the argument boot = "nonparametric" is done by sampling +with replacement from the original data set. Bootstrapping with the argument +boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +assuming equal variance between groups, in case of continuous data. For +binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +resampling always produces 0 or 1, respectively. In this case data is +sampled from binom(N_i,(Y_i+1/4)/(N_i+1/2)). Bootstrapping with argument +boot = "semiparametric" is done by sampling with replacement from the +residuals.

    +

    All sampling is made within dose groups.

    +
    +
    +

    Author

    +

    Signe M. Jensen

    +
    + +
    +

    Examples

    + 
    
+## Data on root length in ryegrass after exposure to ferulic acid
+require(drc)
+require(drcData)
+data(ryegrass)
+
+ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+
+## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk
+bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", R = 50)
+#>       BMD      BMDL
+#>  1.041279 0.8640942
+
+## BMD from the same definitions but using parametric bootstrap
+bmdBoot(ryegrass.m1, 0.05, backgType = "hybridSD", def = "hybridAdd", bootType="parametric",R = 50)
+#>       BMD      BMDL
+#>  1.041279 0.7704424
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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a/docs/reference/bmdHetVar.html b/docs/reference/bmdHetVar.html new file mode 100644 index 0000000..3cf32cc --- /dev/null +++ b/docs/reference/bmdHetVar.html @@ -0,0 +1,291 @@ + +Benchmark dose estimation with heterogeneous variance — bmdHetVar • bmd + + +

    +
    + + + +
    +
    +
    +

    Benchmark dose estimation with heterogeneous variance

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit based on the +hybrid method from dose response model fits with the option to specify a +heterogeneous variance structure, where the variance depends on the dose +level and/or the fitted values

    +
    + +
    + 
    bmdHetVar(
+  object,
+  bmr,
+  backgType = c("absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  def = c("hybridExc", "hybridAdd"),
+  interval = c("boot", "none"),
+  R = 1000,
+  level = 0.95,
+  bootType = "nonparametric",
+  progressInfo = TRUE,
+  display = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    object
    +

    dose-response model with a heterogeneous variance structure of +class drcHetVar

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. The options are "absolute", "hybridSD" and "hybridPercentile".

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +"hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +distribution function and sigma(0) is the SD for the control group.

    +

    "hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma(0) is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 2 SD +for "hybridSD" background and 0.9 for "hybridPercentile"

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +(additional hybrid), available.

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0)/ (1- p0), where x0 is the level for which the response is considered +adverse, phi is the normal distribution function and sigma(BMD) is the SD at +the benchmark dose.

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0, where x0 is the level for which the response is considered adverse, phi +is the normal distribution function and sigma(BMD) is the SD at the +benchmark dose.

    + + +
    interval
    +

    character string specifying the type of confidence interval +to use: "boot" (default) or "none"

    +

    "boot" - BMDL is based on percentile bootstrapping.

    +

    "none" - no confidence interval is computed.

    + + +
    R
    +

    number of bootstrap samples. Ignored if interval = "none"

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + + +
    bootType
    +

    character string specifying the type of bootstrap samples. +Options are "nonparametric" (observations are drawn without replacement from +the original data set), "semi-parametric" (standardised residuals are drawn +with replacement and subsequently rescaled according to the model) and +"parametric" (new observations are simulated from the distribution given by +the fitted model).

    + + +
    progressInfo
    +

    logical. If TRUE, progress info is be printed while +bootstrap confidence intervals are estimated. Default is TRUE.

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + +
    +
    +

    Value

    +

    A list of five elements: Results contain the estimated BMD and BMDL, +bmrScaled is the response value corresponding to the BMD, interval gives the +lower (BMDL) and upper (BMDU) end of the confidence interval of BMD

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    REFERENCES TO BE ADDED/WRITTEN

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+library(bmd)
+# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT.
+
+# ryegrass data
+set.seed(123)
+ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2),
+                                  data = ryegrass, fct = LL.4())
+plot(ryegrass.LL.4.hetVar)
+#> Loading required namespace: gridExtra
+
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, 
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, 
+          display = TRUE) # increase R
+#> Performing bootstrap
+#> 
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+#>           BMD      BMDL
+#> [1,] 0.823838 0.5889243
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, 
+          def = "hybridExc", R = 50, level = 0.95, 
+          bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap
+#> Performing bootstrap
+#> 
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+#>           BMD      BMDL
+#> [1,] 0.823838 0.4823374
+
+# barley data
+set.seed(123)
+barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4())
+plot(barley.LL.4.hetVar)
+
+bmdHetVar(barley.LL.4.hetVar, bmr = 0.1, backgType = "hybridSD", backg = 1, 
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#> 
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+#>           BMD     BMDL
+#> [1,] 218.0105 123.6738
+
+# GiantKelp data
+set.seed(123)
+GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), 
+                                     data = GiantKelp, fct = LL.4())
+plot(GiantKelp.LL.4.hetVarSq)
+
+bmdHetVar(GiantKelp.LL.4.hetVarSq, bmr = 0.1, backgType = "hybridSD", backg = 1, 
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#> 
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+#>           BMD     BMDL
+#> [1,] 3.045686 0.404048
+
+GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), 
+                                        data = GiantKelp, fct = LL.4())
+plot(GiantKelp.LL.4.hetVarLogSq)
+
+bmdHetVar(GiantKelp.LL.4.hetVarLogSq, bmr = 0.1, backgType = "hybridSD", backg = 1, 
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#> 
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+#>           BMD      BMDL
+#> [1,] 4.412019 0.4280083
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdHetVarMA.html b/docs/reference/bmdHetVarMA.html new file mode 100644 index 0000000..f2a3711 --- /dev/null +++ b/docs/reference/bmdHetVarMA.html @@ -0,0 +1,280 @@ + +Benchmark dose estimation with heterogeneous variance based on model averaging (MA) — bmdHetVarMA • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation with heterogeneous variance based on model averaging (MA)

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit based on the +hybrid method from a list of dose response model fits with the option to +specify a heterogeneous variance structure, where the variance depends on +the dose level and/or the fitted values

    +
    + +
    + 
    bmdHetVarMA(
+  modelList,
+  modelWeights = c("AIC", "BIC"),
+  bmr,
+  backgType = c("absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  def = c("hybridExc", "hybridAdd"),
+  interval = c("boot", "none"),
+  R = 1000,
+  level = 0.95,
+  progressInfo = TRUE,
+  display = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    modelList
    +

    a list of dose-response models with a heterogeneous +variance structure of class drcHetVar

    + + +
    modelWeights
    +

    character string specifying the type of weights used, +"AIC" or "BIC", or a numeric vector of the same length as the modelList with +user defined weights

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. The options are "absolute", "hybridSD" and "hybridPercentile".

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = 1 - phi((back - f(0))/sigma(0)) for "hybridExc" and +"hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma(0) + +f(0)) - f(0))/sigma(0)) = 1 - phi(backg), where phi is the normal +distribution function and sigma(0) is the SD for the control group.

    +

    "hybridPercentile" - the background risk is specified by the user in terms +of percentile from the control group distribution (assuming a normal +distribution). p0 = 1 - phi((x0 - f(0))/sigma(0)) = 1 - backg. where x0 is +the level for which the response is considered adverse, phi is the normal +distribution function and sigma(0) is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 2 SD +for "hybridSD" background and 0.9 for "hybridPercentile"

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "hybridExc" (excess hybrid), "hybridAdd" +(additional hybrid), available.

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0)/ (1- p0), where x0 is the level for which the response is considered +adverse, phi is the normal distribution function and sigma(BMD) is the SD at +the benchmark dose.

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma(BMD)) - +p0, where x0 is the level for which the response is considered adverse, phi +is the normal distribution function and sigma(BMD) is the SD at the +benchmark dose.

    + + +
    interval
    +

    character string specifying the type of confidence interval +to use: "boot" (default) or "none"

    +

    "boot" - BMDL is based on nonparametric percentile bootstrapping.

    +

    "none" - no confidence interval is computed.

    + + +
    R
    +

    number of bootstrap samples. Ignored if interval = "none"

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + + +
    progressInfo
    +

    logical. If TRUE, progress info is be printed while +bootstrap confidence intervals are estimated. Default is TRUE.

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + +
    +
    +

    Value

    +

    A list of four elements: Results contain the estimated BMD and BMDL, +Boot.samples.used gives the number of boot samples that resulted in +succesful estimations and were accordingly used in the estimation of BMDL +(and BMDU), Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach, and modelWeights +includes the estimated weights.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    REFERENCES TO BE ADDED/WRITTEN

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+library(bmd)
+# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT.
+
+# ryegrass data
+set.seed(123)
+ryegrass.hetVar.list <- list(
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LL.4()),
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = LN.4()),
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W1.4()),
+  drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2), data = ryegrass, fct = W2.4()))
+bmdHetVarMA(ryegrass.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridPercentile",
+            backg = 0.1, def = "hybridExc", R = 100, level = 0.95)
+#> Performing bootstrap
+#> 
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+#>        BMD_MA   BMDL_MA
+#> [1,] 1.093996 0.7095869
+bmdHetVarMA(ryegrass.hetVar.list, modelWeights = c(0.4, 0.2, 0.1, 0.3), bmr = 0.1, 
+            backgType = "hybridPercentile", backg = 0.1, 
+            def = "hybridExc", R = 50, level = 0.95) # user-defined weights
+#> Performing bootstrap
+#> 
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+#>        BMD_MA   BMDL_MA
+#> [1,] 0.964126 0.7893021
+
+# barley data
+set.seed(123)
+barley.hetVar.list <- list(drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), 
+                                     data = barley, fct = LL.4()),
+                           drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), 
+                                     data = barley, fct = W2.4()))
+bmdHetVarMA(barley.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD", backg = 2,
+            def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#> 
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+#>        BMD_MA  BMDL_MA
+#> [1,] 218.9167 151.2401
+
+# GiantKelp data
+set.seed(123)
+GiantKelp.hetVar.list <- list(
+  drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), data = GiantKelp, fct = LL.4()),
+  drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), data = GiantKelp, fct = LL.4()))
+bmdHetVarMA(GiantKelp.hetVar.list, modelWeights = "AIC", bmr = 0.1, backgType = "hybridSD",
+            backg = 1, def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, 
+            display = TRUE)
+#> Performing bootstrap
+#> 
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+#>        BMD_MA   BMDL_MA
+#> [1,] 4.073336 0.6266271
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdIso.html b/docs/reference/bmdIso.html new file mode 100644 index 0000000..adb8c0a --- /dev/null +++ b/docs/reference/bmdIso.html @@ -0,0 +1,269 @@ + +Benchmark dose estimation from isotonic regression — bmdIso • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation from isotonic regression

    + + +
    + +
    +

    The function monotonizes the sequence of response values based on the +pool-adjacent violators algorithm and based on these use linear +interpolating splines to build an isotonic regression model. From this model +a benchmark dose is estimated.

    +
    + +
    + 
    bmdIso(
+  formula,
+  data,
+  type,
+  bmr,
+  p0,
+  backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point"),
+  display = FALSE
+)
    +
    + +
    +

    Arguments

    + + +
    formula
    +

    an object of class "formula" expressing the dose-response +relationship. Details of model specification are given under 'Details'

    + + +
    data
    +

    data frame containing the variables in the model

    + + +
    type
    +

    character string specifying the type of data used in the model. +"continuous", "binomial" or "Poisson"

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    p0
    +

    background probability for hybrid definitions

    + + +
    backgType
    +

    character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "absolute", "hybridSD" and +"hybridPercentile"

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative" and +"added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +"hybridAdd" (additional hybrid), and "point" are for continuous response. +"relative", "extra", and "point" are for count response data.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response

    +

    "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response

    +

    "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + +
    +
    +

    Value

    +

    A matrix with two columns, one containing BMD and the other +containing BMDL.

    +
    +
    +

    Details

    +

    Formula should be specified as in the form number/total ~ dose for binomial +data. For details about the use of isotonic regression for BMD estimation +see Piegorsch et al. (20014) and Lin et al. (2015).

    +
    +
    +

    References

    +

    Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +(2014). Benchmark dose analysis via nonparametric regression modeling. Risk +Analysis, 34(1), 135-151

    +

    Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +benchmark dose estimation with continuous dose-response data. Scandinavian +Journal of Statistics, 42, 713-731

    +
    +
    +

    Author

    +

    Signe M. Jensen

    +
    + +
    +

    Examples

    + 
    
+## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014)
+formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0),
+                          tumor.incidence = c(0, 0, 0, 3, 21, 150),
+                          total = c(122, 27, 126, 113, 34, 182))
+                          
+# Estimating BMD from isotonic regression using excess risk definition and a BMR=0.1
+bmdIso(tumor.incidence/total ~ conc, 
+      data=formaldehyde, 
+      type="binomial",
+      bmr=0.1,
+      backgType = "modelBased",
+      def = "excess")
+#> [1] 6.49705
+      
+      
+## Data on root length in ryegrass after exposure to ferulic acid
+require(drc)
+require(drcData)
+data(ryegrass)
+
+# As isotonic regression only wors for increasing dose-response relationship 
+# the association is turned
+ryegrass1<-ryegrass
+ryegrass1$rootl<-100-ryegrass1$rootl
+
+# Estimating BMD from isotonic regression using relative risk definition
+# and a BMR=0.05
+bmdIso(rootl ~ conc, 
+      data=ryegrass1, 
+      type="continuous",
+      bmr=0.05,
+      backgType = "modelBased",
+      def = "relative")
+#> [1] 3.682826
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdIsoBoot.html b/docs/reference/bmdIsoBoot.html new file mode 100644 index 0000000..0497dc6 --- /dev/null +++ b/docs/reference/bmdIsoBoot.html @@ -0,0 +1,282 @@ + +Benchmark dose estimation from isotonic regression — bmdIsoBoot • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation from isotonic regression

    + + +
    + +
    +

    The function estimates BMD and BMDL using bootstrap based on isotonic +regression.

    +
    + +
    + 
    bmdIsoBoot(
+  formula,
+  data,
+  type,
+  bmr,
+  R = 1000,
+  boot = "resample",
+  backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point")
+)
    +
    + +
    +

    Arguments

    + + +
    formula
    +

    an object of class "formula" expressing dose-response +relationship. Details of model specification are given under 'Details'

    + + +
    data
    +

    data frame containing the variables in the model

    + + +
    type
    +

    character string specifying the type of data used in the model. +"continuous" or "binomial" or "Poisson"

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    R
    +

    number of bootstrap samples

    + + +
    boot
    +

    character string specifying type of bootstrap used. "resample" +or "pseudorandom". Only option for count data is "resample"

    + + +
    backgType
    +

    character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "modelBased", "absolute", "hybridSD" and +"hybridPercentile"

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative" and +"added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are for +binomial response whereas "relative", "added", "hybridExc" (excess hybrid), +"hybridAdd" (additional hybrid), and "point" are for continuous response. +"relative", "extra", and "point" are for count response data.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response

    +

    "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and +continuous response

    +

    "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response

    + +
    +
    +

    Value

    +

    A matrix with two columns, one containing BMD and the other +containing BMDL.

    +
    +
    +

    Details

    +

    BMD and BMDL is defined as the median and the 5th percentile in the +bootstrap distribution, respectively.

    +

    Formula should be specified as in the form number/total ~ dose for binomial +data.

    +

    Bootstrapping with the argument boot = "resample" is done by sampling with +replacement from the original data set. Bootstrapping with the argument boot += "pseudorandom" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming +equal variance between groups, in case of continuous data. For binomial +data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of +Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always +produces 0 or 1, respectively. In this case data is sampled from +binom(N_i,(Y_i+1/3)/(N_i+1/3)).

    +

    All sampling is made within dose groups.

    +

    For details about the use of isotonic regression for BMD estimation see +Piegorsch et al. (20014) and Lin et al. (2015).

    +
    +
    +

    References

    +

    Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. +(2014). Benchmark dose analysis via nonparametric regression modeling. Risk +Analysis, 34(1), 135-151

    +

    Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric +benchmark dose estimation with continuous dose-response data. Scandinavian +Journal of Statistics, 42, 713-731

    +
    +
    +

    Author

    +

    Signe M. Jensen

    +
    + +
    +

    Examples

    + 
    
+## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014)
+formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0),
+                          tumor.incidence = c(0, 0, 0, 3, 21, 150),
+                          total = c(122, 27, 126, 113, 34, 182))
+                          
+# BMD and BMDL from isotonic regression using excess risk definition and a BMR=0.1
+bmdIsoBoot(tumor.incidence/total ~ conc, 
+      data=formaldehyde, 
+      type="binomial",
+      bmr=0.1,
+      backgType = "modelBased",
+      def = "excess")
+#> 
+#> 
+#>      BMD     BMDL
+#>  6.49705 6.322712
+      
+      
+## Data on root length in ryegrass after exposure to ferulic acid
+require(drc)
+data(ryegrass)
+
+# As isotonic regression only wors for increasing dose-response relationship
+# the association is turned
+ryegrass1<-ryegrass
+ryegrass1$rootl<-100-ryegrass1$rootl
+
+# Estimating BMD from isotonic regression using relative risk definition and a BMR=0.05
+bmdIsoBoot(rootl ~ conc, 
+      data=ryegrass1, 
+      type="continuous",
+      bmr=0.05,
+      backgType = "modelBased",
+      def = "relative", R = 100)
+#> 
+#> 
+#>       BMD     BMDL
+#>  3.682826 3.249387
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdMA.html b/docs/reference/bmdMA.html new file mode 100644 index 0000000..4faedcc --- /dev/null +++ b/docs/reference/bmdMA.html @@ -0,0 +1,385 @@ + +Model-averaged benchmark dose estimation — bmdMA • bmd + + +
    +
    + + + +
    +
    +
    +

    Model-averaged benchmark dose estimation

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit based on model +averaging from a user-defined list of dose response model fits

    +
    + +
    + 
    bmdMA(
+  modelList,
+  modelWeights,
+  bmr,
+  backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"),
+  backg = NA,
+  def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd",
+    "point"),
+  respTrans = c("none", "log", "sqrt"),
+  interval = c("delta", "sandwich", "inv", "profile"),
+  type = c("curve", "bootstrap", "Kang", "Buckland"),
+  bootstrapType = c("nonparametric", "parametric"),
+  R = 1000,
+  bootInterval = "percentile",
+  level = 0.95,
+  stackingSeed = NULL,
+  stackingSplits = 2,
+  display = TRUE,
+  progressInfo = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    modelList
    +

    list of models of class drc

    + + +
    modelWeights
    +

    character string specifying the type of weights used, +"AIC", "BIC" or "Stack" (Baalkilde, J. R., Hansen, N. R., and Jensen, S. M., +2025), or a vector of the same length as the modelList with user defined +weights

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. For binomial data the options are "modelBased" and "absolute". +For continuous data the options are "absolute", "hybridSD" and +"hybridPercentile"

    +

    "modelBased" - the background risk is obtained from the model as the risk +for dose 0: p0 = f(0)

    +

    "absolute" - the background risk is specified by the user through the backg +argument: p0 = backg for binomial response and for the "relative", "extra" +and "added" definition for continuous response. p0 = 1 - phi((back - +f(0))/sigma) for "hybridExc" and "hybridAdd" definitions.

    +

    "hybridSD" - the background risk is specified by the user in terms of number +of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + +f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution +function and sigma is the SD for the control group. "hybridPercentile" - +the background risk is specified by the user in terms of percentile from the +control group distribution (assuming a normal distribution). p0 = 1 - +phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the +response is considered adverse, phi is the normal distribution function and +sigma is the SD for the control group

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk for binomial response (1 for decreasing +dose-response models), 2 SD for "hybridSD" background and 0.9 for +"hybridpercentile"

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess" , "additional" and "point" are for +binomial response whereas "relative", "extra", "added", "hybridExc" (excess +hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous +response

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for both binomial and continuous +response

    +

    "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for +continuous response

    +

    "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for +continuous response

    +

    "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous +response

    +

    "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ +(1- p0), where x0 is the level for which the response is considered adverse, +phi is the normal distribution function and sigma is the SD for the control +group. Works for continuous response

    +

    "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, +where x0 is the level for which the response is considered adverse, phi is +the normal distribution function and sigma is the SD for the control group. +Works for continuous response

    + + +
    respTrans
    +

    if the dose-response model is fitted with a transformed +response, specifying this option ensures that the background level for the +BMD is computed on the original scale. Options include "none" (default), +"log" (natural logarithm) and "sqrt"(square root).

    + + +
    interval
    +

    character string specifying the type of confidence interval +to use for the individual models (no effect when type = "bootstrap" or +"curve"): "delta" (default), "sandwich", "inv" or "profile"

    +

    "delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method

    +

    "sandwich" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method where the sandwich covariance matrix is used

    +

    "inv" - BMDL is based on inverse regression, that is the dose associated +with the upper limit of the point wise confidence interval of the +dose-response curve. Not possible if type = "Buckland"

    +

    "profile" - BMDL is based on the lower limit of a profile likelihood +confidence interval. Not possible if type = "Buckland"

    + + +
    type
    +

    character string specifying how to estimate BMD and BMDL: +"curve", "bootstrap", "Kang" or "Buckland"

    +

    "curve" -

    +

    "bootstrap" -

    +

    "Kang" -

    +

    "Buckland" -

    + + +
    bootstrapType
    +

    character string indicating type of bootstrap sampling +to be used if type="bootstrap" or "curve". "nonparametric" (default), or +"parametric" (see details)

    + + +
    R
    +

    number of bootstrap samples to use. Default is 1000

    + + +
    bootInterval
    +

    character string indicating how to estimate the +bootstrap confidence intervals used to find BMDL type="bootstrap". +"percentile" (default) or "BCa" (Bias corrected and adjusted)

    + + +
    level
    +

    numeric value specifying the level of the confidence interval +underlying BMDL. Default is 0.95. Note that the full CI is also computed. +The full CI has level 1-2*(1-level)

    + + +
    stackingSeed
    +

    integer or NULL: Random seed to use in the data split in +the estimation of the Stacking Weights when modelWeights = "Stack". +The global seed is reset to the initial value after estimation of the +weights, so this option does not interfere with a globally set seed.

    + + +
    stackingSplits
    +

    integer or "LOO": When modelWeights = "Stack", +the Stacking Weights are estimated, which are based on V-fold +cross-validation. The stackingSplits argument sets the number V of data +splits used in the cross validation. The "LOO" (Leave one out) is a shortcut +to setting V equal to the number of observations in the data set.

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + + +
    progressInfo
    +

    logical. If TRUE, a progressbar is shown when computing +bootstrap confidence intervals.

    + +
    +
    +

    Value

    +

    A list of five elements: Results contain the estimated BMD and BMDL, +Boot.samples.used gives the number of boot samples that resulted in +succesful estimations and were accordingly used in the estimation of BMDL +(and BMDU), Interval gives BMDL and BMDU, which is identical to the +confidence interval for the percentile interval approach, SE gives the +estimated SE for the "Buckland" method, and modelWeights includes the +estimated weights.

    +
    +
    +

    Details

    +

    This package project is still under development. The aim to provide an R +package calculating the benchmark dose (BMD) and the lower limit of the +corresponding 95% confidence interval (BMDL) for continuous and quantal +dose-response data for a range of dose-response model based on the available +definitions of the benchmark dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +

    Bootstrapping with the argument boot = "nonparametric" is done by sampling +with replacement from the original data set. Bootstrapping with the argument +boot = "parametric" is done by sampling from norm(mean(Y_i),sd(Y_0)), +assuming equal variance between groups, in case of continuous data. For +binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). +In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the +resampling always produces 0 or 1, respectively. In this case data is +sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)).

    +

    All sampling is made within dose groups.

    +
    +
    +

    References

    +

    Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, Biometrics +57, 698–706.

    +

    Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, Critical Reviews in Toxicology 32, 133–153.

    +

    Baalkilde, J. R., Hansen, N. R., and Jensen, S. M. (2025) Stacking Weights +and Model Space Selection in Frequentist Model Averaging for Benchmark Dose +Estimation, Environmetrics 36(2), e70002.

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+
+## Fitting 4 different two-parameter models to binomial data
+deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial")
+deguelin.m2 <- drm(r/n~dose, weights=n, data=deguelin, fct=W1.2(), type="binomial")
+deguelin.m3 <- drm(r/n~dose, weights=n, data=deguelin, fct=W2.2(), type="binomial")
+deguelin.m4 <- drm(r/n~dose, weights=n, data=deguelin, fct=LN.2(), type="binomial")
+
+
+## Model averaged BMD for 5% additional risk with estimated background risk 
+## and BMDL based on Buckland et al.
+bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, 
+      backgType = "modelBased", def = "additional",
+      type = "Buckland")
+#>    BMD_MA   BMDL_MA
+#>  1.357897 0.5643594
+
+## Model averaged BMD for 5% additional risk with estimated background risk
+## and BMDL based on an average of the model curves
+bmdMA(list(deguelin.m1,deguelin.m2,deguelin.m3,deguelin.m4), modelWeights="AIC", 0.05, 
+      backgType = "modelBased", def = "additional",
+      type = "curve", bootstrapType = "parametric", bootInterval = "percentile", R=50)
+#> Performing bootstrap
+#> 
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+#>    BMD_MA   BMDL_MA
+#>  1.338646 0.5943252
+
+
+## Fitting 4 different two-parameter models to binomial data
+ryegrass.m1<-drm(rootl~conc, data=ryegrass, fct=LL.4())
+ryegrass.m2<-drm(rootl~conc, data=ryegrass, fct=W1.4())
+ryegrass.m3<-drm(rootl~conc, data=ryegrass, fct=W2.4())
+ryegrass.m4<-drm(rootl~conc, data=ryegrass, fct=LN.4())
+
+## Model-averaged BMD and bootstrap BMDL for bmr=5% and using the hybrid approach
+## to estimate the background risk.  
+bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="AIC", bmr=0.05, 
+      backgType = "hybridSD", def = "hybridAdd", type = "bootstrap",
+      bootstrapType = "nonparametric", bootInterval = "percentile", R = 50)
+#> Performing bootstrap
+#> 
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+#>    BMD_MA   BMDL_MA
+#>  1.179957 0.9312072
+
+
+## Model-averaged BMD using the Stacking Weights
+bmdMA(list(ryegrass.m1,ryegrass.m2,ryegrass.m3,ryegrass.m4), modelWeights="Stack", bmr=0.05, 
+      backgType = "hybridSD", def = "hybridAdd", type = "bootstrap",
+      bootstrapType = "nonparametric", bootInterval = "percentile", R = 50)
+#> Loading required namespace: CVXR
+#> Performing bootstrap
+#> 
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+#>    BMD_MA   BMDL_MA
+#>  1.313847 0.7801128
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdMACurve.html b/docs/reference/bmdMACurve.html new file mode 100644 index 0000000..6dcbea9 --- /dev/null +++ b/docs/reference/bmdMACurve.html @@ -0,0 +1,102 @@ + +Help funtion to bmdMA — bmdMACurve • bmd + + +
    +
    + + + +
    +
    +
    +

    Help funtion to bmdMA

    + + +
    + +
    +

    Help funtion to bmdMA

    +
    + +
    + 
    bmdMACurve(modelList, modelWeights, bmrScaled0, searchInterval = "dataBased")
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdOrdinal.html b/docs/reference/bmdOrdinal.html new file mode 100644 index 0000000..078f101 --- /dev/null +++ b/docs/reference/bmdOrdinal.html @@ -0,0 +1,258 @@ + +Benchmark dose estimation for ordinal dose-response models — bmdOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation for ordinal dose-response models

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit from ordinal +dose response model fits

    +
    + +
    + 
    bmdOrdinal(
+  object,
+  bmr,
+  backgType = c("modelBased", "absolute"),
+  backg = NA,
+  def = c("excess", "additional", "point"),
+  interval = c("delta", "sandwich", "profile", "bootstrap"),
+  level = 0.95,
+  R = 500,
+  bootType = c("nonparametric", "parametric", "model", "hierarchical"),
+  display = TRUE,
+  progressInfo = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    object
    +

    object of class drcOrdinal

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. The options are "modelBased" and "absolute".

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument.

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk.

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are available +for ordinal response.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data.

    + + +
    interval
    +

    character string specifying the type of confidence interval +to use: "delta" (default), "sandwich", "profile" or "bootstrap"

    +

    "delta" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method

    +

    "sandwich" - BMDL is based on the lower limit of a Wald confidence interval +based on the delta method, where the sandwich covariance matrix is used

    +

    "bootstrap" - BMDL is based on bmd estimates on resampled data sets. The +type of bootstrap applied can be specified by the "bootType" argument. +Default is "nonparametric".

    +

    "none" - No confidence interval is computed.

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + + +
    R
    +

    integer specifying the number of data sets resampled from the +original data set when computing the confidence interval by bootstrap.

    + + +
    bootType
    +

    character string specifying the resampling procedure for the +data sets used for bootstrap.

    +

    "nonparametric" - Bootstrapping is done by sampling with replacement from +the original data set.

    +

    "parametric" - Bootstrapping is done by sampling from a multinomial +distribution with probabilites given by the number of observations for each +level. If all observations for one group are in the same level, shrinkage is +used to avoid that the resampling always produces that particular level. In +this case data is sampled from a multinomial distribution with probabilities +(1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +particular group, and |K| is the number of levels.

    +

    "model" - New data sets are resampled from the fitted model.

    +

    "hierarchical" - If the experiment design is hierarchical (i.e. observations +are grouped according to a categorical variable, for instance litter), a +special resampling procedure is suggested (Blessinger 2020)

    +

    All resampling is done within the dose values.

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + + +
    progressInfo
    +

    logical. If TRUE, a progressbar is displayed when +calculating bootstrap confidence intervals

    + +
    +
    +

    Value

    +

    A list of four elements: Results contain the estimated BMD and BMDL, +interval gives the lower (BMDL) and upper (BMDU) end of the confidence +interval of BMD.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous, quantal, quantal and ordinal dose-response data for a range of +dose-response models based on the available definitions of the benchmark +dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +
    +
    +

    References

    +

    Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, Biometrics +57, 698–706.

    +

    Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, Critical Reviews in Toxicology 32, 133–153.

    +

    Blessinger, T. D., Euling, S. Y., Wang, L., Hogan, K. A., Cai, C., +Klinefelter, G., Saillenfait, A.M. (2020) Environment International +134

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+data(guthion)
+
+guthionS <- subset(guthion, trt == "S")
+
+guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), 
+                          weights = "total", dose = "dose", data = guthionS, fct = LL.2())
+bmdOrdinal(guthionS.LL, bmr = 0.1, backgType = "modelBased", def = "excess", R = 50)
+#>                    BMD     BMDL
+#> moribund+dead 20.50104 17.11484
+#> dead          20.59249 16.69573
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bmdOrdinalMA.html b/docs/reference/bmdOrdinalMA.html new file mode 100644 index 0000000..bfabdbd --- /dev/null +++ b/docs/reference/bmdOrdinalMA.html @@ -0,0 +1,270 @@ + +Benchmark dose estimation for ordinal dose-response models — bmdOrdinalMA • bmd + + +
    +
    + + + +
    +
    +
    +

    Benchmark dose estimation for ordinal dose-response models

    + + +
    + +
    +

    Estimation of benchmark doses and benchmark dose lower limit based on model +averaging from a user-defined list of ordinal dose-response model fits

    +
    + +
    + 
    bmdOrdinalMA(
+  modelList,
+  modelWeights = c("AIC", "BIC"),
+  bmr,
+  backgType = c("modelBased", "absolute"),
+  backg = NA,
+  def = c("excess", "additional", "point"),
+  type = c("bootstrap", "Kang"),
+  level = 0.95,
+  R = 500,
+  bootType = c("nonparametric", "parametric"),
+  display = TRUE,
+  progressInfo = TRUE
+)
    +
    + +
    +

    Arguments

    + + +
    modelList
    +

    A list of ordinal dose-response models of class +drcOrdinal

    + + +
    modelWeights
    +

    character string specifying the type of weights used, +"AIC" or "BIC", or a numeric vector of the same length as the modelList with +user defined weights

    + + +
    bmr
    +

    numeric value of benchmark response level for which to calculate +the benchmark dose

    + + +
    backgType
    +

    character string specifying how the background level is +specified. The options are "modelBased" and "absolute".

    +

    "modelBased" - the background level is obtained from the model as the level +for dose 0: p0 = f(0)

    +

    "absolute" - the background level is specified by the user through the backg +argument.

    + + +
    backg
    +

    numeric value specifying the background level. Defaults to 0 +for "absolute" background risk.

    + + +
    def
    +

    character string specifying the definition of the benchmark dose +to use in the calculations. "excess", "additional" and "point" are available +for ordinal response.

    +

    "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for +binomial response. BMR should be between 0 and 1.

    +

    "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial +response. BMR should be between 0 and 1.

    +

    "point" - The response level for which to find BMD is directly defined +through the BMR level: BMR = f(BMD). Works for binomial, count and +continuous response data.

    + + +
    type
    +

    specify the model averaging type used for the confidence +intervals. Options are "Kang" (confidence intervals computed as weighted +averages of individual confidence intervals) and "bootstrap"

    + + +
    level
    +

    numeric value specifying the levle of the confidence interval +underlying BMDL. Default is 0.95

    + + +
    R
    +

    integer specifying the number of data sets resampled from the +original data set when computing the confidence interval by bootstrap.

    + + +
    bootType
    +

    character string specifying the resampling procedure for the +data sets used for bootstrap.

    +

    "nonparametric" - Bootstrapping is done by sampling with replacement from +the original data set.

    +

    "parametric" - Bootstrapping is done by sampling from a multinomial +distribution with probabilites given by the number of observations for each +level. If all observations for one group are in the same level, shrinkage is +used to avoid that the resampling always produces that particular level. In +this case data is sampled from a multinomial distribution with probabilities +(1/|K|^2)/(N_i + 1/|K|) for the levels with 0 observations, and (N_i + +1/|K|^2)/(N_i + 1/|K|), where N_i is the number of observatiions for the +particular group, and |K| is the number of levels.

    +

    All resampling is done within the dose values.

    + + +
    display
    +

    logical. If TRUE the results are displayed; otherwise they +are not

    + + +
    progressInfo
    +

    logical. If TRUE, a progressbar is displayed when +calculating bootstrap confidence intervals

    + +
    +
    +

    Value

    +

    A list of four elements: Results contain the estimated BMD and BMDL, +interval gives the lower (BMDL) and upper (BMDU) end of the confidence +interval of BMD.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous, quantal, quantal and ordinal dose-response data for a range of +dose-response models based on the available definitions of the benchmark +dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +
    +
    +

    References

    +

    Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) +Benchmark Dose Calculation from Epidemiological Data, Biometrics +57, 698–706.

    +

    Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous +Data, Critical Reviews in Toxicology 32, 133–153.

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+data(guthion)
+
+guthionS <- subset(guthion, trt == "S")
+
+guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), 
+                          weights = "total", dose = "dose", data = guthionS, fct = LL.2())
+guthionS.LN <- drmOrdinal(levels = c("alive", "moribund", "dead"), 
+                          weights = "total", dose = "dose", data = guthionS, fct = LN.2())
+guthionS.W1 <- drmOrdinal(levels = c("alive", "moribund", "dead"),
+                          weights = "total", dose = "dose", data = guthionS, fct = W1.2())
+guthionS.W2 <- drmOrdinal(levels = c("alive", "moribund", "dead"),
+                          weights = "total", dose = "dose", data = guthionS, fct = W2.2())
+
+bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), 
+             modelWeights = "AIC", bmr = 0.1, 
+             backgType = "modelBased", def = "excess", type = "Kang")
+#>                 BMD_MA  BMDL_MA
+#> moribund+dead 20.20305 17.45350
+#> dead          20.49732 17.26269
+bmdOrdinalMA(list(guthionS.LL, guthionS.LN, guthionS.W1, guthionS.W2), 
+             modelWeights = "AIC", bmr = 0.1, 
+             backgType = "modelBased", def = "excess", type = "bootstrap", R = 50)
+#> Loading required namespace: reshape2
+#> Loading required namespace: tidyr
+#> Performing bootstrap
+#> 
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+#>                 BMD_MA  BMDL_MA
+#> moribund+dead 20.20305 16.60024
+#> dead          20.49732 16.32929
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bootDataGen.html b/docs/reference/bootDataGen.html new file mode 100644 index 0000000..0c2eaeb --- /dev/null +++ b/docs/reference/bootDataGen.html @@ -0,0 +1,102 @@ + +Help funtion to bmdBoot — bootDataGen • bmd + + +
    +
    + + + +
    +
    +
    +

    Help funtion to bmdBoot

    + + +
    + +
    +

    Help funtion to bmdBoot

    +
    + +
    + 
    bootDataGen(object, R = 1000, bootType = "nonparametric", aggregated = TRUE)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/bootDataGenOrdinal.html b/docs/reference/bootDataGenOrdinal.html new file mode 100644 index 0000000..c6eaf5f --- /dev/null +++ b/docs/reference/bootDataGenOrdinal.html @@ -0,0 +1,106 @@ + +Help funtion to bmdOrdinal and bmdOrdinalMA — bootDataGenOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    Help funtion to bmdOrdinal and bmdOrdinalMA

    + + +
    + +
    +

    Help funtion to bmdOrdinal and bmdOrdinalMA

    +
    + +
    + 
    bootDataGenOrdinal(
+  object,
+  R = 500,
+  bootType = c("nonparametric", "parametric", "model", "hierarchical")
+)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/coef.drcHetVar.html b/docs/reference/coef.drcHetVar.html new file mode 100644 index 0000000..fbbe3f9 --- /dev/null +++ b/docs/reference/coef.drcHetVar.html @@ -0,0 +1,103 @@ + +S3 method — coef.drcHetVar • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+coef(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/drmHetVar-1.png b/docs/reference/drmHetVar-1.png new file mode 100644 index 0000000000000000000000000000000000000000..4a4df5d574fd4d9810720dfd992e2c03bdc85061 GIT binary patch literal 82354 zcmcG$cRbhs`!@X69%v(>rBVsWPN<|5%E%rmWRtxqmC8q=kQEX_Mn?8Zl1)N(rLyb!+fHt^N@s_-oDeOXtP$H$G<0=D6ao_2w5;EGZOb5Auh~``4&0g|detDSleP zE@YtH-brCHZ)tQo@Pwm(AcM_z-7TkOYkxf2GqlcB;T)%e+Bu_1)pQ4w1SK``!E;Fo zjUA4+j7;9@7sYEv?7I>lenwWE(NmS~oDKa}?h|EF+^sVUMP?uGZvMn47+BUnV^_Jq zOt3R>Mkl2*WZJ2w+eq18cm49kQ7BJrnQZ9){hp$~YlY^&-+z){mHVGxiCJey_4oTd zm$!_p`1`Hci+$f#|NYiY_*~(}e}CEjk=uU`H@2OM^WXpddHDb1fq$jtxD6S0SBKgJ zJh8kjCdLtP$yed()hH_=6U%cHx5R2LYQKPhqgx-o&d=`{vY=4x_b^bG_qI9ftEs3Q zu1GOXT*rKXf%=Hw#lu@4e%06@^uQqK$kC%uSxdTZ-7D4(KH4X=;=u9dvFL!?2Ul(~kc-VdC|6i*hle4iWQJo{8{lL!lr>nZvLr@T+HSERgUv|=sh`e`m;Cw)ass=m_2lwpl%>l*H*3OlKMS+*>> z-_s%iqH4uInm7HsR zi*?AUprZV|?d$71F!1^c+Xw276>{q8Z>)q8^mz+|Qe>&vjLV4?40vQ$Or?QL@~G?$bV_e{bYT 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a/docs/reference/drmHetVar.html b/docs/reference/drmHetVar.html new file mode 100644 index 0000000..bacda30 --- /dev/null +++ b/docs/reference/drmHetVar.html @@ -0,0 +1,208 @@ + +Dose response modeling with heterogeneous variance — drmHetVar • bmd + + +

    +
    + + + +
    +
    +
    +

    Dose response modeling with heterogeneous variance

    + + +
    + +
    +

    Fit a dose-response model with heterogeneous variance dependending on dose +level.

    +
    + +
    + 
    drmHetVar(formula, var.formula, data, fct, curveStart = NULL)
    +
    + +
    +

    Arguments

    + + +
    formula
    +

    formula for the dose-response relationship

    + + +
    var.formula
    +

    one-sided formula specifying the dependance of the dose +values and/or the fitted values on the point-wise standard error

    + + +
    data
    +

    data.frame containing the observations

    + + +
    fct
    +

    a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well as information used for calculation of ED values. Currently +available functions include, among others, the four- and five-parameter +log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +drc::getMeanFunctions for a full list.

    + + +
    curveStart
    +

    numerical of length equal to the number of parameters for +the curve. Starting values for the curve parameters (optional).

    + +
    +
    +

    Value

    +

    dose-response model with a heterogeneous variance structure of class +drcHetVar.

    +

    The primary objective is to use this model for benchmark dose estimation +based on the hybrid method with a heterogeneous variance structure. This can +be done using the bmdHetVar function.

    +

    A plot method is available, which can be useful for assessing the fit of the +variance structure.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    REFERENCES TO BE ADDED/WRITTEN

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+library(bmd)
+# install.packages("gridExtra") # OPTIONAL - USED FOR PLOTTING A drcHetVar OBJECT.
+
+# ryegrass data
+set.seed(123)
+ryegrass.LL.4.hetVar <- drmHetVar(rootl ~ conc, ~ fitted + I(fitted^2),
+                                  data = ryegrass, fct = LL.4())
+plot(ryegrass.LL.4.hetVar)
+
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1,
+          def = "hybridExc", R = 50, level = 0.95, progressInfo = TRUE, display = TRUE)
+#> Performing bootstrap
+#> 
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+#>           BMD      BMDL
+#> [1,] 0.823838 0.5889243
+bmdHetVar(ryegrass.LL.4.hetVar, bmr = 0.1, backgType = "hybridPercentile", backg = 0.1, 
+          def = "hybridExc", R = 50, level = 0.95, 
+          bootType = "parametric", progressInfo = TRUE, display = TRUE) # parametric bootstrap
+#> Performing bootstrap
+#> 
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+#>           BMD      BMDL
+#> [1,] 0.823838 0.4823374
+
+# barley data
+set.seed(123)
+barley.LL.4.hetVar <- drmHetVar(weight ~ Dose, ~ fitted + I(fitted^2), data = barley, fct = LL.4())
+plot(barley.LL.4.hetVar)
+
+
+# GiantKelp data
+set.seed(123)
+GiantKelp.LL.4.hetVarSq <- drmHetVar(tubeLength ~ dose, ~ fitted + I(fitted^2), 
+                                     data = GiantKelp, fct = LL.4())
+plot(GiantKelp.LL.4.hetVarSq)
+
+
+GiantKelp.LL.4.hetVarLogSq <- drmHetVar(tubeLength ~ dose, ~ log(dose+1) + I(log(dose+1)^2), 
+                                        data = GiantKelp, fct = LL.4())
+plot(GiantKelp.LL.4.hetVarLogSq)
+
+
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/drmMMRE.html b/docs/reference/drmMMRE.html new file mode 100644 index 0000000..888029f --- /dev/null +++ b/docs/reference/drmMMRE.html @@ -0,0 +1,190 @@ + +Dose response modeling with hierarchical variance structure — drmMMRE • bmd + + +
    +
    + + + +
    +
    +
    +

    Dose response modeling with hierarchical variance structure

    + + +
    + +
    +

    Fits a meta-analytic hierarchical dose-response model.

    +
    + +
    + 
    drmMMRE(formula, exp_id, data, fct, type = c("continuous", "binomial"))
    +
    + +
    +

    Arguments

    + + +
    formula
    +

    a symbolic description of the model to be fit of the form +'response ~ dose'

    + + +
    exp_id
    +

    the name of the column in the data set that specifies the +hierarchical structure of the data

    + + +
    data
    +

    a data frame containing the variables in the model.

    + + +
    fct
    +

    a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well as information used for calculation of ED values. Currently +available functions include, among others, the four- and five-parameter +log-logistic models LL.4, LL.5 and the Weibull model W1.4. Use +drc::getMeanFunctions for a full list.

    + + +
    type
    +

    a character string specifying the distribution of the data. The +default is "continuous", corresponding to assuming a normal distribution. +"binary" imply a binomial distribution.

    + +
    +
    +

    Value

    +

    meta-analytic dose-response model with a hierarchical variance +structure of class drcMMRE.

    +

    The primary objective is to use this model for benchmark dose estimation +based on dose-response data with a heterogeneous variance structure.

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    Fitting the meta-analytic model relies on a multivariate meta-analytic model +provided by the function rma.mv in the "metafor" package, which can +be installed by running remotes::install_github("wviechtb/metafor")

    +

    Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor +package. Journal of Statistical Software, 36(3), 1-48. +doi:10.18637/jss.v036.i03

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+library(metafor)
+#> Warning: package 'metafor' was built under R version 4.4.2
+#> Loading required package: Matrix
+#> Loading required package: metadat
+#> Warning: package 'metadat' was built under R version 4.4.2
+#> Loading required package: numDeriv
+#> 
+#> Loading the 'metafor' package (version 4.6-0). For an
+#> introduction to the package please type: help(metafor)
+library(bmd)
+
+set.seed(1)
+data0 <- data.frame(x = rep(drcData::ryegrass$conc, 2),
+                    y = rep(drcData::ryegrass$rootl, 2) +
+                      c(rnorm(n = nrow(drcData::ryegrass), mean = 2, sd = 0.5),
+                        rnorm(n = nrow(drcData::ryegrass), mean = 2.7, sd = 0.7)),
+                    EXP_ID = rep(as.character(1:2), each = nrow(drcData::ryegrass)))
+
+modMMRE <- drmMMRE(y~x, exp_id = EXP_ID, data = data0, fct = LL.4())
+bmd(modMMRE, bmr = 0.1, backgType = "modelBased", def = "relative")
+#>       BMD     BMDL
+#>  1.669136 1.316628
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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zr00MAm$2f@jsJ>A$f3m|{Wq|Nph@;iGmE4D8oc~}{l_h;KPW~m&R(EzEbv~lsdJ}9 J|Kj-Te*iyAxY+;z literal 0 HcmV?d00001 diff --git a/docs/reference/drmOrdinal.html b/docs/reference/drmOrdinal.html new file mode 100644 index 0000000..d4a4e47 --- /dev/null +++ b/docs/reference/drmOrdinal.html @@ -0,0 +1,182 @@ + +Fitting ordinal dose-response models — drmOrdinal • bmd + + +

    +
    + + + +
    +
    +
    +

    Fitting ordinal dose-response models

    + + +
    + +
    +

    A model fitting function for analysis of ordinal dose-response data.

    +
    + +
    + 
    drmOrdinal(levels, dose, weights, blocks, data, fct, p.epsilon = 1e-16)
    +
    + +
    +

    Arguments

    + + +
    levels
    +

    a character vector of the levels of the response variable in +increasing order, as they appear in the supplied data set

    + + +
    dose
    +

    a character string specifying the column with the dose values in +the supplied data set

    + + +
    weights
    +

    a character string specifying the column containing the +number of observations pr. group

    + + +
    blocks
    +

    a character string specifying the column containing the blocks +of the experiment, if available (optional)

    + + +
    data
    +

    a dataframe containing the observations

    + + +
    fct
    +

    a list with three or more elements specifying the non-linear +function, the accompanying self starter function, the names of the parameter +in the non-linear function and, optionally, the first and second derivatives +as well, for the individual fitted curves. For more information see the help +page for the "drm" function in the "drc" package. Currently available +functions for ordinal dose-response models include, among others, the +log-logistic models LL.4, the log-normal model +LN.4 and the two Weibull models W1.4 +and W2.4. Use getMeanFunctions for a +full list.

    + + +
    p.epsilon
    +

    numeric value specifying the lower bound for the +probabilites for each level returned by the function pFun created when +fitting the model. Default value is 10^(-16)

    + +
    +
    +

    Value

    +

    An object of (S3) class 'drcOrdinal'.

    +
    +
    +

    Details

    +

    This functions fits a dose-response model for ordinal dose-response data by +fitting a series of binomial dose-response models.

    +
    +
    +

    References

    +

    # ADD REFERENCES

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+data(guthion)
+guthionS <- subset(guthion, trt == "S")
+
+guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "total",
+                          dose = "dose", data = guthionS, fct = LL.2())
+
+plot(guthionS.LL, xlim = c(15,55)) # uses ggplot
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/expandBinomial.html b/docs/reference/expandBinomial.html new file mode 100644 index 0000000..4f6896b --- /dev/null +++ b/docs/reference/expandBinomial.html @@ -0,0 +1,153 @@ + +Utility function — expandBinomial • bmd + + +
    +
    + + + +
    +
    +
    +

    Utility function

    + + +
    + +
    +

    Utility function for expanding binomial data

    +
    + +
    + 
    expandBinomial(data, number, total, dose, curveid = character(0))
    +
    + +
    +

    Arguments

    + + +
    data
    +

    a data.frame

    + + +
    number
    +

    the name of the column in the data set containing the number +of affected individuals per dose level

    + + +
    total
    +

    the name of the column in the data set containing the total +number of individuals per dose level

    + + +
    dose
    +

    the name of the column in the data set containing the dose +values

    + + +
    curveid
    +

    the name of the column in the data set specifying the curveid +(if available)

    + +
    +
    +

    Value

    +

    data.frame

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +
    +
    +

    Author

    +

    Signe M. Jensen and Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    if (FALSE) { # \dontrun{
+} # }
+ 
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/getStackingWeights.html b/docs/reference/getStackingWeights.html new file mode 100644 index 0000000..34b3401 --- /dev/null +++ b/docs/reference/getStackingWeights.html @@ -0,0 +1,156 @@ + +Model-average dose-response curves — getStackingWeights • bmd + + +
    +
    + + + +
    +
    +
    +

    Model-average dose-response curves

    + + +
    + +
    +

    Computing stacking weights.

    +
    + +
    + 
    getStackingWeights(modelList, nSplits = 2)
    +
    + +
    +

    Arguments

    + + +
    modelList
    +

    list of models of class drc

    + + +
    nSplits
    +

    integer. The Stacking Weights are based on V-fold +cross-validation. The nSplits argument sets the number V of data splits used +in the cross validation.

    + +
    +
    +

    Value

    +

    numeric

    +
    +
    +

    Details

    +

    The aim to provide an R package calculating the benchmark dose (BMD) and the +lower limit of the corresponding 95% confidence interval (BMDL) for +continuous and quantal dose-response data for a range of dose-response +models based on the available definitions of the benchmark dose concepts.

    +

    Details on the implemented definitions and methods can be found in Crump +(2002)

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+library(bmd)
+library(drc)
+library(drcData)
+
+# fit models to aconiazide data
+aconiazide.LL.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LL.3())
+aconiazide.LN.3 <- drm(weightChange ~ dose,data = aconiazide,fct = LN.3())
+aconiazide.W1.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W1.3())
+aconiazide.W2.3 <- drm(weightChange ~ dose,data= aconiazide,fct = W2.3())
+
+getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+                                  aconiazide.W1.3, aconiazide.W2.3))
+#> [1] 2.221066e-07 1.741480e-07 5.000002e-01 4.999994e-01
+getStackingWeights(modelList = list(aconiazide.LL.3, aconiazide.LN.3,
+                                  aconiazide.W1.3, aconiazide.W2.3),
+                  nSplits = 7)
+#> [1] 3.155175e-08 6.086256e-10 7.142857e-01 2.857143e-01
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/index.html b/docs/reference/index.html new file mode 100644 index 0000000..a51b90d --- /dev/null +++ b/docs/reference/index.html @@ -0,0 +1,260 @@ + +Package index • bmd + + +
    +
    + + + +
    +
    +
    +

    Reference

    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    All functions

    +

    +
    +

    AIC(<drcHetVar>)

    +

    S3 method

    +

    AIC(<drcOrdinal>)

    +

    S3 method

    +

    BCa()

    +

    Help funtion to bmdBoot

    +

    BIC(<drcHetVar>)

    +

    S3 method

    +

    BIC(<drcOrdinal>)

    +

    S3 method

    +

    bmd-package bmd

    +

    BMD: Benchmark Dose Modeling

    +

    bmd()

    +

    Benchmark dose estimation

    +

    bmdBoot()

    +

    Benchmark dose estimation using bootstrap

    +

    bmdHetVar()

    +

    Benchmark dose estimation with heterogeneous variance

    +

    bmdHetVarMA()

    +

    Benchmark dose estimation with heterogeneous variance based on model averaging (MA)

    +

    bmdIso()

    +

    Benchmark dose estimation from isotonic regression

    +

    bmdIsoBoot()

    +

    Benchmark dose estimation from isotonic regression

    +

    bmdMA()

    +

    Model-averaged benchmark dose estimation

    +

    bmdMACurve()

    +

    Help funtion to bmdMA

    +

    bmdOrdinal()

    +

    Benchmark dose estimation for ordinal dose-response models

    +

    bmdOrdinalMA()

    +

    Benchmark dose estimation for ordinal dose-response models

    +

    bootDataGen()

    +

    Help funtion to bmdBoot

    +

    bootDataGenOrdinal()

    +

    Help funtion to bmdOrdinal and bmdOrdinalMA

    +

    coef(<drcHetVar>)

    +

    S3 method

    +

    drmHetVar()

    +

    Dose response modeling with heterogeneous variance

    +

    drmMMRE()

    +

    Dose response modeling with hierarchical variance structure

    +

    drmOrdinal()

    +

    Fitting ordinal dose-response models

    +

    expandBinomial()

    +

    Utility function

    +

    getStackingWeights()

    +

    Model-average dose-response curves

    +

    invBmd()

    +

    Help funtion to bmd

    +

    logLik(<drcHetVar>)

    +

    S3 method

    +

    logLik(<drcOrdinal>)

    +

    S3 method

    +

    MACurve()

    +

    Model-average dose-response curves

    +

    monotonicityTest()

    +

    Test for Monotonicity of Relationship Between Two Variables

    +

    PAV()

    +

    Pool-adjacent-violators monotonizing

    +

    plot(<bmd>)

    +

    Plotting benchmark doses

    +

    plot(<drcHetVar>)

    +

    S3 method

    +

    plot(<drcOrdinal>)

    +

    S3 method

    +

    print(<bmdOrdinal>)

    +

    S3 method

    +

    print(<drcHetVar>)

    +

    S3 method

    +

    print(<drcMMRE>)

    +

    S3 method

    +

    print(<drcOrdinal>)

    +

    S3 method

    +

    qplotBmd()

    +

    Plotting benchmark doses using ggplot2

    +

    qplotDrc()

    +

    Plotting fitted dose-response curves using ggplot2

    +

    trendTest()

    +

    Test for Trend in Relationship Between Two Variables

    +

    vcov(<drcMMRE>)

    +

    S3 method

    + + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/invBmd.html b/docs/reference/invBmd.html new file mode 100644 index 0000000..b43a0d6 --- /dev/null +++ b/docs/reference/invBmd.html @@ -0,0 +1,114 @@ + +Help funtion to bmd — invBmd • bmd + + +
    +
    + + + +
    +
    +
    +

    Help funtion to bmd

    + + +
    + +
    +

    Help funtion to bmd

    +
    + +
    + 
    invBmd(
+  object,
+  bmr,
+  level = 0.9,
+  slope,
+  backgType = "modelBased",
+  backg = NA,
+  catLev = NA,
+  extFactor = 10,
+  def,
+  useSD = useSD,
+  sandwich.vcov = FALSE
+)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/logLik.drcHetVar.html b/docs/reference/logLik.drcHetVar.html new file mode 100644 index 0000000..603e703 --- /dev/null +++ b/docs/reference/logLik.drcHetVar.html @@ -0,0 +1,103 @@ + +S3 method — logLik.drcHetVar • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+logLik(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/logLik.drcOrdinal.html b/docs/reference/logLik.drcOrdinal.html new file mode 100644 index 0000000..be3ff46 --- /dev/null +++ b/docs/reference/logLik.drcOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — logLik.drcOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcOrdinal'
+logLik(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/monotonicityTest.html b/docs/reference/monotonicityTest.html new file mode 100644 index 0000000..1a0aa9c --- /dev/null +++ b/docs/reference/monotonicityTest.html @@ -0,0 +1,209 @@ + +Test for Monotonicity of Relationship Between Two Variables — monotonicityTest • bmd + + +
    +
    + + + +
    +
    +
    +

    Test for Monotonicity of Relationship Between Two Variables

    + + +
    + +
    +

    Conducts a test for monotonicity between a numeric independent variable +x and a numeric dependent variable y using specified +statistical tests.

    +
    + +
    + 
    monotonicityTest(
+  x,
+  y,
+  data,
+  test = c("jonckheere", "bartholomew"),
+  level = 0.05,
+  ...
+)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A numeric vector or the name of the independent variable (if +data is provided).

    + + +
    y
    +

    A numeric vector or the name of the dependent variable (if +data is provided).

    + + +
    data
    +

    An optional data frame containing the variables x and +y. If provided, x and y should be column names in +data.

    + + +
    test
    +

    A character string specifying the test to use. Must be one of +"jonckheere" (default) or "bartholomew".

    + + +
    level
    +

    Significance level for the test. Defaults to 0.05.

    + + +
    ...
    +

    Additional arguments passed to the underlying test functions.

    + +
    +
    +

    Value

    +

    A list with the following components:

    +
    p.value
    +

    The p-value of +the test.

    +
    acceptMonotonicity
    +

    A logical value indicating whether +monotonicity is accepted (TRUE) or rejected (FALSE) based on +the specified significance level.

    + +
    +
    +

    Details

    +

    The function tests the monotonicity of the relationship between x and +y based on the specified test:

    • "jonckheere": +Uses the Jonckheere-Terpstra test to assess monotonic trends.

      • +

    • "bartholomew": Uses Bartholomew's test to assess monotonicity.

      • +

    The direction of the monotonicity (increasing or decreasing) is determined +by the sign of the coefficient from a simple linear model lm(y ~ x).

    +
    +
    +

    References

    +

    A. R. Jonckheere (1954). "A Distribution-Free k-Sample Test +Against Ordered Alternatives." D. J. Bartholomew (1961). "Ordered tests in +the analysis of variance." OECD (2006). Rapport No. 54, Annexes.

    +
    +
    +

    See also

    +

    .jonckheereTest, .bartholomewTest

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+# Example with custom data
+x <- c(1, 2, 3, 4, 5)
+y <- c(2, 4, 6, 8, 10)
+result <- monotonicityTest(x, y, test = "jonckheere")
+print(result)
+#> $p.value
+#> [1] 0.007152939
+#> 
+#> $acceptMonotonicity
+#> [1] TRUE
+#> 
+
+data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6))
+result <- monotonicityTest("conc", "rootl", data = drcData::ryegrass, test = "bartholomew")
+#> Loading required namespace: isotone
+print(result)
+#> $p.value
+#> [1] 0
+#> 
+#> $acceptMonotonicity
+#> [1] TRUE
+#> 
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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zngXRK-NC|rC8z7hQoijv|JA%xVJ7C_^5Ftp&Py9VNB4qOcxjH5Hd}J2HuBQn55R&7 zm-aEn#F)aNGH>m(rz0WK4oO!}jzV|5mHYso0;`ap;B;}Ec+0Wv!OFOj3p2tm@ zRSU27N6VSpy6QdjQL~b=kzc-{fV~7_LTaW1 z%lPm@Kt0TIgpcEZs|hn~y?^lt@hFgyS~*rQt2eV6(4n*O*VXWY%Q1!u!j_IZz>s0y zVDmw=O6u2dbi-d_SuFX9UGYr)S($}!ci7V7-DA(;?*LEhnvV&_IFL;A?eh;mK}EK1x>HU)7~jS~xqhWn{bm`GU~Trw83f zC%tEKE%Pm#@9vcso?5!MktNG^U7~MXoY<}YEofs;-g@}ISX>#hs*@XB{nPo_Tgvuy zREm`IxaLM)r6_2$O!_pKl;?sx#YBBBPP_RQbON;Q(%!pV>C*m<2seeLWANLhZCzJR zNu#orr5<^or#H?M8~cXi!vD5^L{LF!1$Q%kUl*>R)uHQ_<&DEh)XjwC&}Hgble=#V zTN}4GZ|{0&X$}_l?iHd|auoTY(?9*|$+I-5;4YZX?JXWHJs_z*G&6ot$+5iAHCz!h z7&FxX&=JtGn$O}3bo$djOm*zKZs~F;30v@9PlEZ^4CnR=y1=|*c2rtc)ZzeZ4OUOw ff7-uWpmN@2yt5s1dEoMr`ae8ey$@3Nhh6wDnrno@ literal 0 HcmV?d00001 diff --git a/docs/reference/plot.bmd.html b/docs/reference/plot.bmd.html new file mode 100644 index 0000000..01b9884 --- /dev/null +++ b/docs/reference/plot.bmd.html @@ -0,0 +1,365 @@ + +Plotting benchmark doses — plot.bmd • bmd + + +
    +
    + + + +
    +
    +
    +

    Plotting benchmark doses

    + + +
    + +
    +

    plot.bmd displays benchmark dose values with options to plot +confidence intervals as well.

    +
    + +
    + 
    # S3 method for class 'bmd'
+plot(x, ..., interval = c("BMDL", "twosided", "none"))
    +
    + +
    +

    Arguments

    + + +
    x
    +

    an object of class 'bmd'.

    + + +
    ...
    +

    arguments to be passed on to plot.drc, if add = +FALSE

    + + +
    interval
    +

    option to plot only the lower limit of the confidence +interval for the benchmark dose ("BMDL", default), both limit of the +confidence interval ("twosided"), or no confidence interval ("none").

    + +
    +
    +

    Value

    +

    Creates a plot. No value returned.

    +
    +
    +

    Details

    +

    This function is a simple function to plot benchmark dose values along with +the fitted curve.

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde.

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+
+## Fitting model and calculating BMD. 
+model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative")
+#>       BMD     BMDL
+#>  1.499026 1.169727
+
+## Plotting
+plot(bmd0)
+
+
+# Plot both limits of confidence interval
+plot(bmd0, interval = "twosided")
+
+
+# Pass argument to plot.bmd to plot confidence band around curve
+plot(bmd0, type = "confidence")
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+
+
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/plot.drcHetVar.html b/docs/reference/plot.drcHetVar.html new file mode 100644 index 0000000..3ebbcbc --- /dev/null +++ b/docs/reference/plot.drcHetVar.html @@ -0,0 +1,103 @@ + +S3 method — plot.drcHetVar • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+plot(x, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/plot.drcOrdinal.html b/docs/reference/plot.drcOrdinal.html new file mode 100644 index 0000000..eca5641 --- /dev/null +++ b/docs/reference/plot.drcOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — plot.drcOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcOrdinal'
+plot(x, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/print.bmdOrdinal.html b/docs/reference/print.bmdOrdinal.html new file mode 100644 index 0000000..3bacf8b --- /dev/null +++ b/docs/reference/print.bmdOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — print.bmdOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'bmdOrdinal'
+print(x, ..., digits = max(3, getOption("digits") - 3))
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/print.drcHetVar.html b/docs/reference/print.drcHetVar.html new file mode 100644 index 0000000..2bb0e3b --- /dev/null +++ b/docs/reference/print.drcHetVar.html @@ -0,0 +1,103 @@ + +S3 method — print.drcHetVar • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcHetVar'
+print(x, ..., digits = max(3, getOption("digits") - 3))
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/print.drcMMRE.html b/docs/reference/print.drcMMRE.html new file mode 100644 index 0000000..b2fe957 --- /dev/null +++ b/docs/reference/print.drcMMRE.html @@ -0,0 +1,103 @@ + +S3 method — print.drcMMRE • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcMMRE'
+print(x, ..., digits = max(3, getOption("digits") - 3))
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/print.drcOrdinal.html b/docs/reference/print.drcOrdinal.html new file mode 100644 index 0000000..20d1ae1 --- /dev/null +++ b/docs/reference/print.drcOrdinal.html @@ -0,0 +1,103 @@ + +S3 method — print.drcOrdinal • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcOrdinal'
+print(x, ..., digits = max(3, getOption("digits") - 3))
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/qplotBmd-1.png b/docs/reference/qplotBmd-1.png new file mode 100644 index 0000000000000000000000000000000000000000..6f8ac78d3c531474a7ebb418eb1a324630de3236 GIT binary patch literal 41544 zcmbrm2UJv9)HPUU+ia_?V!%)+Nem=G1bP}P%wZJ6p$q5tVI%uN)k{|f=D(i z8HplM2?~fPK{CufugY)cpEa{)t@&N6yJ@L<@4j9{*5M_imce~YR6+|efuPrjVB<-grq zgs(2jTGFqxVDzk6v-IDN*nP5hf^g81C6`}Z9(C^2iJFPybcUg^n)ygVHX zi|D2~o_P&cnXRW(CIr5p#Co`X_3G8J;wp3J&J7D@vE1hLi`#6K7Cxka_ z7`)z65}_Gh+5K|*|F#`GUfZ}{^|*8AzNeV(k!-IOv?c+WV-FW@aQJ@jX!M=jZQhf4 z)>#yPerHQ>_R5U!)o0pDQrgnRILQO;*(;IJRv)-1bNq9NX|`9>p9)J^znT2+h^pVUgNVI_Xxr-1$>3jh!sO<~V%wKV9GDpt^N5@58PWX8$|J^3b6$c7%T1p^QEM zEm*K3JJusGFyCB&f4TD>w}tImN}`r?KBwAuwB0OJRaNyYYtgPswrx0Z{>@ww{^yi5 zF3(JrK3ZB_qHFSa>Gqr7yUI*-v6XBQA)&1^maBQNC(l{+;vhdnSPxHl$!<~G+0y0E z1yeMIdK-(bRumOgu6uW*XzOevo6-usG>3%P*jQzwKbI5-Hmcr}in#sgYz{VW%^D4^ z)~;PauU>6>eTBt(nbTm!;kLK8Pg*{LHCpnI=BB`+CXXtM?gdXS6zq#D*LrLq&EdYU 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zwQsK{rA6HMpk_5=Zu4;FfJ%7WCr00f_z(j}Ls`TLh#5K4akx|pZs1~Y@xHg+S+8mL z>s(cfsNn+@w)55r3^e?w+OlJiE3cWZjXmY{Y{v!^LV`tR1y-eT**WJCRQgxnHggUx_Cxip zRxy@?Twxms+edHcxN-A*e0-eFdWV7aL{cr*l4a9!@3??m@6 zD}NKl#{ICjR$)1iZZd!*i+NPW0VpINpekQ?yLvYCD>8#aOx|OE8Yap&YFQT~HLF%0 zrq3WaS&HM5R?nU`Uh<`~GO4)bE?wf%<7k6wnBfWwgmDF&L=*1{b8+s4*y6XXov3E} zqx3ope?m@Jbne=9F6Y<& a9}Fw5?sk1}<{kM~7SpVzCQM$q<=+4pD$DTz literal 0 HcmV?d00001 diff --git a/docs/reference/qplotBmd.html b/docs/reference/qplotBmd.html new file mode 100644 index 0000000..6a7f7f5 --- /dev/null +++ b/docs/reference/qplotBmd.html @@ -0,0 +1,678 @@ + +Plotting benchmark doses using ggplot2 — qplotBmd • bmd + + +
    +
    + + + +
    +
    +
    +

    Plotting benchmark doses using ggplot2

    + + +
    + +
    +

    qplotBmd displays benchmark dose values with options to plot +confidence intervals as well using ggplot2.

    +
    + +
    + 
    qplotBmd(
+  x,
+  ...,
+  interval = c("BMDL", "twosided", "none"),
+  col = FALSE,
+  add = FALSE
+)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    an object of class 'bmd'.

    + + +
    ...
    +

    arguments to be passed on to qplotDrc, if add = FALSE

    + + +
    interval
    +

    option to plot only the lower limit of the confidence +interval for the benchmark dose ("BMDL", default), both limit of the +confidence interval ("twosided"), or no confidence interval ("none").

    + + +
    col
    +

    logical. If TRUE then multiple curves specified by "curveid" in +the dose-response model are distinguised by colours rather than point shapes +and line types

    + + +
    add
    +

    logical. If TRUE then the functions returns a list of plot layers +to be added to an already existing ggplot.

    + +
    +
    +

    Value

    +

    A ggplot object. If the option add is used, a list of +ggplot layers is returned.

    +
    +
    +

    Details

    +

    This function is a simple function to plot benchmark dose values

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde.

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+
+## Fitting model and calculating BMD. 
+model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
+bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative")
+#>       BMD     BMDL
+#>  1.499026 1.169727
+
+# Plot
+qplotBmd(bmd0, interval = "twosided", add = FALSE)
+
+
+qplotDrc(model,type="confidence") +
+  qplotBmd(bmd0, interval = "twosided", add = TRUE)
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+
+
+qplotBmd(bmd0, interval = "twosided", add = FALSE)
+
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
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    +
    + + + +
    +
    +
    +

    Plotting fitted dose-response curves using ggplot2

    + + +
    + +
    +

    qplotDrc displays fitted curves and observations in the same plot +window, distinguishing between curves by different plot symbols and line +types or colours using ggplot2.

    +
    + +
    + 
    qplotDrc(
+  x,
+  add = FALSE,
+  level = NULL,
+  type = c("average", "all", "bars", "none", "obs", "confidence"),
+  gridsize = 250,
+  xtrans = "pseudo_log",
+  xlab,
+  xlim,
+  ytrans = NULL,
+  ylab,
+  ylim,
+  col = FALSE,
+  normal = FALSE,
+  normRef = 1,
+  confidence.level = 0.95
+)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    an object of class 'drc'.

    + + +
    add
    +

    logical. If TRUE then the functions returns a list of plot layers +to be added to an already existing ggplot.

    + + +
    level
    +

    vector of curve levels to plot. To plot only the curves +specified by their names.

    + + +
    type
    +

    a character string specifying how to plot the data. There are +currently 5 options: "average" (averages and fitted curve(s); default), +"none" (only the fitted curve(s)), "obs" (only the data points), "all" (all +data points and fitted curve(s)), "bars" (averages and fitted curve(s) with +model-based standard errors (see Details)), and "confidence" (confidence +bands for fitted curve(s)).

    + + +
    gridsize
    +

    numeric. Number of points in the grid used for plotting the +fitted curves.

    + + +
    xtrans
    +

    Transformation to use on the x-axis. The default is +"pesudo_log", which is a logarithmic transformation with a smooth transition +to 0. Other options include (among others) "log" and "identity". Can be +overridden by adding a scale using the scale_x_continuous function.

    + + +
    xlab
    +

    an optional label for the x axis.

    + + +
    xlim
    +

    a numeric vector of length two, containing the lower and upper +limit for the x axis.

    + + +
    ytrans
    +

    Transformation to use on the y-axis. The default is no +transformation. Other options include (among others) "pseudo_log" and "log" +and. Can be overridden by adding a scale using the scale_y_continuous +function.

    + + +
    ylab
    +

    an optional label for the y axis.

    + + +
    ylim
    +

    a numeric vector of length two, containing the lower and upper +limit for the y axis.

    + + +
    col
    +

    logical. If TRUE default ggplot colours are used, can be +overridden by scale_color_manual. If FALSE (default) no colours are +used.

    + + +
    normal
    +

    logical. If TRUE the plot of the normalized data and fitted +curves are shown (for details see Weimer et al. (2012) for details).

    + + +
    normRef
    +

    numeric specifying the reference for the normalization +(default is 1).

    + + +
    confidence.level
    +

    confidence level for error bars and confidence +bands. Defaults to 0.95.

    + +
    +
    +

    Value

    +

    A ggplot object. If the option add is used, a list of +ggplot layers is returned.

    +
    +
    +

    Details

    +

    This function largely seeks to mimic the behaviour of the plot method +for the drc package using the ggplot2 package for plotting.

    +

    The use of xlim allows changing the range of the x axis, +extrapolating the fitted dose-response curves. Note that changing the range +on the x axis may also entail a change of the range on the y axis.

    +

    See colors for the available colours.

    +

    Suitable labels are automatically provided.

    +

    The model-based standard errors used for the error bars are calculated as +the fitted value plus/minus the estimated error times the 1-(alpha/2) +quantile in the t distribution with degrees of freedom equal to the residual +degrees of freedom for the model (or using a standard normal distribution in +case of binomial and poisson data), where alpha=1-confidence.level. The +standard errors are obtained using the predict method with the arguments +interval = "confidence" and level=confidence.level.

    +
    +
    +

    References

    +

    Weimer, M., Jiang, X., Ponta, O., Stanzel, S., Freyberger, A., +Kopp-Schneider, A. (2012) The impact of data transformations on +concentration-response modeling. Toxicology Letters, 213, +292–298.

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde. Based on plot.drc by Christian Ritz and +Jens C. Streibig with Contributions from Xiaoyan Wang and Greg Warnes.

    +
    + +
    +

    Examples

    + 
    
+library(drc)
+library(drcData)
+library(ggplot2)
+
+## Fitting models to be plotted below
+ryegrass.m1 <- drm(rootl~conc, data = ryegrass, fct = LL.4())
+ryegrass.m2 <- drm(rootl~conc, data = ryegrass, fct = LL.3())  # lower limit fixed at 0
+
+## Plotting observations and fitted curve for the first model
+p <- qplotDrc(ryegrass.m1) 
+p
+
+
+## Add confidence region for the first model.
+p + qplotDrc(ryegrass.m1, type="confidence", add = TRUE)$confBandLayer 
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+
+
+## Plot both models
+p + qplotDrc(ryegrass.m2, add = TRUE)$curveLayer
+
+
+## Fitting model to be plotted below
+spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4())
+
+## Plot with no colours
+qplotDrc(spinach.m1)
+
+
+## Plot with default colours
+qplotDrc(spinach.m1, col = TRUE)
+
+
+## Plot with specified colours
+qplotDrc(spinach.m1, col = TRUE) + 
+  scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+                                "darkslategray4", "plum4"))
+
+
+## Plot of curves 1 and 2 only
+qplotDrc(spinach.m1, level = c(1,4))
+
+
+## Plot with confidence regions
+qplotDrc(spinach.m1, col = TRUE, type = "confidence")
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+
+
+## Plot points and add confidence regions. Confidence regions are coloured by the "fill" aesthetic.
+## Customising the x scale by adding a new scale.
+qplotDrc(spinach.m1, col = TRUE, type = "confidence") +
+  qplotDrc(spinach.m1, col = TRUE, type = "average", add = TRUE)$obsLayer + 
+  scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+                                "darkslategray4", "plum4"))+ 
+  scale_fill_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod",
+                               "darkslategray4", "plum4")) +
+  scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1)))
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Warning: Recycling array of length 1 in array-vector arithmetic is deprecated.
+#>   Use c() or as.vector() instead.
+#> Scale for x is already present.
+#> Adding another scale for x, which will replace the existing scale.
+
+
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/trendTest.html b/docs/reference/trendTest.html new file mode 100644 index 0000000..bbec0a9 --- /dev/null +++ b/docs/reference/trendTest.html @@ -0,0 +1,247 @@ + +Test for Trend in Relationship Between Two Variables — trendTest • bmd + + +
    +
    + + + +
    +
    +
    +

    Test for Trend in Relationship Between Two Variables

    + + +
    + +
    +

    Conducts a test for trends between a numeric independent variable x +and a numeric dependent variable y using specified statistical tests.

    +
    + +
    + 
    trendTest(x, y, data, test = c("william", "shirley", "tukey"), level = 0.05)
    +
    + +
    +

    Arguments

    + + +
    x
    +

    A numeric vector or the name of the independent variable (if +data is provided).

    + + +
    y
    +

    A numeric vector or the name of the dependent variable (if +data is provided).

    + + +
    data
    +

    An optional data frame containing the variables x and +y. If provided, x and y should be column names in +data.

    + + +
    test
    +

    A character string specifying the test to use. Must be one of +"william", "shirley", or "tukey" (default).

    + + +
    level
    +

    Significance level for the test. Defaults to 0.05.

    + +
    +
    +

    Value

    +

    A list with the following components:

    +
    p.values
    +

    A numeric +vector of p-values for the tests (if applicable).

    +
    decisions
    +

    A +character vector indicating whether the trend is "accept" or +"reject" based on the test results.

    +
    acceptTrend
    +

    A logical +value indicating whether a trend is accepted (TRUE) or rejected +(FALSE) based on the specified significance level.

    + +
    +
    +

    Details

    +

    The function tests for a trend in the relationship between x and +y based on the specified test:

    • "william": +Applies Williams' test to assess trend significance.

      • +

    • "shirley": Uses Shirley's test for trend analysis with ordered +alternatives.

      • +

    • "tukey": Implements the Tukey trend test using +multiple marginal models.

      • +

    The direction of the trend (increasing or decreasing) is determined by the +slope of the linear model lm(y ~ x).

    +
    +
    +

    References

    +

    Williams, D. A. (1971). "A test for differences between +treatment means when several dose levels are compared with a zero dose +control." Biometrics, 27(1), 103-117. Shirley, E. (1977). "A non-parametric +equivalent of Williams' test for contrasting increasing dose levels of a +treatment." Biometrics, 33(2), 386-389. Schaarschmidt, F. et al. (2021). +"The Tukey trend test: Multiplicity adjustment using multiple marginal +models" Biometrics, 78(2), 789-797.

    +
    +
    +

    See also

    +

    .williamsTest, .shirleyTest, .tukeytrendfit

    +
    +
    +

    Author

    +

    Jens Riis Baalkilde

    +
    + +
    +

    Examples

    + 
    
+# Example with custom data
+x <- c(1, 2, 3, 4, 5)
+y <- c(2, 4, 6, 8, 10)
+result <- trendTest(x, y, test = "tukey")
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+#> Warning: essentially perfect fit: summary may be unreliable
+print(result)
+#> $p.values
+#>       xari: xari       xord: xord xarilog: xarilog 
+#>     0.000000e+00     0.000000e+00     2.084999e-13 
+#> 
+#> $decisions
+#>       xari: xari       xord: xord xarilog: xarilog 
+#>         "accept"         "accept"         "accept" 
+#> 
+#> $acceptTrend
+#> [1] TRUE
+#> 
+
+# Example with a data frame
+data <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 9, 8, 7, 6))
+result <- trendTest("x", "y", data = data, test = "shirley")
+print(result)
+#> $p.values
+#> NULL
+#> 
+#> $decisions
+#>     ctr     
+#> mu1 "reject"
+#> mu2 "reject"
+#> mu3 "reject"
+#> mu4 "accept"
+#> 
+#> $acceptTrend
+#> [1] TRUE
+#> 
+
+
    +
    +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/reference/vcov.drcMMRE.html b/docs/reference/vcov.drcMMRE.html new file mode 100644 index 0000000..46cacdb --- /dev/null +++ b/docs/reference/vcov.drcMMRE.html @@ -0,0 +1,103 @@ + +S3 method — vcov.drcMMRE • bmd + + +
    +
    + + + +
    +
    +
    +

    S3 method

    + + +
    + +
    +

    S3 method

    +
    + +
    + 
    # S3 method for class 'drcMMRE'
+vcov(object, ...)
    +
    + + +
    + +
    + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +
    + + + + + + + + diff --git a/docs/sitemap.xml b/docs/sitemap.xml new file mode 100644 index 0000000..1b9da5b --- /dev/null +++ b/docs/sitemap.xml @@ -0,0 +1,57 @@ + +/404.html +/articles/basic-bmd-functions.html +/articles/bmd_Package.html +/articles/index.html +/articles/model-averaging.html +/articles/specialized-models.html +/articles/statistical-tests.html +/articles/utilities.html +/articles/visualization.html +/authors.html +/index.html +/LICENSE-text.html +/reference/AIC.drcHetVar.html +/reference/AIC.drcOrdinal.html +/reference/BCa.html +/reference/BIC.drcHetVar.html +/reference/BIC.drcOrdinal.html +/reference/bmd-package.html +/reference/bmd.html +/reference/bmdBoot.html +/reference/bmdHetVar.html +/reference/bmdHetVarMA.html +/reference/bmdIso.html +/reference/bmdIsoBoot.html +/reference/bmdMA.html +/reference/bmdMACurve.html +/reference/bmdOrdinal.html +/reference/bmdOrdinalMA.html +/reference/bootDataGen.html +/reference/bootDataGenOrdinal.html +/reference/coef.drcHetVar.html +/reference/drmHetVar.html +/reference/drmMMRE.html +/reference/drmOrdinal.html +/reference/expandBinomial.html +/reference/getStackingWeights.html +/reference/index.html +/reference/invBmd.html +/reference/logLik.drcHetVar.html +/reference/logLik.drcOrdinal.html +/reference/MACurve.html +/reference/monotonicityTest.html +/reference/PAV.html +/reference/plot.bmd.html +/reference/plot.drcHetVar.html +/reference/plot.drcOrdinal.html +/reference/print.bmdOrdinal.html +/reference/print.drcHetVar.html +/reference/print.drcMMRE.html +/reference/print.drcOrdinal.html +/reference/qplotBmd.html +/reference/qplotDrc.html +/reference/trendTest.html +/reference/vcov.drcMMRE.html + + diff --git a/vignettes/visualization.Rmd b/vignettes/visualization.Rmd index a371e53..78fbf42 100644 --- a/vignettes/visualization.Rmd +++ b/vignettes/visualization.Rmd @@ -10,7 +10,9 @@ vignette: > ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, - comment = "#>" + comment = "#>", + warning = FALSE, + message = FALSE ) ``` @@ -19,3 +21,163 @@ library(bmd) ``` Visualization functions included in the `bmd` package are: "qplotDrc", "qplotBmd", "plot.bmd". + + +```{r} +library(drc) + +library(drcData) + + + +## Fitting model and calculating BMD. + +model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4()) + +bmd0 <- bmd(model, bmr = 0.1, backgType = "modelBased", def = "relative") + + + +## Plotting + +plot(bmd0) + + + +# Plot both limits of confidence interval + +plot(bmd0, interval = "twosided") + + + +# Pass argument to plot.bmd to plot confidence band around curve + +plot(bmd0, type = "confidence") + +``` + + + +```{r} +# Plot + +qplotBmd(bmd0, interval = "twosided", add = FALSE) + + + +qplotDrc(model,type="confidence") + + + qplotBmd(bmd0, interval = "twosided", add = TRUE) + + + +qplotBmd(bmd0, interval = "twosided", add = FALSE) + + +``` + + +## qplotDrc + +```{r} + +library(drc) + +library(drcData) + +library(ggplot2) + + + +## Fitting models to be plotted below + +ryegrass.m1 <- drm(rootl~conc, data = ryegrass, fct = LL.4()) + +ryegrass.m2 <- drm(rootl~conc, data = ryegrass, fct = LL.3()) # lower limit fixed at 0 + + + +## Plotting observations and fitted curve for the first model + +p <- qplotDrc(ryegrass.m1) + +p + + + +## Add confidence region for the first model. + +p + qplotDrc(ryegrass.m1, type="confidence", add = TRUE)$confBandLayer + + + +## Plot both models + +p + qplotDrc(ryegrass.m2, add = TRUE)$curveLayer + + + +## Fitting model to be plotted below + +spinach.m1 <- drm(SLOPE~DOSE, CURVE, data = spinach, fct = LL.4()) + + + +## Plot with no colours + +qplotDrc(spinach.m1) + + + +## Plot with default colours + +qplotDrc(spinach.m1, col = TRUE) + + + +## Plot with specified colours + +qplotDrc(spinach.m1, col = TRUE) + + + scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", + + "darkslategray4", "plum4")) + + + +## Plot of curves 1 and 2 only + +qplotDrc(spinach.m1, level = c(1,4)) + + + +## Plot with confidence regions + +qplotDrc(spinach.m1, col = TRUE, type = "confidence") + + + +## Plot points and add confidence regions. Confidence regions are coloured by the "fill" aesthetic. + +## Customising the x scale by adding a new scale. + +qplotDrc(spinach.m1, col = TRUE, type = "confidence") + + + qplotDrc(spinach.m1, col = TRUE, type = "average", add = TRUE)$obsLayer + + + scale_color_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", + + "darkslategray4", "plum4"))+ + + scale_fill_manual(values = c("darkolivegreen4", "lightcoral", "goldenrod", + + "darkslategray4", "plum4")) + + + scale_x_continuous(trans = scales:::pseudo_log_trans(sigma = 0.2, base = exp(1))) + + + + +``` + + From 2d04caac592483c54cd87a11f608cd6fcf6bc417 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Fri, 4 Jul 2025 18:04:08 +0200 Subject: [PATCH 05/17] updated S3 documentation --- NAMESPACE | 2 ++ R/AIC.drcOrdinal.R | 10 +++++++++- R/bmd-package.R | 2 +- R/logLik.drcHetVar.R | 10 ++++++++-- R/logLik.drcOrdinal.R | 10 ++++++++-- R/plot.bmd.R | 4 ++-- R/plot.drcHetVar.R | 10 ++++++++-- R/plot.drcOrdinal.R | 9 ++++++++- R/print.bmd.R | 10 ++++++++++ R/print.bmdHetVar.R | 10 ++++++++++ R/print.bmdOrdinal.R | 11 +++++++++-- R/print.drcMMRE.R | 11 +++++++++-- R/print.drcOrdinal.R | 11 +++++++++-- man/AIC.drcOrdinal.Rd | 14 ++++++++++++-- man/bmd-package.Rd | 1 - man/logLik.drcHetVar.Rd | 12 ++++++++++-- man/logLik.drcOrdinal.Rd | 12 ++++++++++-- man/plot.bmd.Rd | 3 +-- man/plot.drcHetVar.Rd | 12 ++++++++++-- man/plot.drcOrdinal.Rd | 12 ++++++++++-- man/print.bmd.Rd | 21 +++++++++++++++++++++ man/print.bmdHetVar.Rd | 21 +++++++++++++++++++++ man/print.bmdOrdinal.Rd | 14 ++++++++++++-- man/print.drcMMRE.Rd | 14 ++++++++++++-- man/print.drcOrdinal.Rd | 14 ++++++++++++-- 25 files changed, 224 insertions(+), 36 deletions(-) create mode 100644 man/print.bmd.Rd create mode 100644 man/print.bmdHetVar.Rd diff --git a/NAMESPACE b/NAMESPACE index fbb6e16..9f45c0a 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -10,6 +10,8 @@ S3method(logLik,drcOrdinal) S3method(plot,bmd) S3method(plot,drcHetVar) S3method(plot,drcOrdinal) +S3method(print,bmd) +S3method(print,bmdHetVar) S3method(print,bmdOrdinal) S3method(print,drcHetVar) S3method(print,drcMMRE) diff --git a/R/AIC.drcOrdinal.R b/R/AIC.drcOrdinal.R index b70815f..7cc332f 100644 --- a/R/AIC.drcOrdinal.R +++ b/R/AIC.drcOrdinal.R @@ -1,5 +1,13 @@ -#' @title S3 method +#' AIC Method for drcOrdinal Objects +#' +#' Calculates the Akaike Information Criterion for drcOrdinal model objects. +#' +#' @param object A drcOrdinal model object +#' @param ... Additional arguments (not used) +#' @param k The penalty per parameter to be used; default is 2 +#' +#' @return The AIC value #' @export AIC.drcOrdinal <- function(object, ..., k = 2) { dots <- list(...) diff --git a/R/bmd-package.R b/R/bmd-package.R index 7c7c46a..d524bd6 100644 --- a/R/bmd-package.R +++ b/R/bmd-package.R @@ -14,5 +14,5 @@ #' @importFrom utils setTxtProgressBar txtProgressBar #' #' @name bmd-package -#' @aliases bmd +#' @aliases bmd-package "_PACKAGE" \ No newline at end of file diff --git a/R/logLik.drcHetVar.R b/R/logLik.drcHetVar.R index 1f4303c..4025409 100644 --- a/R/logLik.drcHetVar.R +++ b/R/logLik.drcHetVar.R @@ -1,5 +1,11 @@ - -#' @title S3 method +#' Log-Likelihood Method for drcHetVar Objects +#' +#' Extracts the log-likelihood from drcHetVar model objects. +#' +#' @param object A drcHetVar model object +#' @param ... Additional arguments (not used) +#' +#' @return The log-likelihood value #' @export logLik.drcHetVar <- function(object, ...){ - object$sumList$numObs/2 * log(2*pi) - object$value/2 diff --git a/R/logLik.drcOrdinal.R b/R/logLik.drcOrdinal.R index 3a24219..c6178c0 100644 --- a/R/logLik.drcOrdinal.R +++ b/R/logLik.drcOrdinal.R @@ -1,5 +1,11 @@ - -#' @title S3 method +#' Log-Likelihood Method for drcOrdinal Objects +#' +#' Extracts the log-likelihood from drcOrdinal model objects. +#' +#' @param object A drcOrdinal model object +#' @param ... Additional arguments (not used) +#' +#' @return The log-likelihood value #' @export logLik.drcOrdinal <- function(object, ...){ dots <- list(...) diff --git a/R/plot.bmd.R b/R/plot.bmd.R index 69b1d86..03b14c8 100644 --- a/R/plot.bmd.R +++ b/R/plot.bmd.R @@ -1,4 +1,4 @@ -#' Plotting benchmark doses +#' Plotting method for benchmark doses modeling object #' #' \code{plot.bmd} displays benchmark dose values with options to plot #' confidence intervals as well. @@ -6,7 +6,7 @@ #' This function is a simple function to plot benchmark dose values along with #' the fitted curve. #' -#' @aliases plot.bmd \method{plot}{bmd} +#' @aliases plot.bmd #' @param x an object of class 'bmd'. #' @param ... arguments to be passed on to \code{plot.drc}, if \code{add = #' FALSE} diff --git a/R/plot.drcHetVar.R b/R/plot.drcHetVar.R index 218e3de..97c1d03 100644 --- a/R/plot.drcHetVar.R +++ b/R/plot.drcHetVar.R @@ -1,5 +1,11 @@ - -#' @title S3 method +#' Plot Method for drcHetVar Objects +#' +#' Plots the fitted dose-response curve for drcHetVar model objects. +#' +#' @param x A drcHetVar model object +#' @param ... Additional graphical parameters passed to plot +#' +#' @return Invisibly returns the x object #' @export plot.drcHetVar <- function(x, ...){ object <- x diff --git a/R/plot.drcOrdinal.R b/R/plot.drcOrdinal.R index ed1375f..6f48e9c 100644 --- a/R/plot.drcOrdinal.R +++ b/R/plot.drcOrdinal.R @@ -1,5 +1,12 @@ -#' @title S3 method +#' Plot Method for drcOrdinal Objects +#' +#' Plots the fitted dose-response curve for drcOrdinal model objects. +#' +#' @param x A drcOrdinal model object +#' @param ... Additional graphical parameters passed to plot +#' +#' @return Invisibly returns the x object #' @export plot.drcOrdinal <- function(x, ...){ object <- x diff --git a/R/print.bmd.R b/R/print.bmd.R index ee19688..b5cf362 100644 --- a/R/print.bmd.R +++ b/R/print.bmd.R @@ -1,3 +1,13 @@ +#' Print Method for bmd Objects +#' +#' Prints a summary of a bmd model object. +#' +#' @param x A bmd model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object +#' @export "print.bmd" <- function(x, ..., digits = max(3, getOption("digits") - 3)) { object <- x diff --git a/R/print.bmdHetVar.R b/R/print.bmdHetVar.R index 9457125..bfd3210 100644 --- a/R/print.bmdHetVar.R +++ b/R/print.bmdHetVar.R @@ -1,3 +1,13 @@ +#' Print Method for drcHetVar Objects +#' +#' Prints a summary of a drcHetVar model object. +#' +#' @param x A drcHetVar model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object +#' @export "print.bmdHetVar" <- function(x, ..., digits = max(3, getOption("digits") - 3)) { object <- x diff --git a/R/print.bmdOrdinal.R b/R/print.bmdOrdinal.R index 6b974dc..4a12f55 100644 --- a/R/print.bmdOrdinal.R +++ b/R/print.bmdOrdinal.R @@ -1,5 +1,12 @@ - -#' @title S3 method +#' Print Method for bmdOrdinalr Objects +#' +#' Prints a summary of a bmdOrdinal model object. +#' +#' @param x A bmdOrdinal model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object #' @export print.bmdOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) { diff --git a/R/print.drcMMRE.R b/R/print.drcMMRE.R index c13cd88..14a1817 100644 --- a/R/print.drcMMRE.R +++ b/R/print.drcMMRE.R @@ -1,5 +1,12 @@ - -#' @title S3 method +#' Print Method for drcMMRE Objects +#' +#' Prints a summary of a drcMMRE model object. +#' +#' @param x A drcMMRE model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object #' @export print.drcMMRE <- function (x, ..., digits = max(3, getOption("digits") - 3)) { diff --git a/R/print.drcOrdinal.R b/R/print.drcOrdinal.R index 508c94c..cfa8354 100644 --- a/R/print.drcOrdinal.R +++ b/R/print.drcOrdinal.R @@ -1,5 +1,12 @@ -print.drcOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) -#' @title S3 method +#' Print Method for drcOrdinal Objects +#' +#' Prints a summary of a drcOrdinal model object. +#' +#' @param x A drcOrdinal model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object #' @export print.drcOrdinal <- function(x, ..., digits = max(3, getOption("digits") - 3)) { diff --git a/man/AIC.drcOrdinal.Rd b/man/AIC.drcOrdinal.Rd index 40e9c1b..287e193 100644 --- a/man/AIC.drcOrdinal.Rd +++ b/man/AIC.drcOrdinal.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/AIC.drcOrdinal.R \name{AIC.drcOrdinal} \alias{AIC.drcOrdinal} -\title{S3 method} +\title{AIC Method for drcOrdinal Objects} \usage{ \method{AIC}{drcOrdinal}(object, ..., k = 2) } +\arguments{ +\item{object}{A drcOrdinal model object} + +\item{...}{Additional arguments (not used)} + +\item{k}{The penalty per parameter to be used; default is 2} +} +\value{ +The AIC value +} \description{ -S3 method +Calculates the Akaike Information Criterion for drcOrdinal model objects. } diff --git a/man/bmd-package.Rd b/man/bmd-package.Rd index ca769fc..7c4282d 100644 --- a/man/bmd-package.Rd +++ b/man/bmd-package.Rd @@ -3,7 +3,6 @@ \docType{package} \name{bmd-package} \alias{bmd-package} -\alias{bmd} \title{BMD: Benchmark Dose Modeling} \description{ A package for benchmark dose modeling in toxicology and risk assessment diff --git a/man/logLik.drcHetVar.Rd b/man/logLik.drcHetVar.Rd index 6adb0a7..e935cee 100644 --- a/man/logLik.drcHetVar.Rd +++ b/man/logLik.drcHetVar.Rd @@ -2,10 +2,18 @@ % Please edit documentation in R/logLik.drcHetVar.R \name{logLik.drcHetVar} \alias{logLik.drcHetVar} -\title{S3 method} +\title{Log-Likelihood Method for drcHetVar Objects} \usage{ \method{logLik}{drcHetVar}(object, ...) } +\arguments{ +\item{object}{A drcHetVar model object} + +\item{...}{Additional arguments (not used)} +} +\value{ +The log-likelihood value +} \description{ -S3 method +Extracts the log-likelihood from drcHetVar model objects. } diff --git a/man/logLik.drcOrdinal.Rd b/man/logLik.drcOrdinal.Rd index caba8ae..f5eadcd 100644 --- a/man/logLik.drcOrdinal.Rd +++ b/man/logLik.drcOrdinal.Rd @@ -2,10 +2,18 @@ % Please edit documentation in R/logLik.drcOrdinal.R \name{logLik.drcOrdinal} \alias{logLik.drcOrdinal} -\title{S3 method} +\title{Log-Likelihood Method for drcOrdinal Objects} \usage{ \method{logLik}{drcOrdinal}(object, ...) } +\arguments{ +\item{object}{A drcOrdinal model object} + +\item{...}{Additional arguments (not used)} +} +\value{ +The log-likelihood value +} \description{ -S3 method +Extracts the log-likelihood from drcOrdinal model objects. } diff --git a/man/plot.bmd.Rd b/man/plot.bmd.Rd index 41b2edb..534eca0 100644 --- a/man/plot.bmd.Rd +++ b/man/plot.bmd.Rd @@ -2,8 +2,7 @@ % Please edit documentation in R/plot.bmd.R \name{plot.bmd} \alias{plot.bmd} -\alias{\method{plot}{bmd}} -\title{Plotting benchmark doses} +\title{Plotting method for benchmark doses modeling object} \usage{ \method{plot}{bmd}(x, ..., interval = c("BMDL", "twosided", "none")) } diff --git a/man/plot.drcHetVar.Rd b/man/plot.drcHetVar.Rd index 94a4ef2..aaa6140 100644 --- a/man/plot.drcHetVar.Rd +++ b/man/plot.drcHetVar.Rd @@ -2,10 +2,18 @@ % Please edit documentation in R/plot.drcHetVar.R \name{plot.drcHetVar} \alias{plot.drcHetVar} -\title{S3 method} +\title{Plot Method for drcHetVar Objects} \usage{ \method{plot}{drcHetVar}(x, ...) } +\arguments{ +\item{x}{A drcHetVar model object} + +\item{...}{Additional graphical parameters passed to plot} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Plots the fitted dose-response curve for drcHetVar model objects. } diff --git a/man/plot.drcOrdinal.Rd b/man/plot.drcOrdinal.Rd index 4721bc4..5466eb5 100644 --- a/man/plot.drcOrdinal.Rd +++ b/man/plot.drcOrdinal.Rd @@ -2,10 +2,18 @@ % Please edit documentation in R/plot.drcOrdinal.R \name{plot.drcOrdinal} \alias{plot.drcOrdinal} -\title{S3 method} +\title{Plot Method for drcOrdinal Objects} \usage{ \method{plot}{drcOrdinal}(x, ...) } +\arguments{ +\item{x}{A drcOrdinal model object} + +\item{...}{Additional graphical parameters passed to plot} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Plots the fitted dose-response curve for drcOrdinal model objects. } diff --git a/man/print.bmd.Rd b/man/print.bmd.Rd new file mode 100644 index 0000000..f48b628 --- /dev/null +++ b/man/print.bmd.Rd @@ -0,0 +1,21 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.bmd.R +\name{print.bmd} +\alias{print.bmd} +\title{Print Method for bmd Objects} +\usage{ +\method{print}{bmd}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\arguments{ +\item{x}{A bmd model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} +\description{ +Prints a summary of a bmd model object. +} diff --git a/man/print.bmdHetVar.Rd b/man/print.bmdHetVar.Rd new file mode 100644 index 0000000..942fdc6 --- /dev/null +++ b/man/print.bmdHetVar.Rd @@ -0,0 +1,21 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/print.bmdHetVar.R +\name{print.bmdHetVar} +\alias{print.bmdHetVar} +\title{Print Method for drcHetVar Objects} +\usage{ +\method{print}{bmdHetVar}(x, ..., digits = max(3, getOption("digits") - 3)) +} +\arguments{ +\item{x}{A drcHetVar model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} +\description{ +Prints a summary of a drcHetVar model object. +} diff --git a/man/print.bmdOrdinal.Rd b/man/print.bmdOrdinal.Rd index 7f79e87..d3539fb 100644 --- a/man/print.bmdOrdinal.Rd +++ b/man/print.bmdOrdinal.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/print.bmdOrdinal.R \name{print.bmdOrdinal} \alias{print.bmdOrdinal} -\title{S3 method} +\title{Print Method for bmdOrdinalr Objects} \usage{ \method{print}{bmdOrdinal}(x, ..., digits = max(3, getOption("digits") - 3)) } +\arguments{ +\item{x}{A bmdOrdinal model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Prints a summary of a bmdOrdinal model object. } diff --git a/man/print.drcMMRE.Rd b/man/print.drcMMRE.Rd index a9583e1..e252907 100644 --- a/man/print.drcMMRE.Rd +++ b/man/print.drcMMRE.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/print.drcMMRE.R \name{print.drcMMRE} \alias{print.drcMMRE} -\title{S3 method} +\title{Print Method for drcMMRE Objects} \usage{ \method{print}{drcMMRE}(x, ..., digits = max(3, getOption("digits") - 3)) } +\arguments{ +\item{x}{A drcMMRE model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Prints a summary of a drcMMRE model object. } diff --git a/man/print.drcOrdinal.Rd b/man/print.drcOrdinal.Rd index b80e518..03d1f5e 100644 --- a/man/print.drcOrdinal.Rd +++ b/man/print.drcOrdinal.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/print.drcOrdinal.R \name{print.drcOrdinal} \alias{print.drcOrdinal} -\title{S3 method} +\title{Print Method for drcOrdinal Objects} \usage{ \method{print}{drcOrdinal}(x, ..., digits = max(3, getOption("digits") - 3)) } +\arguments{ +\item{x}{A drcOrdinal model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Prints a summary of a drcOrdinal model object. } From 8a7de655c2a825951c10a946b3b96224b327a581 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Fri, 4 Jul 2025 18:42:29 +0200 Subject: [PATCH 06/17] solve the AIC.drcHetVar issue --- R/logLik.drcHetVar.R | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/R/logLik.drcHetVar.R b/R/logLik.drcHetVar.R index 4025409..9cc096b 100644 --- a/R/logLik.drcHetVar.R +++ b/R/logLik.drcHetVar.R @@ -11,13 +11,28 @@ logLik.drcHetVar <- function(object, ...){ - object$sumList$numObs/2 * log(2*pi) - object$value/2 } -#' @title S3 method +#' AIC Method for drcHetVar Objects +#' +#' Extracts the AIC from drcHetVar model objects. +#' +#' @param object A drcHetVar model object +#' @param ... Additional arguments (not used) +#' @param k Numeric value for penalty term in AIC calculation (default is 2) +#' +#' @return The log-likelihood value #' @export AIC.drcHetVar <- function(object, ..., k = 2){ 2*object$sumList$numPar - k*logLik(object) } -#' @title S3 method +#' BIC Method for drcHetVar Objects +#' +#' Extracts the BIC from drcHetVar model objects. +#' +#' @param object A drcHetVar model object +#' @param ... Additional arguments (not used) +#' +#' @return The log-likelihood value #' @export BIC.drcHetVar <- function(object, ...){ object$sumList$numPar*log(object$sumList$numObs) - 2*logLik(object) From c373bc2c0b350dba7d7a6fedc5bd3a512244afde Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Fri, 4 Jul 2025 18:42:58 +0200 Subject: [PATCH 07/17] solve the AIC.drcHetVar issue --- man/AIC.drcHetVar.Rd | 14 ++++++++++++-- man/BIC.drcHetVar.Rd | 12 ++++++++++-- 2 files changed, 22 insertions(+), 4 deletions(-) diff --git a/man/AIC.drcHetVar.Rd b/man/AIC.drcHetVar.Rd index d717015..32be632 100644 --- a/man/AIC.drcHetVar.Rd +++ b/man/AIC.drcHetVar.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/logLik.drcHetVar.R \name{AIC.drcHetVar} \alias{AIC.drcHetVar} -\title{S3 method} +\title{AIC Method for drcHetVar Objects} \usage{ \method{AIC}{drcHetVar}(object, ..., k = 2) } +\arguments{ +\item{object}{A drcHetVar model object} + +\item{...}{Additional arguments (not used)} + +\item{k}{Numeric value for penalty term in AIC calculation (default is 2)} +} +\value{ +The log-likelihood value +} \description{ -S3 method +Extracts the AIC from drcHetVar model objects. } diff --git a/man/BIC.drcHetVar.Rd b/man/BIC.drcHetVar.Rd index bb878bf..b0cb508 100644 --- a/man/BIC.drcHetVar.Rd +++ b/man/BIC.drcHetVar.Rd @@ -2,10 +2,18 @@ % Please edit documentation in R/logLik.drcHetVar.R \name{BIC.drcHetVar} \alias{BIC.drcHetVar} -\title{S3 method} +\title{BIC Method for drcHetVar Objects} \usage{ \method{BIC}{drcHetVar}(object, ...) } +\arguments{ +\item{object}{A drcHetVar model object} + +\item{...}{Additional arguments (not used)} +} +\value{ +The log-likelihood value +} \description{ -S3 method +Extracts the BIC from drcHetVar model objects. } From 2bf40ef75231906157cb2ad5777ba8cf79f45282 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Sun, 6 Jul 2025 15:16:29 +0200 Subject: [PATCH 08/17] fixed print.drcHetVar documentation issue --- R/print.drcHetVar.R | 11 +++++++++-- man/print.drcHetVar.Rd | 14 ++++++++++++-- 2 files changed, 21 insertions(+), 4 deletions(-) diff --git a/R/print.drcHetVar.R b/R/print.drcHetVar.R index 09728c5..6040736 100644 --- a/R/print.drcHetVar.R +++ b/R/print.drcHetVar.R @@ -1,5 +1,12 @@ - -#' @title S3 method +#' Print Method for drcHetVar Objects +#' +#' Prints a summary of a drcHetVar model object. +#' +#' @param x A drcHetVar model object +#' @param ... Additional arguments (not used) +#' @param digits Number of significant digits to use for printing values +#' +#' @return Invisibly returns the x object #' @export print.drcHetVar <- function(x, ..., digits = max(3, getOption("digits") - 3)){ object <- x diff --git a/man/print.drcHetVar.Rd b/man/print.drcHetVar.Rd index ef0dc4f..f7ab367 100644 --- a/man/print.drcHetVar.Rd +++ b/man/print.drcHetVar.Rd @@ -2,10 +2,20 @@ % Please edit documentation in R/print.drcHetVar.R \name{print.drcHetVar} \alias{print.drcHetVar} -\title{S3 method} +\title{Print Method for drcHetVar Objects} \usage{ \method{print}{drcHetVar}(x, ..., digits = max(3, getOption("digits") - 3)) } +\arguments{ +\item{x}{A drcHetVar model object} + +\item{...}{Additional arguments (not used)} + +\item{digits}{Number of significant digits to use for printing values} +} +\value{ +Invisibly returns the x object +} \description{ -S3 method +Prints a summary of a drcHetVar model object. } From c478a9423edb2e6fc0d649b323f1decbf365f176 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Tue, 8 Jul 2025 12:48:30 +0200 Subject: [PATCH 09/17] fixed Bca issue --- NAMESPACE | 1 - R/BCa.R | 26 ++++++++++++++++++++++---- bmd.Rproj | 6 +++--- man/BCa.Rd | 28 ++++++++++++++++++++++++++-- 4 files changed, 51 insertions(+), 10 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 9f45c0a..5e4e9a6 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -17,7 +17,6 @@ S3method(print,drcHetVar) S3method(print,drcMMRE) S3method(print,drcOrdinal) S3method(vcov,drcMMRE) -export(BCa) export(MACurve) export(PAV) export(bmd) diff --git a/R/BCa.R b/R/BCa.R index c069272..b6ca8e1 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,7 +1,25 @@ -#' Help funtion to bmdBoot -#' -#' -#' @export +#' Calculate BCa (Bias-Corrected and Accelerated) Bootstrap Confidence Interval +#' +#' Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. +#' The BCa method adjusts for both bias and skewness in the bootstrap distribution. +#' +#' @param obs Observed value of the statistic (scalar) +#' @param data Original dataset (data frame or matrix) +#' @param bootSample Vector of bootstrap replicates of the statistic (length = R) +#' @param bootjack Vector of jackknife replicates of the statistic (length = n) +#' @param level Confidence level (e.g., 0.95 for 95% confidence interval) +#' +#' @return A numeric vector of length 2 containing the lower and upper confidence limits. +#' +#' @details +#' The BCa method combines: +#' - Bias correction (z0) based on the proportion of bootstrap replicates below the observed value +#' - Acceleration (a) estimated from jackknife influence values +#' - Normal quantiles adjusted for bias and acceleration +#' +#' @references +#' Efron, B. (1987). Better Bootstrap Confidence Intervals. *Journal of the American Statistical Association*, 82(397), 171-185. +#' BCa <- function(obs, data, bootSample, bootjack, level){ R <- length(bootSample) b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) diff --git a/bmd.Rproj b/bmd.Rproj index b1ded45..929b948 100644 --- a/bmd.Rproj +++ b/bmd.Rproj @@ -1,8 +1,8 @@ Version: 1.0 -RestoreWorkspace: Default -SaveWorkspace: Default -AlwaysSaveHistory: Default +RestoreWorkspace: No +SaveWorkspace: No +AlwaysSaveHistory: No EnableCodeIndexing: Yes UseSpacesForTab: Yes diff --git a/man/BCa.Rd b/man/BCa.Rd index 40c7c39..37e4010 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -2,10 +2,34 @@ % Please edit documentation in R/BCa.R \name{BCa} \alias{BCa} -\title{Help funtion to bmdBoot} +\title{Calculate BCa (Bias-Corrected and Accelerated) Bootstrap Confidence Interval} \usage{ BCa(obs, data, bootSample, bootjack, level) } +\arguments{ +\item{obs}{Observed value of the statistic (scalar)} + +\item{data}{Original dataset (data frame or matrix)} + +\item{bootSample}{Vector of bootstrap replicates of the statistic (length = R)} + +\item{bootjack}{Vector of jackknife replicates of the statistic (length = n)} + +\item{level}{Confidence level (e.g., 0.95 for 95% confidence interval)} +} +\value{ +A numeric vector of length 2 containing the lower and upper confidence limits. +} \description{ -Help funtion to bmdBoot +Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. +The BCa method adjusts for both bias and skewness in the bootstrap distribution. +} +\details{ +The BCa method combines: + - Bias correction (z0) based on the proportion of bootstrap replicates below the observed value + - Acceleration (a) estimated from jackknife influence values + - Normal quantiles adjusted for bias and acceleration +} +\references{ +Efron, B. (1987). Better Bootstrap Confidence Intervals. *Journal of the American Statistical Association*, 82(397), 171-185. } From b2b098ddb1e92c7bc49d8865f1002f568d34572c Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Wed, 9 Jul 2025 11:13:02 +0200 Subject: [PATCH 10/17] fixed Bca issue again --- NAMESPACE | 1 + R/BCa.R | 73 ++++++++++++++++++++++++++++++++++++++++++++--------- man/BCa.Rd | 74 +++++++++++++++++++++++++++++++++++++++++++++--------- 3 files changed, 124 insertions(+), 24 deletions(-) diff --git a/NAMESPACE b/NAMESPACE index 5e4e9a6..9f45c0a 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -17,6 +17,7 @@ S3method(print,drcHetVar) S3method(print,drcMMRE) S3method(print,drcOrdinal) S3method(vcov,drcMMRE) +export(BCa) export(MACurve) export(PAV) export(bmd) diff --git a/R/BCa.R b/R/BCa.R index b6ca8e1..63d6655 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,25 +1,74 @@ #' Calculate BCa (Bias-Corrected and Accelerated) Bootstrap Confidence Interval #' +#' @description #' Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. -#' The BCa method adjusts for both bias and skewness in the bootstrap distribution. +#' The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally +#' provides better coverage than standard bootstrap confidence intervals. #' -#' @param obs Observed value of the statistic (scalar) -#' @param data Original dataset (data frame or matrix) -#' @param bootSample Vector of bootstrap replicates of the statistic (length = R) -#' @param bootjack Vector of jackknife replicates of the statistic (length = n) -#' @param level Confidence level (e.g., 0.95 for 95% confidence interval) +#' @param obs numeric; The observed value of the statistic computed from the original sample +#' @param data data.frame or matrix; The original dataset from which bootstrap samples are drawn +#' @param bootSample numeric vector; Bootstrap replicates of the statistic. Must be of length R +#' where R is the number of bootstrap replicates +#' @param bootjack numeric vector; Jackknife replicates of the statistic. Must be of length n +#' where n is the number of observations in data +#' @param level numeric; Confidence level between 0 and 1 (e.g., 0.95 for 95% confidence interval) #' -#' @return A numeric vector of length 2 containing the lower and upper confidence limits. +#' @return A numeric vector of length 2 containing: +#' \itemize{ +#' \item lower: The lower confidence limit +#' \item upper: The upper confidence limit +#' } #' #' @details -#' The BCa method combines: -#' - Bias correction (z0) based on the proportion of bootstrap replicates below the observed value -#' - Acceleration (a) estimated from jackknife influence values -#' - Normal quantiles adjusted for bias and acceleration +#' The BCa method computes confidence intervals using three components: +#' +#' 1. Bias correction (z0): +#' #$# z_0 = \Phi^{-1}(\frac{\#\{\theta^*(b) \leq \hat{\theta}\}}{B}) #$# +#' where B is the number of bootstrap replicates. +#' +#' 2. Acceleration (a): +#' #$# a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}} #$# +#' where θ_(i) are the jackknife values. +#' +#' 3. The confidence limits are then computed as: +#' #$# \alpha_{1,2} = \Phi(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}) #$# +#' +#' @section Warning: +#' The function assumes that: +#' - The bootstrap samples are independent +#' - The statistic of interest is smooth (continuously differentiable) +#' - There are sufficient bootstrap replicates (typically >1000) +#' - The jackknife values are properly computed +#' +#' @examples +#' \dontrun{ +#' # Example with mean as the statistic +#' data <- rnorm(100) +#' obs_mean <- mean(data) +#' +#' # Generate bootstrap samples +#' R <- 1000 +#' boot_means <- replicate(R, mean(sample(data, replace = TRUE))) +#' +#' # Generate jackknife samples +#' jack_means <- sapply(1:length(data), +#' function(i) mean(data[-i])) +#' +#' # Calculate 95% CI +#' BCa(obs_mean, data, boot_means, jack_means, 0.95) +#' } #' #' @references -#' Efron, B. (1987). Better Bootstrap Confidence Intervals. *Journal of the American Statistical Association*, 82(397), 171-185. +#' Efron, B. (1987). Better Bootstrap Confidence Intervals. +#' *Journal of the American Statistical Association*, 82(397), 171-185. +#' +#' DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. +#' *Statistical Science*, 11(3), 189-212. +#' +#' @seealso +#' \code{\link{quantile}} for the underlying quantile computation #' +#' @export BCa <- function(obs, data, bootSample, bootjack, level){ R <- length(bootSample) b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) diff --git a/man/BCa.Rd b/man/BCa.Rd index 37e4010..800d97e 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -7,29 +7,79 @@ BCa(obs, data, bootSample, bootjack, level) } \arguments{ -\item{obs}{Observed value of the statistic (scalar)} +\item{obs}{numeric; The observed value of the statistic computed from the original sample} -\item{data}{Original dataset (data frame or matrix)} +\item{data}{data.frame or matrix; The original dataset from which bootstrap samples are drawn} -\item{bootSample}{Vector of bootstrap replicates of the statistic (length = R)} +\item{bootSample}{numeric vector; Bootstrap replicates of the statistic. Must be of length R +where R is the number of bootstrap replicates} -\item{bootjack}{Vector of jackknife replicates of the statistic (length = n)} +\item{bootjack}{numeric vector; Jackknife replicates of the statistic. Must be of length n +where n is the number of observations in data} -\item{level}{Confidence level (e.g., 0.95 for 95% confidence interval)} +\item{level}{numeric; Confidence level between 0 and 1 (e.g., 0.95 for 95% confidence interval)} } \value{ -A numeric vector of length 2 containing the lower and upper confidence limits. +A numeric vector of length 2 containing: +\itemize{ + \item lower: The lower confidence limit + \item upper: The upper confidence limit +} } \description{ Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. -The BCa method adjusts for both bias and skewness in the bootstrap distribution. +The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally +provides better coverage than standard bootstrap confidence intervals. } \details{ -The BCa method combines: - - Bias correction (z0) based on the proportion of bootstrap replicates below the observed value - - Acceleration (a) estimated from jackknife influence values - - Normal quantiles adjusted for bias and acceleration +The BCa method computes confidence intervals using three components: + +1. Bias correction (z0): +#$# z_0 = \Phi^{-1}(\frac{\#\{\theta^*(b) \leq \hat{\theta}\}}{B}) #$# +where B is the number of bootstrap replicates. + +2. Acceleration (a): +#$# a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}} #$# +where θ_(i) are the jackknife values. + +3. The confidence limits are then computed as: +#$# \alpha_{1,2} = \Phi(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}) #$# +} +\section{Warning}{ + +The function assumes that: +- The bootstrap samples are independent +- The statistic of interest is smooth (continuously differentiable) +- There are sufficient bootstrap replicates (typically >1000) +- The jackknife values are properly computed +} + +\examples{ +\dontrun{ +# Example with mean as the statistic +data <- rnorm(100) +obs_mean <- mean(data) + +# Generate bootstrap samples +R <- 1000 +boot_means <- replicate(R, mean(sample(data, replace = TRUE))) + +# Generate jackknife samples +jack_means <- sapply(1:length(data), + function(i) mean(data[-i])) + +# Calculate 95\% CI +BCa(obs_mean, data, boot_means, jack_means, 0.95) +} + } \references{ -Efron, B. (1987). Better Bootstrap Confidence Intervals. *Journal of the American Statistical Association*, 82(397), 171-185. +Efron, B. (1987). Better Bootstrap Confidence Intervals. +*Journal of the American Statistical Association*, 82(397), 171-185. + +DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. +*Statistical Science*, 11(3), 189-212. +} +\seealso{ +\code{\link{quantile}} for the underlying quantile computation } From 77fa233cbcf21a482695017b68f2a10b9b6dc38c Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Thu, 10 Jul 2025 12:50:11 +0200 Subject: [PATCH 11/17] updated all docs to fix warnings in build --- R/BCa.R | 65 ++++++++-------- R/BIC.drcOrdinal.R | 86 ++++++++++++++++++++- R/bmdMACurve.R | 99 +++++++++++++++++++++++- R/bootDataGen.R | 117 ++++++++++++++++++++++++++++- R/bootDataGenOrdinal.R | 130 +++++++++++++++++++++++++++++++- R/coef.drcHetVar.R | 55 +++++++++++++- R/drmMMRE.R | 15 +++- R/expandBinomial.R | 4 - R/invBmd.R | 134 ++++++++++++++++++++++++++++++++- man/BCa.Rd | 24 +++--- man/BIC.drcOrdinal.Rd | 88 +++++++++++++++++++++- man/bmdMACurve.Rd | 109 ++++++++++++++++++++++++++- man/bootDataGen.Rd | 127 ++++++++++++++++++++++++++++++- man/bootDataGenOrdinal.Rd | 142 ++++++++++++++++++++++++++++++++++- man/coef.drcHetVar.Rd | 55 +++++++++++++- man/expandBinomial.Rd | 6 -- man/invBmd.Rd | 154 +++++++++++++++++++++++++++++++++++++- man/vcov.drcMMRE.Rd | 16 +++- 18 files changed, 1350 insertions(+), 76 deletions(-) diff --git a/R/BCa.R b/R/BCa.R index 63d6655..eae70f0 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,6 +1,5 @@ #' Calculate BCa (Bias-Corrected and Accelerated) Bootstrap Confidence Interval #' -#' @description #' Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. #' The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally #' provides better coverage than standard bootstrap confidence intervals. @@ -23,22 +22,24 @@ #' The BCa method computes confidence intervals using three components: #' #' 1. Bias correction (z0): -#' #$# z_0 = \Phi^{-1}(\frac{\#\{\theta^*(b) \leq \hat{\theta}\}}{B}) #$# -#' where B is the number of bootstrap replicates. +#' \deqn{z_0 = \Phi^{-1}\left(\frac{\text{number of } \theta^*_b \leq \hat{\theta}}{B}\right)}{z_0 = qnorm(proportion of bootstrap samples <= observed value)} +#' where B is the number of bootstrap replicates and \eqn{\theta^*_b}{theta*_b} represents the b-th bootstrap replicate. #' #' 2. Acceleration (a): -#' #$# a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}} #$# -#' where θ_(i) are the jackknife values. +#' \deqn{a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}}}{a = sum((theta-bar - theta_i)^3) / (6 * [sum((theta-bar - theta_i)^2)]^(3/2))} +#' where \eqn{\theta_{(i)}}{theta_i} are the jackknife values. #' #' 3. The confidence limits are then computed as: -#' #$# \alpha_{1,2} = \Phi(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}) #$# +#' \deqn{\alpha_{1,2} = \Phi\left(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}\right)}{alpha_(1,2) = Phi(z_0 + (z_0 +/- z_alpha)/(1 - a*(z_0 +/- z_alpha)))} #' #' @section Warning: #' The function assumes that: -#' - The bootstrap samples are independent -#' - The statistic of interest is smooth (continuously differentiable) -#' - There are sufficient bootstrap replicates (typically >1000) -#' - The jackknife values are properly computed +#' \itemize{ +#' \item The bootstrap samples are independent +#' \item The statistic of interest is smooth (continuously differentiable) +#' \item There are sufficient bootstrap replicates (typically >1000) +#' \item The jackknife values are properly computed +#' } #' #' @examples #' \dontrun{ @@ -60,37 +61,37 @@ #' #' @references #' Efron, B. (1987). Better Bootstrap Confidence Intervals. -#' *Journal of the American Statistical Association*, 82(397), 171-185. +#' \emph{Journal of the American Statistical Association}, 82(397), 171-185. #' #' DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. -#' *Statistical Science*, 11(3), 189-212. +#' \emph{Statistical Science}, 11(3), 189-212. #' #' @seealso #' \code{\link{quantile}} for the underlying quantile computation #' #' @export BCa <- function(obs, data, bootSample, bootjack, level){ -R <- length(bootSample) -b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) + R <- length(bootSample) + b <- qnorm((sum(bootSample > obs)+sum(bootSample==obs)/2)/R) -n <- nrow(data) -n1 <- n-1 -obsn <- obs*n -pv <- i <- 0 -while(i < n){ - i = i+1 -pv[i] = obsn-n1*bootjack[i] -} -pv<-pv[!is.na(pv)] - -je <- mean(pv)-pv -a <- sum(je^3)/(6*sum(je^2))^(3/2) - -alpha <- (1-level)*2 -z <- qnorm(c(alpha/2,1-alpha/2)) # Std. norm. limits -p <- pnorm((z-b)/(1-a*(z-b))-b) # correct & convert to proportions - -quantile(bootSample,p=p) # ABC percentile lims. + n <- nrow(data) + n1 <- n-1 + obsn <- obs*n + pv <- i <- 0 + while(i < n){ + i = i+1 + pv[i] = obsn-n1*bootjack[i] + } + pv<-pv[!is.na(pv)] + + je <- mean(pv)-pv + a <- sum(je^3)/(6*sum(je^2))^(3/2) + + alpha <- (1-level)*2 + z <- qnorm(c(alpha/2,1-alpha/2)) # Std. norm. limits + p <- pnorm((z-b)/(1-a*(z-b))-b) # correct & convert to proportions + + quantile(bootSample,p=p) # ABC percentile lims. } diff --git a/R/BIC.drcOrdinal.R b/R/BIC.drcOrdinal.R index 40a7942..91a18fc 100644 --- a/R/BIC.drcOrdinal.R +++ b/R/BIC.drcOrdinal.R @@ -1,5 +1,87 @@ - -#' @title S3 method +#' BIC Method for drcOrdinal Objects +#' +#' @description +#' S3 method to calculate the Bayesian Information Criterion (BIC) for fitted +#' ordinal dose-response models. This method extends the generic `BIC()` function +#' to handle `drcOrdinal` objects which contain multiple fitted dose-response models +#' for different response categories. +#' +#' @param object An object of class "drcOrdinal" containing fitted ordinal +#' dose-response models +#' @param ... Additional arguments passed to the method. Currently supports: +#' \itemize{ +#' \item \code{epsilon}: Small positive value to avoid log(0) in likelihood +#' calculations (default: 1e-16) +#' } +#' +#' @details +#' The BIC is calculated using the standard formula: +#' \deqn{BIC = k \log(n) - 2 \log(L)}{BIC = k * log(n) - 2 * log(L)} +#' where: +#' \itemize{ +#' \item \eqn{k}{k} is the total number of parameters across all models in the ordinal fit +#' \item \eqn{n}{n} is the total number of observations (sum of weights) +#' \item \eqn{L}{L} is the likelihood of the fitted model +#' } +#' +#' For ordinal dose-response models, the total number of parameters is the sum +#' of parameters from all individual models in the `drmList` component, and the +#' sample size is calculated as the sum of weights in the data. +#' +#' The `epsilon` parameter is used in the `logLik()` calculation to prevent +#' numerical issues when probabilities approach zero. +#' +#' @return A numeric value representing the BIC of the fitted ordinal dose-response model. +#' Lower values indicate better model fit when comparing models. +#' +#' @section Model Comparison: +#' BIC penalizes model complexity more heavily than AIC, making it useful for: +#' \itemize{ +#' \item Comparing ordinal dose-response models with different numbers of parameters +#' \item Model selection in situations where simpler models are preferred +#' \item Avoiding overfitting in dose-response modeling +#' } +#' +#' @note +#' This method assumes that the `drcOrdinal` object contains: +#' \itemize{ +#' \item A `drmList` component with fitted dose-response models +#' \item A `data` component with the original data including weights +#' \item A `weights` component specifying the column name for observation weights +#' } +#' +#' @seealso +#' \code{\link{BIC}} for the generic BIC function, +#' \code{\link{AIC.drcOrdinal}} for the corresponding AIC method, +#' \code{\link{logLik.drcOrdinal}} for the log-likelihood method +#' +#' @examples +#' \dontrun{ +#' # Assuming you have a fitted drcOrdinal object +#' ordinal_model <- drm(response ~ dose, +#' weights = count, +#' data = ordinal_data, +#' fct = cumulative.logit()) +#' +#' # Calculate BIC +#' bic_value <- BIC(ordinal_model) +#' +#' # Compare models +#' model1_bic <- BIC(ordinal_model1) +#' model2_bic <- BIC(ordinal_model2) +#' +#' # Lower BIC indicates better model +#' if(model1_bic < model2_bic) { +#' cat("Model 1 is preferred\n") +#' } else { +#' cat("Model 2 is preferred\n") +#' } +#' +#' # Use custom epsilon for numerical stability +#' bic_custom <- BIC(ordinal_model, epsilon = 1e-12) +#' } +#' +#' @method BIC drcOrdinal #' @export BIC.drcOrdinal <- function(object, ...){ dots <- list(...) diff --git a/R/bmdMACurve.R b/R/bmdMACurve.R index 3bda697..f9ae013 100644 --- a/R/bmdMACurve.R +++ b/R/bmdMACurve.R @@ -1,6 +1,103 @@ -#' Help funtion to bmdMA +#' Calculate Model-Averaged BMD Curve, helper to bmdMA +#' +#' @description +#' Helper function for `bmdMA` that computes Benchmark Dose (BMD) values using +#' model averaging. The function creates a weighted average of multiple dose-response +#' models and finds the dose corresponding to a specified benchmark response level. +#' +#' @param modelList list; A list of fitted dose-response models from which to compute +#' the model average. Each model should be a fitted object with components +#' including `fct`, `parmMat`, `dataList`, etc. +#' @param modelWeights numeric vector; Weights for model averaging, typically derived +#' from model selection criteria (e.g., AIC weights). Must sum to 1 and have +#' the same length as `modelList` +#' @param bmrScaled0 numeric; The benchmark response level(s) for which to calculate +#' BMD. For single curves, a scalar value; for multiple curves, a vector with +#' length equal to the number of curves +#' @param searchInterval character or numeric; Search interval for root finding. +#' If "dataBased" (default), uses data range with small lower bound adjustment. +#' If numeric, should be a vector of length 2 for single curves, or a matrix +#' with 2 columns for multiple curves specifying [lower, upper] bounds +#' +#' @details +#' The function handles two scenarios: #' +#' **Single Curve Analysis:** +#' Creates a weighted combination of model functions: +#' \deqn{f_{MA}(x) = \sum_{i=1}^{m} w_i \cdot f_i(x)}{f_MA(x) = sum of w_i * f_i(x)} +#' where \eqn{w_i}{w_i} are model weights and \eqn{f_i(x)}{f_i(x)} are individual model functions. #' +#' **Multiple Curve Analysis:** +#' Computes BMD separately for each curve using the same model averaging approach +#' but applied to curve-specific data and parameters. +#' +#' The BMD is found by solving: +#' \deqn{f_{MA}(BMD) = BMR}{f_MA(BMD) = BMR} +#' using root finding algorithms. +#' +#' **Model Function Construction:** +#' The function dynamically constructs model functions by: +#' \itemize{ +#' \item Extracting function templates from `mtList()` +#' \item Substituting fixed parameters and estimated coefficients +#' \item Handling special cases like Fractional Polynomial models +#' \item Creating weighted combinations of all models +#' } +#' +#' @return An object of class "bmd" containing: +#' \itemize{ +#' \item \strong{Results}: A matrix with BMD values. For single curves, a 1x1 matrix; +#' for multiple curves, an nx1 matrix where n is the number of curves +#' \item \strong{MACurve}: The model-averaged function used for BMD calculation. +#' For single curves, returns the combined function; for multiple curves, returns NULL +#' } +#' +#' @section Search Interval: +#' When `searchInterval = "dataBased"`: +#' \itemize{ +#' \item Lower bound: Second smallest dose value divided by 10,000 +#' \item Upper bound: Maximum dose value in the dataset +#' } +#' +#' Custom intervals can be provided to avoid convergence issues or focus on +#' specific dose ranges of interest. +#' +#' @section Model Support: +#' The function supports various dose-response models including: +#' \itemize{ +#' \item Standard 4-parameter and 5-parameter models +#' \item Fractional Polynomial models (special handling) +#' \item Models with fixed parameters +#' } +#' +#' @note +#' This is primarily an internal helper function for `bmdMA`. Direct usage requires +#' properly formatted model lists and weights. The function assumes all models in +#' `modelList` are compatible and fitted to the same dataset structure. +#' +#' @seealso +#' \code{\link{bmdMA}} for the main model averaging function, +#' \code{\link{uniroot}} for the root finding algorithm used internally +#' +#' @examples +#' \dontrun{ +#' # Typically called internally by bmdMA, but can be used directly: +#' +#' # Assume you have a list of fitted models and weights +#' models <- list(model1, model2, model3) # fitted drc models +#' weights <- c(0.5, 0.3, 0.2) # AIC weights +#' bmr <- 0.1 # 10% benchmark response +#' +#' # Calculate model-averaged BMD +#' result <- bmdMACurve(models, weights, bmr) +#' +#' # Extract BMD value +#' bmd_value <- result$Results[1, 1] +#' +#' # Use the averaged curve function +#' curve_function <- result$MACurve +#' } +#' #' @export bmdMACurve<-function(modelList,modelWeights,bmrScaled0, searchInterval="dataBased"){ nCurves <- ncol(modelList[[1]]$parmMat) diff --git a/R/bootDataGen.R b/R/bootDataGen.R index 9489d55..0122313 100644 --- a/R/bootDataGen.R +++ b/R/bootDataGen.R @@ -1,6 +1,121 @@ -#' Help funtion to bmdBoot +#' Generate Bootstrap Data for BMD Analysis +#' +#' @description +#' Helper function for `bmdBoot` that generates bootstrap datasets from fitted +#' dose-response models. Supports multiple bootstrap methods (nonparametric, +#' parametric, and semiparametric) and handles different response types +#' (binomial, continuous, Poisson, negative binomial). +#' +#' @param object A fitted dose-response model object (typically from `drm()`) +#' containing the original data and model specifications +#' @param R integer; Number of bootstrap replicates to generate (default: 1000) +#' @param bootType character; Type of bootstrap resampling method. Options are: +#' \itemize{ +#' \item \code{"nonparametric"}: Resamples observations within dose groups +#' \item \code{"parametric"}: Generates new data from fitted distributions +#' \item \code{"semiparametric"}: Uses fitted values plus resampled residuals +#' } +#' @param aggregated logical; For binomial data, whether to return aggregated +#' (summary) format or expanded (individual observation) format (default: TRUE) +#' +#' @details +#' The function implements different bootstrap strategies based on data type and method: #' +#' **Nonparametric Bootstrap:** +#' \itemize{ +#' \item \strong{Binomial}: Expands binomial data to individual observations, +#' resamples within dose groups, then optionally re-aggregates +#' \item \strong{Continuous/Count}: Resamples observations within dose groups +#' from the original dataset +#' } #' +#' **Parametric Bootstrap:** +#' \itemize{ +#' \item \strong{Binomial}: Generates new binomial observations using estimated +#' success probabilities, with continuity correction (adds 0.25/0.5) for +#' boundary cases +#' \item \strong{Continuous}: Generates normal random variables using +#' dose-specific means and standard deviations from original data +#' } +#' +#' **Semiparametric Bootstrap:** +#' \itemize{ +#' \item \strong{Continuous only}: Uses fitted values plus resampled residuals +#' \item \strong{Binomial}: Not supported (throws error) +#' } +#' +#' @return A list of length R containing bootstrap datasets. Each element is a +#' data.frame with the same structure as the original data, containing: +#' \itemize{ +#' \item Dose variable (same name as original) +#' \item Response variable(s) (same name(s) as original) +#' \item For binomial data: number of successes and total observations +#' \item For multi-curve data: curve identifier (if present) +#' } +#' +#' @section Data Type Handling: +#' +#' **Binomial Data:** +#' \itemize{ +#' \item Handles both aggregated (n successes out of N trials) and expanded formats +#' \item Preserves dose group structure during resampling +#' \item Applies continuity correction in parametric bootstrap +#' } +#' +#' **Continuous Data:** +#' \itemize{ +#' \item Maintains dose group structure +#' \item Preserves within-group variability patterns +#' \item Uses original data (`origData`) when available +#' } +#' +#' **Count Data (Poisson/Negative Binomial):** +#' \itemize{ +#' \item Treated similarly to continuous data for nonparametric bootstrap +#' \item Resamples within dose groups +#' } +#' +#' @section Multi-curve Support: +#' The function handles multi-curve dose-response data by preserving curve +#' identifiers during bootstrap resampling, ensuring that the bootstrap samples +#' maintain the original experimental structure. +#' +#' @note +#' This is an internal helper function for `bmdBoot`. It assumes the input object +#' has the standard structure from `drm()` fitting, including components like +#' `data`, `origData`, `call`, `type`, etc. +#' +#' **Important considerations:** +#' \itemize{ +#' \item Semiparametric bootstrap requires model residuals and fitted values +#' \item Parametric bootstrap assumes distributional assumptions are met +#' \item Large R values may require substantial memory for complex datasets +#' } +#' +#' @seealso +#' \code{\link{bmdBoot}} for the main bootstrap BMD function, +#' +#' @examples +#' \dontrun{ +#' # Typically called internally by bmdBoot, but can be used directly: +#' +#' # Fit a dose-response model +#' model <- drm(response/total ~ dose, weights = total, +#' data = binomial_data, fct = LL.4()) +#' +#' # Generate nonparametric bootstrap samples +#' boot_data <- bootDataGen(model, R = 100, bootType = "nonparametric") +#' +#' # Generate parametric bootstrap samples +#' boot_data_param <- bootDataGen(model, R = 100, bootType = "parametric") +#' +#' # For continuous data with semiparametric bootstrap +#' cont_model <- drm(response ~ dose, data = continuous_data, fct = LL.4()) +#' boot_data_semi <- bootDataGen(cont_model, R = 100, bootType = "semiparametric") +#' +#' # Access first bootstrap sample +#' first_sample <- boot_data[[1]] +#' } bootDataGen <- function(object, R=1000, bootType="nonparametric",aggregated=TRUE){ if(bootType=="nonparametric"){ if(object$type=="binomial"){ diff --git a/R/bootDataGenOrdinal.R b/R/bootDataGenOrdinal.R index cf3a7a0..5ec8164 100644 --- a/R/bootDataGenOrdinal.R +++ b/R/bootDataGenOrdinal.R @@ -1,7 +1,135 @@ -#' Help funtion to bmdOrdinal and bmdOrdinalMA +#' Generate Bootstrap Data for Ordinal Dose-Response Analysis +#' +#' @description +#' Helper function for `bmdOrdinal` and `bmdOrdinalMA` that generates bootstrap +#' datasets from fitted ordinal dose-response models. Supports multiple bootstrap +#' methods tailored for ordinal response data with different resampling strategies. +#' +#' @param object A fitted ordinal dose-response model object containing the original +#' data, model specifications, response levels, and fitted parameters +#' @param R integer; Number of bootstrap replicates to generate (default: 500) +#' @param bootType character; Type of bootstrap resampling method. Options are: +#' \itemize{ +#' \item \code{"nonparametric"}: Resamples individual observations within dose groups +#' \item \code{"parametric"}: Generates new observations using estimated category probabilities +#' \item \code{"model"}: Generates observations using fitted model probabilities +#' \item \code{"hierarchical"}: Hierarchical resampling accounting for block structure +#' } +#' +#' @details +#' The function implements four distinct bootstrap strategies for ordinal data: #' +#' **Nonparametric Bootstrap:** +#' \itemize{ +#' \item Expands ordinal data to individual observations +#' \item Resamples observations within each original data row +#' \item Maintains the empirical distribution within dose groups +#' \item Most conservative approach, makes no distributional assumptions +#' } #' +#' **Parametric Bootstrap:** +#' \itemize{ +#' \item Estimates category probabilities from original data +#' \item Applies continuity correction for boundary cases: +#' \deqn{p_{corrected} = \frac{1/K^2}{n + 1/K} \text{ when } p = 0}{p_corrected = (1/K^2)/(n + 1/K) when p = 0} +#' \deqn{p_{corrected} = \frac{n + 1/K^2}{n + 1/K} \text{ when } p = 1}{p_corrected = (n + 1/K^2)/(n + 1/K) when p = 1} +#' where K is the number of response categories and n is the sample size +#' \item Generates new observations using multinomial sampling +#' } #' +#' **Model-Based Bootstrap:** +#' \itemize{ +#' \item Uses fitted model probabilities (\code{object$pFun}) for each dose +#' \item Generates observations directly from the fitted dose-response relationship +#' \item Assumes the fitted model accurately represents the true relationship +#' } +#' +#' **Hierarchical Bootstrap:** +#' \itemize{ +#' \item Accounts for block/cluster structure in the data +#' \item Requires \code{object$blocks} to be specified +#' \item Uses weighted resampling within dose groups +#' \item Maintains hierarchical correlation structure +#' } +#' +#' @return A list of length R containing bootstrap datasets. Each element is a +#' data.frame with the same structure as the original ordinal data, containing: +#' \itemize{ +#' \item Dose variable (same name as original) +#' \item Count columns for each response category +#' \item For hierarchical: block identifier and total counts +#' \item All columns from original data structure preserved +#' } +#' +#' @section Data Processing: +#' The function uses several data manipulation steps: +#' \itemize{ +#' \item \strong{Expansion}: Converts aggregated ordinal data to individual observations +#' \item \strong{Resampling}: Applies the specified bootstrap method +#' \item \strong{Aggregation}: Converts back to count format using \code{reshape2::dcast} +#' \item \strong{Completion}: Ensures all response categories are present (fills with 0 if missing) +#' } +#' +#' @section Dependencies: +#' This function requires the following packages: +#' \itemize{ +#' \item \code{reshape2}: For data reshaping operations +#' \item \code{dplyr}: For data manipulation (hierarchical bootstrap only) +#' \item \code{tidyr}: For data tidying operations (hierarchical bootstrap only) +#' } +#' +#' The function will stop with an informative error if required packages are not installed. +#' +#' @section Continuity Correction: +#' For parametric bootstrap, when category probabilities are 0 or 1, a continuity +#' correction is applied to prevent degenerate sampling. This ensures all categories +#' have some probability of being selected, improving bootstrap stability. +#' +#' @note +#' This is an internal helper function for ordinal BMD bootstrap procedures. It assumes +#' the input object has the standard structure from ordinal dose-response fitting, +#' including components like \code{data}, \code{levels}, \code{dose}, \code{pFun}, etc. +#' +#' **Method Selection Guidelines:** +#' \itemize{ +#' \item Use \code{"nonparametric"} for robust, assumption-free bootstrap +#' \item Use \code{"parametric"} when sample sizes are small +#' \item Use \code{"model"} to assess model-based uncertainty +#' \item Use \code{"hierarchical"} for clustered/blocked experimental designs +#' } +#' +#' @seealso +#' \code{\link{bmdOrdinal}} for ordinal BMD estimation, +#' \code{\link{bmdOrdinalMA}} for model-averaged ordinal BMD,, +#' \code{\link[reshape2]{dcast}} for data reshaping +#' +#' @examples +#' \dontrun{ +#' # Typically called internally, but can be used directly: +#' +#' # Assume you have a fitted ordinal model +#' ordinal_model <- fitOrdinalModel(response ~ dose, data = ordinal_data) +#' +#' # Generate nonparametric bootstrap samples +#' boot_data_np <- bootDataGenOrdinal(ordinal_model, R = 100, +#' bootType = "nonparametric") +#' +#' # Generate parametric bootstrap samples +#' boot_data_param <- bootDataGenOrdinal(ordinal_model, R = 100, +#' bootType = "parametric") +#' +#' # Generate model-based bootstrap samples +#' boot_data_model <- bootDataGenOrdinal(ordinal_model, R = 100, +#' bootType = "model") +#' +#' # For hierarchical data with blocks +#' boot_data_hier <- bootDataGenOrdinal(ordinal_model, R = 100, +#' bootType = "hierarchical") +#' +#' # Access first bootstrap sample +#' first_sample <- boot_data_np[[1]] +#' head(first_sample) +#' } bootDataGenOrdinal <- function(object, R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical")){ bootType <- match.arg(bootType) diff --git a/R/coef.drcHetVar.R b/R/coef.drcHetVar.R index 19d95a6..032786a 100644 --- a/R/coef.drcHetVar.R +++ b/R/coef.drcHetVar.R @@ -1,5 +1,56 @@ - -#' @title S3 method +#' Extract Coefficients from Heteroscedastic Dose-Response Models +#' +#' @description +#' S3 method to extract coefficients from fitted heteroscedastic dose-response models. +#' This method extends the generic `coef()` function to handle `drcHetVar` objects, +#' which contain both dose-response curve parameters and variance model parameters. +#' +#' @param object An object of class "drcHetVar" containing a fitted heteroscedastic +#' dose-response model with separate curve and variance parameters +#' @param ... Additional arguments (currently unused but included for S3 method consistency) +#' +#' @details +#' Heteroscedastic dose-response models fit two components simultaneously: +#' \itemize{ +#' \item \strong{Curve parameters}: Describe the dose-response relationship +#' (e.g., slope, inflection point, asymptotes) +#' \item \strong{Variance parameters}: Model how the response variance changes +#' with dose or fitted values +#' } +#' +#' This method combines both parameter sets into a single named vector for easy +#' access and interpretation. Parameter names are prefixed to distinguish between +#' the two model components: +#' \itemize{ +#' \item \code{"Curve:"} prefix for dose-response curve parameters +#' \item \code{"Sigma:"} prefix for variance model parameters +#' } +#' +#' @return A named numeric vector containing all model parameters: +#' \itemize{ +#' \item Curve parameters with names prefixed by "Curve:" +#' \item Variance parameters with names prefixed by "Sigma:" +#' } +#' +#' @note +#' This method assumes the `drcHetVar` object contains: +#' \itemize{ +#' \item \code{curvePar}: Named vector of curve parameters +#' \item \code{sigmaPar}: Named vector of variance parameters +#' } +#' +#' The original parameter names from the fitting procedure are preserved but +#' prefixed for clarity. +#' +#' @seealso +#' \code{\link{coef}} for the generic coefficient extraction function, +#' +#' @examples +#' \dontrun{ +#' # Assuming you have a fitted heteroscedastic model +#' } +#' +#' @method coef drcHetVar #' @export coef.drcHetVar <- function(object, ...){ curvePar <- object$curvePar diff --git a/R/drmMMRE.R b/R/drmMMRE.R index 4e19f5d..7d1a6bd 100644 --- a/R/drmMMRE.R +++ b/R/drmMMRE.R @@ -160,7 +160,20 @@ drmMMRE <- function(formula, exp_id, data, fct, type = c("continuous", "binomial object } -#' @title S3 method +#' Extract Variance-Covariance Matrix from drcMMRE Objects +#' +#' @description +#' S3 method to extract the variance-covariance matrix from fitted drcMMRE objects +#' by delegating to the underlying model-averaged model. +#' +#' @param object An object of class "drcMMRE" +#' @param ... Additional arguments (currently unused) +#' +#' @return The variance-covariance matrix of the model parameters. +#' +#' @seealso \code{\link{vcov}} for the generic function +#' +#' @method vcov drcMMRE #' @export vcov.drcMMRE <- function(object, ...){ vcov(object$MV_MA_model) diff --git a/R/expandBinomial.R b/R/expandBinomial.R index edda01a..79d0e6c 100644 --- a/R/expandBinomial.R +++ b/R/expandBinomial.R @@ -19,10 +19,6 @@ #' @return data.frame #' @author Signe M. Jensen and Jens Riis Baalkilde #' @keywords models nonlinear -#' @examples \dontrun{ -#' } -#' -#' expandBinomial <- function(data, number, total, dose, curveid = character(0)){ if(length(curveid) == 0){ df<-data.frame(number = c(rep(rep(1,length(data[,number])), data[,number]), diff --git a/R/invBmd.R b/R/invBmd.R index cd3388e..1cd2f49 100644 --- a/R/invBmd.R +++ b/R/invBmd.R @@ -1,7 +1,139 @@ -#' Help funtion to bmd +#' Inverse Regression for Benchmark Dose Calculation +#' +#' @description +#' Helper function for `bmd` that calculates Benchmark Dose (BMD) and confidence +#' intervals using inverse regression. This function handles multiple BMD definitions +#' and background response types by dynamically modifying the dose-response function +#' and its derivatives to solve for the dose corresponding to a specified benchmark response. +#' +#' @param object A fitted dose-response model object containing the model function, +#' derivatives, coefficients, and data information +#' @param bmr numeric; Benchmark response level for which to calculate the BMD +#' @param level numeric; Confidence level for BMD confidence intervals (default: 0.9) +#' @param slope character; Direction of dose-response relationship, either +#' "increasing" or "decreasing" +#' @param backgType character; Type of background response calculation. Options include: +#' "modelBased", "hybridSD", "absolute" +#' @param backg numeric; Background response value (used with certain backgType options). +#' Default: NA +#' @param catLev numeric; Category level for multi-level responses. Default: NA +#' @param extFactor numeric; Extension factor for maximum dose search range (default: 10) +#' @param def character; BMD definition type. Options include: +#' \itemize{ +#' \item "additional"/"added": Additional risk over background +#' \item "excess": Excess risk over background +#' \item "relative": Relative change from background +#' \item "extra": Extra risk (between background and maximum) +#' \item "hybridAdd": Hybrid additional risk using statistical criteria +#' \item "hybridExc": Hybrid excess risk using statistical criteria +#' \item "point": Point estimate (not supported for inverse regression) +#' } +#' @param useSD numeric; Standard deviation value used in hybrid definitions +#' @param sandwich.vcov logical; Whether to use sandwich variance-covariance matrix +#' for robust standard errors (default: FALSE) +#' +#' @details +#' The function implements inverse regression by solving: +#' \deqn{f(BMD) = BMR}{f(BMD) = BMR} +#' where f is the transformed dose-response function based on the specified definition. #' +#' **BMD Definitions:** #' +#' **Additional Risk:** \deqn{f(x) = |f_0(0) - f_0(x)|}{f(x) = |f_0(0) - f_0(x)|} #' +#' **Excess Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} (decreasing) +#' \deqn{f(x) = \frac{f_0(x) - f_0(0)}{1 - f_0(0)}}{f(x) = (f_0(x) - f_0(0))/(1 - f_0(0))} (increasing) +#' +#' **Relative Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} +#' +#' **Extra Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{|f_0(0) - f_0(\infty)|}}{f(x) = |f_0(0) - f_0(x)|/|f_0(0) - f_0(infinity)|} +#' +#' **Hybrid Definitions:** Use normal distribution probabilities: +#' \deqn{f(x) = \Phi\left(\frac{f_0(0) - k \cdot SD - f_0(x)}{SD}\right) - (1-\Phi(k))}{f(x) = Phi((f_0(0) - k*SD - f_0(x))/SD) - (1-Phi(k))} +#' where k is the number of standard deviations (default: 2). +#' +#' @return A matrix with 1 row and 3 columns: +#' \itemize{ +#' \item \strong{BMD}: Benchmark dose estimate +#' \item \strong{BMDL}: Lower confidence limit for BMD +#' \item \strong{BMDU}: Upper confidence limit for BMD +#' } +#' +#' If root finding fails for confidence limits, BMDL is set to 0 and BMDU to Inf. +#' +#' @section Function Modification: +#' The function dynamically modifies the model's derivative function to account +#' for different BMD definitions by: +#' \itemize{ +#' \item Parsing the derivative function body +#' \item Adding appropriate transformation terms +#' \item Handling parameter indexing for fixed vs. estimated parameters +#' \item Supporting both 4-parameter and 5-parameter models +#' } +#' +#' @section Confidence Intervals: +#' Confidence intervals are calculated using the delta method: +#' \deqn{CI = BMD \pm t_{\alpha/2} \sqrt{h(BMD)^T \Sigma h(BMD)}}{CI = BMD +/- t * sqrt(h(BMD)' * Sigma * h(BMD))} +#' where h(BMD) is the gradient vector and Σ is the variance-covariance matrix. +#' +#' For continuous data, t-distribution quantiles are used; for other data types, +#' normal distribution quantiles are used. +#' +#' @section Error Handling: +#' The function includes several error checks: +#' \itemize{ +#' \item Stops if "point" definition is used (not supported) +#' \item Stops if hybrid definitions are used without appropriate backgType +#' \item Stops if no background value is provided when required +#' \item Stops if no solution exists for the specified BMR +#' } +#' +#' @note +#' This is an internal helper function for BMD calculation. It assumes the input +#' object has the standard structure from dose-response model fitting, including +#' components like `fct`, `dataList`, `type`, etc. +#' +#' **Important considerations:** +#' \itemize{ +#' \item The search range is limited to [0, extFactor × max(dose)] +#' \item Hybrid definitions require careful specification of useSD and backg +#' \item Function modification uses string manipulation and may be sensitive to model structure +#' } +#' +#' @seealso +#' \code{\link{bmd}} for the main BMD calculation function, +#' \code{\link{uniroot}} for the root finding algorithm, +#' \code{\link{vcov}} for variance-covariance matrix extraction, +#' \code{\link[sandwich]{sandwich}} for robust variance estimation +#' +#' @examples +#' \dontrun{ +#' # Typically called internally by bmd(), but can be used directly: +#' # Need to be updated +#' # Fit a dose-response model +#' model <- drm(response ~ dose, data = dose_data, fct = LL.4()) +#' +#' # Calculate BMD for 10% additional risk +#' bmd_result <- invBmd(object = model, +#' bmr = 0.1, +#' level = 0.9, +#' slope = "increasing", +#' def = "additional", +#' useSD = sd(model$data$response)) +#' +#' # Extract results +#' bmd_estimate <- bmd_result[1, "BMD"] +#' bmd_lower <- bmd_result[1, "BMDL"] +#' bmd_upper <- bmd_result[1, "BMDU"] +#' +#' # Using hybrid definition with 1.5 standard deviations +#' bmd_hybrid <- invBmd(object = model, +#' bmr = 0.05, +#' def = "hybridAdd", +#' backgType = "hybridSD", +#' backg = 1.5, +#' useSD = sd(model$data$response)) +#' } invBmd <- function(object, bmr, level=0.9, slope, backgType="modelBased", backg=NA, catLev=NA, extFactor=10, def, useSD=useSD, sandwich.vcov=FALSE){ diff --git a/man/BCa.Rd b/man/BCa.Rd index 800d97e..f066bd5 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -35,23 +35,25 @@ provides better coverage than standard bootstrap confidence intervals. The BCa method computes confidence intervals using three components: 1. Bias correction (z0): -#$# z_0 = \Phi^{-1}(\frac{\#\{\theta^*(b) \leq \hat{\theta}\}}{B}) #$# -where B is the number of bootstrap replicates. +\deqn{z_0 = \Phi^{-1}\left(\frac{\text{number of } \theta^*_b \leq \hat{\theta}}{B}\right)}{z_0 = qnorm(proportion of bootstrap samples <= observed value)} +where B is the number of bootstrap replicates and \eqn{\theta^*_b}{theta*_b} represents the b-th bootstrap replicate. 2. Acceleration (a): -#$# a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}} #$# -where θ_(i) are the jackknife values. +\deqn{a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}}}{a = sum((theta-bar - theta_i)^3) / (6 * [sum((theta-bar - theta_i)^2)]^(3/2))} +where \eqn{\theta_{(i)}}{theta_i} are the jackknife values. 3. The confidence limits are then computed as: -#$# \alpha_{1,2} = \Phi(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}) #$# +\deqn{\alpha_{1,2} = \Phi\left(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}\right)}{alpha_(1,2) = Phi(z_0 + (z_0 +/- z_alpha)/(1 - a*(z_0 +/- z_alpha)))} } \section{Warning}{ The function assumes that: -- The bootstrap samples are independent -- The statistic of interest is smooth (continuously differentiable) -- There are sufficient bootstrap replicates (typically >1000) -- The jackknife values are properly computed +\itemize{ + \item The bootstrap samples are independent + \item The statistic of interest is smooth (continuously differentiable) + \item There are sufficient bootstrap replicates (typically >1000) + \item The jackknife values are properly computed +} } \examples{ @@ -75,10 +77,10 @@ BCa(obs_mean, data, boot_means, jack_means, 0.95) } \references{ Efron, B. (1987). Better Bootstrap Confidence Intervals. -*Journal of the American Statistical Association*, 82(397), 171-185. +\emph{Journal of the American Statistical Association}, 82(397), 171-185. DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. -*Statistical Science*, 11(3), 189-212. +\emph{Statistical Science}, 11(3), 189-212. } \seealso{ \code{\link{quantile}} for the underlying quantile computation diff --git a/man/BIC.drcOrdinal.Rd b/man/BIC.drcOrdinal.Rd index 78c3c22..db5254b 100644 --- a/man/BIC.drcOrdinal.Rd +++ b/man/BIC.drcOrdinal.Rd @@ -2,10 +2,94 @@ % Please edit documentation in R/BIC.drcOrdinal.R \name{BIC.drcOrdinal} \alias{BIC.drcOrdinal} -\title{S3 method} +\title{BIC Method for drcOrdinal Objects} \usage{ \method{BIC}{drcOrdinal}(object, ...) } +\arguments{ +\item{object}{An object of class "drcOrdinal" containing fitted ordinal +dose-response models} + +\item{...}{Additional arguments passed to the method. Currently supports: +\itemize{ + \item \code{epsilon}: Small positive value to avoid log(0) in likelihood + calculations (default: 1e-16) +}} +} +\value{ +A numeric value representing the BIC of the fitted ordinal dose-response model. + Lower values indicate better model fit when comparing models. +} \description{ -S3 method +S3 method to calculate the Bayesian Information Criterion (BIC) for fitted +ordinal dose-response models. This method extends the generic `BIC()` function +to handle `drcOrdinal` objects which contain multiple fitted dose-response models +for different response categories. +} +\details{ +The BIC is calculated using the standard formula: +\deqn{BIC = k \log(n) - 2 \log(L)}{BIC = k * log(n) - 2 * log(L)} +where: +\itemize{ + \item \eqn{k}{k} is the total number of parameters across all models in the ordinal fit + \item \eqn{n}{n} is the total number of observations (sum of weights) + \item \eqn{L}{L} is the likelihood of the fitted model +} + +For ordinal dose-response models, the total number of parameters is the sum +of parameters from all individual models in the `drmList` component, and the +sample size is calculated as the sum of weights in the data. + +The `epsilon` parameter is used in the `logLik()` calculation to prevent +numerical issues when probabilities approach zero. +} +\note{ +This method assumes that the `drcOrdinal` object contains: +\itemize{ + \item A `drmList` component with fitted dose-response models + \item A `data` component with the original data including weights + \item A `weights` component specifying the column name for observation weights +} +} +\section{Model Comparison}{ + +BIC penalizes model complexity more heavily than AIC, making it useful for: +\itemize{ + \item Comparing ordinal dose-response models with different numbers of parameters + \item Model selection in situations where simpler models are preferred + \item Avoiding overfitting in dose-response modeling +} +} + +\examples{ +\dontrun{ +# Assuming you have a fitted drcOrdinal object +ordinal_model <- drm(response ~ dose, + weights = count, + data = ordinal_data, + fct = cumulative.logit()) + +# Calculate BIC +bic_value <- BIC(ordinal_model) + +# Compare models +model1_bic <- BIC(ordinal_model1) +model2_bic <- BIC(ordinal_model2) + +# Lower BIC indicates better model +if(model1_bic < model2_bic) { + cat("Model 1 is preferred\n") +} else { + cat("Model 2 is preferred\n") +} + +# Use custom epsilon for numerical stability +bic_custom <- BIC(ordinal_model, epsilon = 1e-12) +} + +} +\seealso{ +\code{\link{BIC}} for the generic BIC function, +\code{\link{AIC.drcOrdinal}} for the corresponding AIC method, +\code{\link{logLik.drcOrdinal}} for the log-likelihood method } diff --git a/man/bmdMACurve.Rd b/man/bmdMACurve.Rd index 62d9e7a..8c28308 100644 --- a/man/bmdMACurve.Rd +++ b/man/bmdMACurve.Rd @@ -2,10 +2,115 @@ % Please edit documentation in R/bmdMACurve.R \name{bmdMACurve} \alias{bmdMACurve} -\title{Help funtion to bmdMA} +\title{Calculate Model-Averaged BMD Curve, helper to bmdMA} \usage{ bmdMACurve(modelList, modelWeights, bmrScaled0, searchInterval = "dataBased") } +\arguments{ +\item{modelList}{list; A list of fitted dose-response models from which to compute +the model average. Each model should be a fitted object with components +including `fct`, `parmMat`, `dataList`, etc.} + +\item{modelWeights}{numeric vector; Weights for model averaging, typically derived +from model selection criteria (e.g., AIC weights). Must sum to 1 and have +the same length as `modelList`} + +\item{bmrScaled0}{numeric; The benchmark response level(s) for which to calculate +BMD. For single curves, a scalar value; for multiple curves, a vector with +length equal to the number of curves} + +\item{searchInterval}{character or numeric; Search interval for root finding. +If "dataBased" (default), uses data range with small lower bound adjustment. +If numeric, should be a vector of length 2 for single curves, or a matrix +with 2 columns for multiple curves specifying [lower, upper] bounds} +} +\value{ +An object of class "bmd" containing: +\itemize{ + \item \strong{Results}: A matrix with BMD values. For single curves, a 1x1 matrix; + for multiple curves, an nx1 matrix where n is the number of curves + \item \strong{MACurve}: The model-averaged function used for BMD calculation. + For single curves, returns the combined function; for multiple curves, returns NULL +} +} \description{ -Help funtion to bmdMA +Helper function for `bmdMA` that computes Benchmark Dose (BMD) values using +model averaging. The function creates a weighted average of multiple dose-response +models and finds the dose corresponding to a specified benchmark response level. +} +\details{ +The function handles two scenarios: + +**Single Curve Analysis:** +Creates a weighted combination of model functions: +\deqn{f_{MA}(x) = \sum_{i=1}^{m} w_i \cdot f_i(x)}{f_MA(x) = sum of w_i * f_i(x)} +where \eqn{w_i}{w_i} are model weights and \eqn{f_i(x)}{f_i(x)} are individual model functions. + +**Multiple Curve Analysis:** +Computes BMD separately for each curve using the same model averaging approach +but applied to curve-specific data and parameters. + +The BMD is found by solving: +\deqn{f_{MA}(BMD) = BMR}{f_MA(BMD) = BMR} +using root finding algorithms. + +**Model Function Construction:** +The function dynamically constructs model functions by: +\itemize{ + \item Extracting function templates from `mtList()` + \item Substituting fixed parameters and estimated coefficients + \item Handling special cases like Fractional Polynomial models + \item Creating weighted combinations of all models +} +} +\note{ +This is primarily an internal helper function for `bmdMA`. Direct usage requires +properly formatted model lists and weights. The function assumes all models in +`modelList` are compatible and fitted to the same dataset structure. +} +\section{Search Interval}{ + +When `searchInterval = "dataBased"`: +\itemize{ + \item Lower bound: Second smallest dose value divided by 10,000 + \item Upper bound: Maximum dose value in the dataset +} + +Custom intervals can be provided to avoid convergence issues or focus on +specific dose ranges of interest. +} + +\section{Model Support}{ + +The function supports various dose-response models including: +\itemize{ + \item Standard 4-parameter and 5-parameter models + \item Fractional Polynomial models (special handling) + \item Models with fixed parameters +} +} + +\examples{ +\dontrun{ +# Typically called internally by bmdMA, but can be used directly: + +# Assume you have a list of fitted models and weights +models <- list(model1, model2, model3) # fitted drc models +weights <- c(0.5, 0.3, 0.2) # AIC weights +bmr <- 0.1 # 10\% benchmark response + +# Calculate model-averaged BMD +result <- bmdMACurve(models, weights, bmr) + +# Extract BMD value +bmd_value <- result$Results[1, 1] + +# Use the averaged curve function +curve_function <- result$MACurve +} + +} +\seealso{ +\code{\link{bmdMA}} for the main model averaging function, +\code{\link{uniroot}} for the root finding algorithm used internally } diff --git a/man/bootDataGen.Rd b/man/bootDataGen.Rd index b59506c..7fcfbf2 100644 --- a/man/bootDataGen.Rd +++ b/man/bootDataGen.Rd @@ -2,10 +2,133 @@ % Please edit documentation in R/bootDataGen.R \name{bootDataGen} \alias{bootDataGen} -\title{Help funtion to bmdBoot} +\title{Generate Bootstrap Data for BMD Analysis} \usage{ bootDataGen(object, R = 1000, bootType = "nonparametric", aggregated = TRUE) } +\arguments{ +\item{object}{A fitted dose-response model object (typically from `drm()`) +containing the original data and model specifications} + +\item{R}{integer; Number of bootstrap replicates to generate (default: 1000)} + +\item{bootType}{character; Type of bootstrap resampling method. Options are: +\itemize{ + \item \code{"nonparametric"}: Resamples observations within dose groups + \item \code{"parametric"}: Generates new data from fitted distributions + \item \code{"semiparametric"}: Uses fitted values plus resampled residuals +}} + +\item{aggregated}{logical; For binomial data, whether to return aggregated +(summary) format or expanded (individual observation) format (default: TRUE)} +} +\value{ +A list of length R containing bootstrap datasets. Each element is a + data.frame with the same structure as the original data, containing: + \itemize{ + \item Dose variable (same name as original) + \item Response variable(s) (same name(s) as original) + \item For binomial data: number of successes and total observations + \item For multi-curve data: curve identifier (if present) + } +} \description{ -Help funtion to bmdBoot +Helper function for `bmdBoot` that generates bootstrap datasets from fitted +dose-response models. Supports multiple bootstrap methods (nonparametric, +parametric, and semiparametric) and handles different response types +(binomial, continuous, Poisson, negative binomial). +} +\details{ +The function implements different bootstrap strategies based on data type and method: + +**Nonparametric Bootstrap:** +\itemize{ + \item \strong{Binomial}: Expands binomial data to individual observations, + resamples within dose groups, then optionally re-aggregates + \item \strong{Continuous/Count}: Resamples observations within dose groups + from the original dataset +} + +**Parametric Bootstrap:** +\itemize{ + \item \strong{Binomial}: Generates new binomial observations using estimated + success probabilities, with continuity correction (adds 0.25/0.5) for + boundary cases + \item \strong{Continuous}: Generates normal random variables using + dose-specific means and standard deviations from original data +} + +**Semiparametric Bootstrap:** +\itemize{ + \item \strong{Continuous only}: Uses fitted values plus resampled residuals + \item \strong{Binomial}: Not supported (throws error) +} +} +\note{ +This is an internal helper function for `bmdBoot`. It assumes the input object +has the standard structure from `drm()` fitting, including components like +`data`, `origData`, `call`, `type`, etc. + +**Important considerations:** +\itemize{ + \item Semiparametric bootstrap requires model residuals and fitted values + \item Parametric bootstrap assumes distributional assumptions are met + \item Large R values may require substantial memory for complex datasets +} +} +\section{Data Type Handling}{ + + +**Binomial Data:** +\itemize{ + \item Handles both aggregated (n successes out of N trials) and expanded formats + \item Preserves dose group structure during resampling + \item Applies continuity correction in parametric bootstrap +} + +**Continuous Data:** +\itemize{ + \item Maintains dose group structure + \item Preserves within-group variability patterns + \item Uses original data (`origData`) when available +} + +**Count Data (Poisson/Negative Binomial):** +\itemize{ + \item Treated similarly to continuous data for nonparametric bootstrap + \item Resamples within dose groups +} +} + +\section{Multi-curve Support}{ + +The function handles multi-curve dose-response data by preserving curve +identifiers during bootstrap resampling, ensuring that the bootstrap samples +maintain the original experimental structure. +} + +\examples{ +\dontrun{ +# Typically called internally by bmdBoot, but can be used directly: + +# Fit a dose-response model +model <- drm(response/total ~ dose, weights = total, + data = binomial_data, fct = LL.4()) + +# Generate nonparametric bootstrap samples +boot_data <- bootDataGen(model, R = 100, bootType = "nonparametric") + +# Generate parametric bootstrap samples +boot_data_param <- bootDataGen(model, R = 100, bootType = "parametric") + +# For continuous data with semiparametric bootstrap +cont_model <- drm(response ~ dose, data = continuous_data, fct = LL.4()) +boot_data_semi <- bootDataGen(cont_model, R = 100, bootType = "semiparametric") + +# Access first bootstrap sample +first_sample <- boot_data[[1]] +} +} +\seealso{ +\code{\link{bmdBoot}} for the main bootstrap BMD function, } diff --git a/man/bootDataGenOrdinal.Rd b/man/bootDataGenOrdinal.Rd index 045fdc3..c5cf24d 100644 --- a/man/bootDataGenOrdinal.Rd +++ b/man/bootDataGenOrdinal.Rd @@ -2,7 +2,7 @@ % Please edit documentation in R/bootDataGenOrdinal.R \name{bootDataGenOrdinal} \alias{bootDataGenOrdinal} -\title{Help funtion to bmdOrdinal and bmdOrdinalMA} +\title{Generate Bootstrap Data for Ordinal Dose-Response Analysis} \usage{ bootDataGenOrdinal( object, @@ -10,6 +10,144 @@ bootDataGenOrdinal( bootType = c("nonparametric", "parametric", "model", "hierarchical") ) } +\arguments{ +\item{object}{A fitted ordinal dose-response model object containing the original +data, model specifications, response levels, and fitted parameters} + +\item{R}{integer; Number of bootstrap replicates to generate (default: 500)} + +\item{bootType}{character; Type of bootstrap resampling method. Options are: +\itemize{ + \item \code{"nonparametric"}: Resamples individual observations within dose groups + \item \code{"parametric"}: Generates new observations using estimated category probabilities + \item \code{"model"}: Generates observations using fitted model probabilities + \item \code{"hierarchical"}: Hierarchical resampling accounting for block structure +}} +} +\value{ +A list of length R containing bootstrap datasets. Each element is a + data.frame with the same structure as the original ordinal data, containing: + \itemize{ + \item Dose variable (same name as original) + \item Count columns for each response category + \item For hierarchical: block identifier and total counts + \item All columns from original data structure preserved + } +} \description{ -Help funtion to bmdOrdinal and bmdOrdinalMA +Helper function for `bmdOrdinal` and `bmdOrdinalMA` that generates bootstrap +datasets from fitted ordinal dose-response models. Supports multiple bootstrap +methods tailored for ordinal response data with different resampling strategies. +} +\details{ +The function implements four distinct bootstrap strategies for ordinal data: + +**Nonparametric Bootstrap:** +\itemize{ + \item Expands ordinal data to individual observations + \item Resamples observations within each original data row + \item Maintains the empirical distribution within dose groups + \item Most conservative approach, makes no distributional assumptions +} + +**Parametric Bootstrap:** +\itemize{ + \item Estimates category probabilities from original data + \item Applies continuity correction for boundary cases: + \deqn{p_{corrected} = \frac{1/K^2}{n + 1/K} \text{ when } p = 0}{p_corrected = (1/K^2)/(n + 1/K) when p = 0} + \deqn{p_{corrected} = \frac{n + 1/K^2}{n + 1/K} \text{ when } p = 1}{p_corrected = (n + 1/K^2)/(n + 1/K) when p = 1} + where K is the number of response categories and n is the sample size + \item Generates new observations using multinomial sampling +} + +**Model-Based Bootstrap:** +\itemize{ + \item Uses fitted model probabilities (\code{object$pFun}) for each dose + \item Generates observations directly from the fitted dose-response relationship + \item Assumes the fitted model accurately represents the true relationship +} + +**Hierarchical Bootstrap:** +\itemize{ + \item Accounts for block/cluster structure in the data + \item Requires \code{object$blocks} to be specified + \item Uses weighted resampling within dose groups + \item Maintains hierarchical correlation structure +} +} +\note{ +This is an internal helper function for ordinal BMD bootstrap procedures. It assumes +the input object has the standard structure from ordinal dose-response fitting, +including components like \code{data}, \code{levels}, \code{dose}, \code{pFun}, etc. + +**Method Selection Guidelines:** +\itemize{ + \item Use \code{"nonparametric"} for robust, assumption-free bootstrap + \item Use \code{"parametric"} when sample sizes are small + \item Use \code{"model"} to assess model-based uncertainty + \item Use \code{"hierarchical"} for clustered/blocked experimental designs +} +} +\section{Data Processing}{ + +The function uses several data manipulation steps: +\itemize{ + \item \strong{Expansion}: Converts aggregated ordinal data to individual observations + \item \strong{Resampling}: Applies the specified bootstrap method + \item \strong{Aggregation}: Converts back to count format using \code{reshape2::dcast} + \item \strong{Completion}: Ensures all response categories are present (fills with 0 if missing) +} +} + +\section{Dependencies}{ + +This function requires the following packages: +\itemize{ + \item \code{reshape2}: For data reshaping operations + \item \code{dplyr}: For data manipulation (hierarchical bootstrap only) + \item \code{tidyr}: For data tidying operations (hierarchical bootstrap only) +} + +The function will stop with an informative error if required packages are not installed. +} + +\section{Continuity Correction}{ + +For parametric bootstrap, when category probabilities are 0 or 1, a continuity +correction is applied to prevent degenerate sampling. This ensures all categories +have some probability of being selected, improving bootstrap stability. +} + +\examples{ +\dontrun{ +# Typically called internally, but can be used directly: + +# Assume you have a fitted ordinal model +ordinal_model <- fitOrdinalModel(response ~ dose, data = ordinal_data) + +# Generate nonparametric bootstrap samples +boot_data_np <- bootDataGenOrdinal(ordinal_model, R = 100, + bootType = "nonparametric") + +# Generate parametric bootstrap samples +boot_data_param <- bootDataGenOrdinal(ordinal_model, R = 100, + bootType = "parametric") + +# Generate model-based bootstrap samples +boot_data_model <- bootDataGenOrdinal(ordinal_model, R = 100, + bootType = "model") + +# For hierarchical data with blocks +boot_data_hier <- bootDataGenOrdinal(ordinal_model, R = 100, + bootType = "hierarchical") + +# Access first bootstrap sample +first_sample <- boot_data_np[[1]] +head(first_sample) +} +} +\seealso{ +\code{\link{bmdOrdinal}} for ordinal BMD estimation, +\code{\link{bmdOrdinalMA}} for model-averaged ordinal BMD,, +\code{\link[reshape2]{dcast}} for data reshaping } diff --git a/man/coef.drcHetVar.Rd b/man/coef.drcHetVar.Rd index bb32d40..7789ae3 100644 --- a/man/coef.drcHetVar.Rd +++ b/man/coef.drcHetVar.Rd @@ -2,10 +2,61 @@ % Please edit documentation in R/coef.drcHetVar.R \name{coef.drcHetVar} \alias{coef.drcHetVar} -\title{S3 method} +\title{Extract Coefficients from Heteroscedastic Dose-Response Models} \usage{ \method{coef}{drcHetVar}(object, ...) } +\arguments{ +\item{object}{An object of class "drcHetVar" containing a fitted heteroscedastic +dose-response model with separate curve and variance parameters} + +\item{...}{Additional arguments (currently unused but included for S3 method consistency)} +} +\value{ +A named numeric vector containing all model parameters: +\itemize{ + \item Curve parameters with names prefixed by "Curve:" + \item Variance parameters with names prefixed by "Sigma:" +} +} \description{ -S3 method +S3 method to extract coefficients from fitted heteroscedastic dose-response models. +This method extends the generic `coef()` function to handle `drcHetVar` objects, +which contain both dose-response curve parameters and variance model parameters. +} +\details{ +Heteroscedastic dose-response models fit two components simultaneously: +\itemize{ + \item \strong{Curve parameters}: Describe the dose-response relationship + (e.g., slope, inflection point, asymptotes) + \item \strong{Variance parameters}: Model how the response variance changes + with dose or fitted values +} + +This method combines both parameter sets into a single named vector for easy +access and interpretation. Parameter names are prefixed to distinguish between +the two model components: +\itemize{ + \item \code{"Curve:"} prefix for dose-response curve parameters + \item \code{"Sigma:"} prefix for variance model parameters +} +} +\note{ +This method assumes the `drcHetVar` object contains: +\itemize{ + \item \code{curvePar}: Named vector of curve parameters + \item \code{sigmaPar}: Named vector of variance parameters +} + +The original parameter names from the fitting procedure are preserved but +prefixed for clarity. +} +\examples{ +\dontrun{ +# Assuming you have a fitted heteroscedastic model +} + +} +\seealso{ +\code{\link{coef}} for the generic coefficient extraction function, } diff --git a/man/expandBinomial.Rd b/man/expandBinomial.Rd index 6829a8c..5cea692 100644 --- a/man/expandBinomial.Rd +++ b/man/expandBinomial.Rd @@ -32,12 +32,6 @@ The aim to provide an R package calculating the benchmark dose (BMD) and the lower limit of the corresponding 95\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. -} -\examples{ -\dontrun{ -} - - } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/invBmd.Rd b/man/invBmd.Rd index 720363e..7c4138c 100644 --- a/man/invBmd.Rd +++ b/man/invBmd.Rd @@ -2,7 +2,7 @@ % Please edit documentation in R/invBmd.R \name{invBmd} \alias{invBmd} -\title{Help funtion to bmd} +\title{Inverse Regression for Benchmark Dose Calculation} \usage{ invBmd( object, @@ -18,6 +18,156 @@ invBmd( sandwich.vcov = FALSE ) } +\arguments{ +\item{object}{A fitted dose-response model object containing the model function, +derivatives, coefficients, and data information} + +\item{bmr}{numeric; Benchmark response level for which to calculate the BMD} + +\item{level}{numeric; Confidence level for BMD confidence intervals (default: 0.9)} + +\item{slope}{character; Direction of dose-response relationship, either +"increasing" or "decreasing"} + +\item{backgType}{character; Type of background response calculation. Options include: +"modelBased", "hybridSD", "absolute"} + +\item{backg}{numeric; Background response value (used with certain backgType options). +Default: NA} + +\item{catLev}{numeric; Category level for multi-level responses. Default: NA} + +\item{extFactor}{numeric; Extension factor for maximum dose search range (default: 10)} + +\item{def}{character; BMD definition type. Options include: +\itemize{ + \item "additional"/"added": Additional risk over background + \item "excess": Excess risk over background + \item "relative": Relative change from background + \item "extra": Extra risk (between background and maximum) + \item "hybridAdd": Hybrid additional risk using statistical criteria + \item "hybridExc": Hybrid excess risk using statistical criteria + \item "point": Point estimate (not supported for inverse regression) +}} + +\item{useSD}{numeric; Standard deviation value used in hybrid definitions} + +\item{sandwich.vcov}{logical; Whether to use sandwich variance-covariance matrix +for robust standard errors (default: FALSE)} +} +\value{ +A matrix with 1 row and 3 columns: +\itemize{ + \item \strong{BMD}: Benchmark dose estimate + \item \strong{BMDL}: Lower confidence limit for BMD + \item \strong{BMDU}: Upper confidence limit for BMD +} + +If root finding fails for confidence limits, BMDL is set to 0 and BMDU to Inf. +} \description{ -Help funtion to bmd +Helper function for `bmd` that calculates Benchmark Dose (BMD) and confidence +intervals using inverse regression. This function handles multiple BMD definitions +and background response types by dynamically modifying the dose-response function +and its derivatives to solve for the dose corresponding to a specified benchmark response. +} +\details{ +The function implements inverse regression by solving: +\deqn{f(BMD) = BMR}{f(BMD) = BMR} +where f is the transformed dose-response function based on the specified definition. + +**BMD Definitions:** + +**Additional Risk:** \deqn{f(x) = |f_0(0) - f_0(x)|}{f(x) = |f_0(0) - f_0(x)|} + +**Excess Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} (decreasing) +\deqn{f(x) = \frac{f_0(x) - f_0(0)}{1 - f_0(0)}}{f(x) = (f_0(x) - f_0(0))/(1 - f_0(0))} (increasing) + +**Relative Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} + +**Extra Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{|f_0(0) - f_0(\infty)|}}{f(x) = |f_0(0) - f_0(x)|/|f_0(0) - f_0(infinity)|} + +**Hybrid Definitions:** Use normal distribution probabilities: +\deqn{f(x) = \Phi\left(\frac{f_0(0) - k \cdot SD - f_0(x)}{SD}\right) - (1-\Phi(k))}{f(x) = Phi((f_0(0) - k*SD - f_0(x))/SD) - (1-Phi(k))} +where k is the number of standard deviations (default: 2). +} +\note{ +This is an internal helper function for BMD calculation. It assumes the input +object has the standard structure from dose-response model fitting, including +components like `fct`, `dataList`, `type`, etc. + +**Important considerations:** +\itemize{ + \item The search range is limited to [0, extFactor × max(dose)] + \item Hybrid definitions require careful specification of useSD and backg + \item Function modification uses string manipulation and may be sensitive to model structure +} +} +\section{Function Modification}{ + +The function dynamically modifies the model's derivative function to account +for different BMD definitions by: +\itemize{ + \item Parsing the derivative function body + \item Adding appropriate transformation terms + \item Handling parameter indexing for fixed vs. estimated parameters + \item Supporting both 4-parameter and 5-parameter models +} +} + +\section{Confidence Intervals}{ + +Confidence intervals are calculated using the delta method: +\deqn{CI = BMD \pm t_{\alpha/2} \sqrt{h(BMD)^T \Sigma h(BMD)}}{CI = BMD +/- t * sqrt(h(BMD)' * Sigma * h(BMD))} +where h(BMD) is the gradient vector and Σ is the variance-covariance matrix. + +For continuous data, t-distribution quantiles are used; for other data types, +normal distribution quantiles are used. +} + +\section{Error Handling}{ + +The function includes several error checks: +\itemize{ + \item Stops if "point" definition is used (not supported) + \item Stops if hybrid definitions are used without appropriate backgType + \item Stops if no background value is provided when required + \item Stops if no solution exists for the specified BMR +} +} + +\examples{ +\dontrun{ +# Typically called internally by bmd(), but can be used directly: +# Need to be updated +# Fit a dose-response model +model <- drm(response ~ dose, data = dose_data, fct = LL.4()) + +# Calculate BMD for 10\% additional risk +bmd_result <- invBmd(object = model, + bmr = 0.1, + level = 0.9, + slope = "increasing", + def = "additional", + useSD = sd(model$data$response)) + +# Extract results +bmd_estimate <- bmd_result[1, "BMD"] +bmd_lower <- bmd_result[1, "BMDL"] +bmd_upper <- bmd_result[1, "BMDU"] + +# Using hybrid definition with 1.5 standard deviations +bmd_hybrid <- invBmd(object = model, + bmr = 0.05, + def = "hybridAdd", + backgType = "hybridSD", + backg = 1.5, + useSD = sd(model$data$response)) +} +} +\seealso{ +\code{\link{bmd}} for the main BMD calculation function, +\code{\link{uniroot}} for the root finding algorithm, +\code{\link{vcov}} for variance-covariance matrix extraction, +\code{\link[sandwich]{sandwich}} for robust variance estimation } diff --git a/man/vcov.drcMMRE.Rd b/man/vcov.drcMMRE.Rd index 5dd8b63..63cb1fa 100644 --- a/man/vcov.drcMMRE.Rd +++ b/man/vcov.drcMMRE.Rd @@ -2,10 +2,22 @@ % Please edit documentation in R/drmMMRE.R \name{vcov.drcMMRE} \alias{vcov.drcMMRE} -\title{S3 method} +\title{Extract Variance-Covariance Matrix from drcMMRE Objects} \usage{ \method{vcov}{drcMMRE}(object, ...) } +\arguments{ +\item{object}{An object of class "drcMMRE"} + +\item{...}{Additional arguments (currently unused)} +} +\value{ +The variance-covariance matrix of the model parameters. +} \description{ -S3 method +S3 method to extract the variance-covariance matrix from fitted drcMMRE objects +by delegating to the underlying model-averaged model. +} +\seealso{ +\code{\link{vcov}} for the generic function } From cb05e98938d279020627eb0004763de7e6fd6f90 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Thu, 10 Jul 2025 13:33:33 +0200 Subject: [PATCH 12/17] updated all docs to fix warnings in build --- .gitignore | 1 + R/BCa.R | 14 -------------- man/BCa.Rd | 14 -------------- 3 files changed, 1 insertion(+), 28 deletions(-) diff --git a/.gitignore b/.gitignore index f10dacb..437421c 100644 --- a/.gitignore +++ b/.gitignore @@ -5,4 +5,5 @@ cache/ bmd.Rproj inst/doc +inst/dev example_extracts/ \ No newline at end of file diff --git a/R/BCa.R b/R/BCa.R index eae70f0..4bcb7a8 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -18,20 +18,6 @@ #' \item upper: The upper confidence limit #' } #' -#' @details -#' The BCa method computes confidence intervals using three components: -#' -#' 1. Bias correction (z0): -#' \deqn{z_0 = \Phi^{-1}\left(\frac{\text{number of } \theta^*_b \leq \hat{\theta}}{B}\right)}{z_0 = qnorm(proportion of bootstrap samples <= observed value)} -#' where B is the number of bootstrap replicates and \eqn{\theta^*_b}{theta*_b} represents the b-th bootstrap replicate. -#' -#' 2. Acceleration (a): -#' \deqn{a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}}}{a = sum((theta-bar - theta_i)^3) / (6 * [sum((theta-bar - theta_i)^2)]^(3/2))} -#' where \eqn{\theta_{(i)}}{theta_i} are the jackknife values. -#' -#' 3. The confidence limits are then computed as: -#' \deqn{\alpha_{1,2} = \Phi\left(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}\right)}{alpha_(1,2) = Phi(z_0 + (z_0 +/- z_alpha)/(1 - a*(z_0 +/- z_alpha)))} -#' #' @section Warning: #' The function assumes that: #' \itemize{ diff --git a/man/BCa.Rd b/man/BCa.Rd index f066bd5..93972cd 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -31,20 +31,6 @@ Computes the BCa confidence interval for a statistic using bootstrap and jackkni The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally provides better coverage than standard bootstrap confidence intervals. } -\details{ -The BCa method computes confidence intervals using three components: - -1. Bias correction (z0): -\deqn{z_0 = \Phi^{-1}\left(\frac{\text{number of } \theta^*_b \leq \hat{\theta}}{B}\right)}{z_0 = qnorm(proportion of bootstrap samples <= observed value)} -where B is the number of bootstrap replicates and \eqn{\theta^*_b}{theta*_b} represents the b-th bootstrap replicate. - -2. Acceleration (a): -\deqn{a = \frac{\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^3}{6[\sum_{i=1}^n (\bar{\theta}_{(\cdot)} - \theta_{(i)})^2]^{3/2}}}{a = sum((theta-bar - theta_i)^3) / (6 * [sum((theta-bar - theta_i)^2)]^(3/2))} -where \eqn{\theta_{(i)}}{theta_i} are the jackknife values. - -3. The confidence limits are then computed as: -\deqn{\alpha_{1,2} = \Phi\left(z_0 + \frac{z_0 \pm z_{\alpha}}{1 - a(z_0 \pm z_{\alpha})}\right)}{alpha_(1,2) = Phi(z_0 + (z_0 +/- z_alpha)/(1 - a*(z_0 +/- z_alpha)))} -} \section{Warning}{ The function assumes that: From 0e777a4fbfa512c009797e9385012da097510fc3 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Fri, 11 Jul 2025 17:04:55 +0200 Subject: [PATCH 13/17] fixed global binding issues, has still calling ::: notes --- .Rbuildignore | 2 +- DESCRIPTION | 1 + NAMESPACE.backup | 29 ----------- R/BCa.R | 31 ++++++------ R/bmd-package.R | 3 +- R/bmd.edfct.R | 16 +++--- R/bmdMACurve.R | 2 +- R/bootDataGenOrdinal.R | 9 +++- R/drmMMRE.R | 3 +- R/drmOrdinal.R | 1 - R/getFctDerivx.R | 39 +++++++------- R/invBmd.R | 4 +- R/plot.drcHetVar.R | 3 +- R/plot.drcOrdinal.R | 11 ++-- R/qplotDrc.R | 12 +++++ man/BCa.Rd | 31 ++++-------- man/BIC.drcOrdinal.Rd | 40 +++++++-------- man/MACurve.Rd | 2 +- man/bmd.Rd | 2 +- man/bmdHetVar.Rd | 2 +- man/bmdHetVarMA.Rd | 2 +- man/bmdMA.Rd | 2 +- man/bmdMACurve.Rd | 72 +++++++++++++------------- man/bmdOrdinal.Rd | 2 +- man/bmdOrdinalMA.Rd | 2 +- man/bootDataGen.Rd | 100 ++++++++++++++++++------------------ man/bootDataGenOrdinal.Rd | 104 +++++++++++++++++++------------------- man/coef.drcHetVar.Rd | 32 ++++++------ man/drmHetVar.Rd | 2 +- man/drmMMRE.Rd | 2 +- man/drmOrdinal.Rd | 3 -- man/expandBinomial.Rd | 2 +- man/getStackingWeights.Rd | 2 +- man/invBmd.Rd | 74 +++++++++++++-------------- 34 files changed, 312 insertions(+), 332 deletions(-) delete mode 100644 NAMESPACE.backup diff --git a/.Rbuildignore b/.Rbuildignore index c19a250..693c8b0 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -4,6 +4,6 @@ cache/ README.Rmd README.md README_files/ -^\\.github$ +^\.github$ docs/ example_extracts/ \ No newline at end of file diff --git a/DESCRIPTION b/DESCRIPTION index 686986a..7d80581 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -35,6 +35,7 @@ License: file LICENSE Encoding: UTF-8 LazyData: true Config/testthat/edition: 3 +Roxygen: list(markdown = TRUE) RoxygenNote: 7.3.2 Depends: R (>= 3.5) diff --git a/NAMESPACE.backup b/NAMESPACE.backup deleted file mode 100644 index 6ccfdc1..0000000 --- a/NAMESPACE.backup +++ /dev/null @@ -1,29 +0,0 @@ -import(drc, ggplot2, dplyr) -importFrom("graphics", "lines") -importFrom("stats", "aggregate", "approx", "as.formula", "coef", - "complete.cases", "confint", "constrOptim", "df.residual", - "dnorm", "fitted", "lm", "model.frame", "model.matrix", - "optim", "pnorm", "predict", "qchisq", "qnorm", "qt", - "quantile", "rbinom", "resid", "residuals", "rnorm", "sd", - "uniroot", "update", "var", "vcov", "AIC", "BIC", "logLik") -importFrom("utils", "setTxtProgressBar", "txtProgressBar") -export(bmd, bmdBoot, bmdIso, bmdIsoBoot, PAV, bmdMA, bootDataGen, bmdMACurve, BCa, invBmd, expandBinomial, - getStackingWeights, drmOrdinal, bmdOrdinal, bmdOrdinalMA, - qplotDrc, qplotBmd, MACurve, monotonicityTest, trendTest, bmdHetVar, drmHetVar, drmMMRE, bmdHetVarMA) - -## S3 methods -S3method(logLik, drcOrdinal) -S3method(logLik, drcHetVar) -S3method(AIC, drcOrdinal) -S3method(AIC, drcHetVar) -S3method(BIC, drcOrdinal) -S3method(BIC, drcHetVar) -S3method(plot, drcOrdinal) -S3method(print, drcOrdinal) -S3method(print, bmdOrdinal) -S3method(print, drcHetVar) -S3method(plot, bmd) -S3method(plot, drcHetVar) -S3method(vcov, drcMMRE) -S3method(print, drcMMRE) -S3method(coef, drcHetVar) \ No newline at end of file diff --git a/R/BCa.R b/R/BCa.R index 4bcb7a8..54b47a3 100644 --- a/R/BCa.R +++ b/R/BCa.R @@ -1,6 +1,10 @@ #' Calculate BCa (Bias-Corrected and Accelerated) Bootstrap Confidence Interval #' -#' Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. +#' @description +#' This function calculates the BCa confidence interval for a given statistic using bootstrap and jackknife estimates. +#' +#' @details +#' It computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. #' The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally #' provides better coverage than standard bootstrap confidence intervals. #' @@ -18,17 +22,8 @@ #' \item upper: The upper confidence limit #' } #' -#' @section Warning: -#' The function assumes that: -#' \itemize{ -#' \item The bootstrap samples are independent -#' \item The statistic of interest is smooth (continuously differentiable) -#' \item There are sufficient bootstrap replicates (typically >1000) -#' \item The jackknife values are properly computed -#' } #' -#' @examples -#' \dontrun{ +#' @examples \dontrun{ #' # Example with mean as the statistic #' data <- rnorm(100) #' obs_mean <- mean(data) @@ -47,13 +42,10 @@ #' #' @references #' Efron, B. (1987). Better Bootstrap Confidence Intervals. -#' \emph{Journal of the American Statistical Association}, 82(397), 171-185. +#' _Journal of the American Statistical Association_, 82(397), 171-185. #' #' DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. -#' \emph{Statistical Science}, 11(3), 189-212. -#' -#' @seealso -#' \code{\link{quantile}} for the underlying quantile computation +#' _Statistical Science_, 11(3), 189-212. #' #' @export BCa <- function(obs, data, bootSample, bootjack, level){ @@ -81,3 +73,10 @@ BCa <- function(obs, data, bootSample, bootjack, level){ } + + + + + + + diff --git a/R/bmd-package.R b/R/bmd-package.R index d524bd6..dc939fc 100644 --- a/R/bmd-package.R +++ b/R/bmd-package.R @@ -15,4 +15,5 @@ #' #' @name bmd-package #' @aliases bmd-package -"_PACKAGE" \ No newline at end of file +"_PACKAGE" + diff --git a/R/bmd.edfct.R b/R/bmd.edfct.R index e518b85..a4561a6 100644 --- a/R/bmd.edfct.R +++ b/R/bmd.edfct.R @@ -9,7 +9,7 @@ bmd.edfct <- function(object){ # Log-logistic if(identical(class(object$fct), "llogistic")){ if(substr(object$fct$name, 3,3) == "."){ - edfct <- function(parm, respl, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm p <- drc:::EDhelper(parmVec, respl, reference, type) @@ -31,7 +31,7 @@ bmd.edfct <- function(object){ return(list(EDp, EDder[notFixed])) } } else if(substr(object$fct$name, 3,3) == "2"){ - edfct <- function(parm, respl, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm @@ -58,7 +58,7 @@ bmd.edfct <- function(object){ # Log-Normal if(identical(class(object$fct), "log-normal")){ - edfct <- function(parm, respl, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm p <- drc:::absToRel(parmVec, respl, type) @@ -102,7 +102,7 @@ bmd.edfct <- function(object){ # Weibull1 if(identical(class(object$fct), "Weibull-1")){ - edfct <- function(parm, respl, reference, type, ...) # function(parm, p, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) # function(parm, p, reference, type, ...) { parmVec[notFixed] <- parm p <- drc:::EDhelper(parmVec, respl, reference, type) @@ -124,7 +124,7 @@ bmd.edfct <- function(object){ # Weibull2 if(identical(class(object$fct), "Weibull-2")){ - edfct <- function(parm, respl, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm @@ -151,7 +151,7 @@ bmd.edfct <- function(object){ } if(identical(class(object$fct), "Boltzmann")){ - edfct <- function(parm, respl, reference, type, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm p <- drc:::EDhelper(parmVec, respl, reference, type) @@ -195,7 +195,7 @@ bmd.edfct <- function(object){ } if(identical(class(object$fct), "braincousens")){ - edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { # if (is.missing(upper)) {upper <- 1000} interval <- c(lower, upper) @@ -242,7 +242,7 @@ bmd.edfct <- function(object){ if(identical(class(object$fct), "fp-logistic")){ p1 <- as.numeric(unlist(strsplit(object$fct$name, split = "[,()]+"))[2]) p2 <- as.numeric(unlist(strsplit(object$fct$name, split = "[,()]+"))[3]) - edfct <- function(parm, respl, reference, type, loged = FALSE, ...) + edfct <- function(parm, respl, reference, type, lower = 1e-3, upper = 10000, loged = FALSE, ...) { parmVec[notFixed] <- parm p <- drc:::EDhelper2(parmVec, respl, reference, type, parmVec[1] > 0) diff --git a/R/bmdMACurve.R b/R/bmdMACurve.R index f9ae013..e95964f 100644 --- a/R/bmdMACurve.R +++ b/R/bmdMACurve.R @@ -17,7 +17,7 @@ #' @param searchInterval character or numeric; Search interval for root finding. #' If "dataBased" (default), uses data range with small lower bound adjustment. #' If numeric, should be a vector of length 2 for single curves, or a matrix -#' with 2 columns for multiple curves specifying [lower, upper] bounds +#' with 2 columns for multiple curves specifying `[lower, upper]` bounds #' #' @details #' The function handles two scenarios: diff --git a/R/bootDataGenOrdinal.R b/R/bootDataGenOrdinal.R index 5ec8164..902337b 100644 --- a/R/bootDataGenOrdinal.R +++ b/R/bootDataGenOrdinal.R @@ -132,7 +132,12 @@ #' } bootDataGenOrdinal <- function(object, R = 500, bootType = c("nonparametric", "parametric", "model", "hierarchical")){ bootType <- match.arg(bootType) - + ## avoiding global binding of variables issues + variable <- NULL + row.num <- NULL + value <- NULL + row.orig <- NULL + rm(list=c("variable", "row.num", "value", "row.orig")) if(!requireNamespace("reshape2")){ stop('package "reshape2" must be installed to use bootstrapping with ordinal dose-response model') } @@ -214,6 +219,8 @@ bootDataGenOrdinal <- function(object, R = 500, bootType = c("nonparametric", "p } resample_fun <- function(levels, dose, weights, blocks, data){ + name <- NULL + rm(list("name")) data %>% dplyr::mutate(row.orig = 1:n()) %>% dplyr::group_by(.data[[dose]]) %>% diff --git a/R/drmMMRE.R b/R/drmMMRE.R index 7d1a6bd..a41af51 100644 --- a/R/drmMMRE.R +++ b/R/drmMMRE.R @@ -57,7 +57,8 @@ #' @export drmMMRE <- function(formula, exp_id, data, fct, type = c("continuous", "binomial")){ call_expr <- match.call() - + Estimate <- NULL # to avoid global binding of variables issues + rm(list="Estimate") # assertions if (!inherits(formula, "formula")) { stop("Argument 'formula' must be a formula.") diff --git a/R/drmOrdinal.R b/R/drmOrdinal.R index 71540a7..76127e6 100644 --- a/R/drmOrdinal.R +++ b/R/drmOrdinal.R @@ -29,7 +29,6 @@ #' fitting the model. Default value is 10^(-16) #' @return An object of (S3) class 'drcOrdinal'. #' @author Signe M. Jensen and Jens Riis Baalkilde -#' @references # ADD REFERENCES #' @keywords models nonlinear #' @examples #' diff --git a/R/getFctDerivx.R b/R/getFctDerivx.R index ec8799b..e65fb53 100644 --- a/R/getFctDerivx.R +++ b/R/getFctDerivx.R @@ -9,32 +9,29 @@ getFctDerivx <- function(object){ # Log-logistic if(identical(class(object$fct), "llogistic")){ if(substr(object$fct$name, 3,3) == "."){ - derivx <- function(x, parm) + derivx <- function(dose, parm) # Changed from 'x' to 'dose' { parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE) parmMat[, notFixed] <- parm - # bNeg <- parmMat[, 1] < 0 - # parmMat[bNeg, 1] <- -parmMat[bNeg, 1] - temp1 <- x/parmMat[, 4] + temp1 <- dose/parmMat[, 4] # Changed from 'x' to 'dose' temp2 <- 1 + (temp1)^parmMat[, 1] temp3 <- parmMat[, 5]*(temp2^(parmMat[, 5] - 1))*(parmMat[, 1]/parmMat[, 4])*temp1^(parmMat[, 1] - 1) temp4 <- temp2^(2*parmMat[, 5]) (-(parmMat[, 3] - parmMat[, 2])*temp3)/temp4 retVec <- (-(parmMat[, 3] - parmMat[, 2])*temp3)/temp4 - # retVec[bNeg] <- -retVec[bNeg] retVec } } else if(substr(object$fct$name, 3,3) == "2"){ - derivx <- function(x, parm) + derivx <- function(dose, parm) # Changed from 'x' to 'dose' { parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE) parmMat[, notFixed] <- parm - temp1 <- exp(parmMat[, 1]*(log(x) - parmMat[, 4])) # x/parmMat[, 4] + temp1 <- exp(parmMat[, 1]*(log(dose) - parmMat[, 4])) # Changed from 'x' to 'dose' temp2 <- 1 + temp1 - temp3 <- parmMat[, 5]*(temp2^(parmMat[, 5] - 1))*temp1*parmMat[, 1]/x + temp3 <- parmMat[, 5]*(temp2^(parmMat[, 5] - 1))*temp1*parmMat[, 1]/dose # Changed from 'x' to 'dose' temp4 <- temp2^(2*parmMat[, 5]) (-(parmMat[, 3] - parmMat[, 2])*temp3)/temp4 @@ -52,7 +49,7 @@ getFctDerivx <- function(object){ dFct <- function (dose, b, c, d, e) { .expr1 <- d - c - .expr5 <- b * (log(dose) - transfe(e)) + .expr5 <- b * (log(dose) - log(e)) # Fixed: changed 'transfe(e)' to 'log(e)' .value <- c + .expr1 * pnorm(.expr5) .grad <- array(0, c(length(.value), 1L), list(NULL, c("dose"))) .grad[, "dose"] <- .expr1 * (dnorm(.expr5) * (b * (1/dose))) @@ -65,45 +62,45 @@ getFctDerivx <- function(object){ # Weibull1 if(identical(class(object$fct), "Weibull-1")){ - derivx <- function(x, parm) + derivx <- function(dose, parm) # Changed from 'x' to 'dose' { parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE) parmMat[, notFixed] <- parm .expr1 <- parmMat[, 3] - parmMat[, 2] # d - c - .expr6 <- exp(parmMat[, 1] * (log(x) - log(parmMat[, 4]))) + .expr6 <- exp(parmMat[, 1] * (log(dose) - log(parmMat[, 4]))) # Changed from 'x' to 'dose' .expr8 <- exp(-.expr6) .value <- parmMat[, 2] + .expr1 * .expr8 - .grad <- array(0, c(length(.value), 1L), list(NULL, c("x"))) - .grad[, "x"] <- -(.expr1 * (.expr8 * (.expr6 * (parmMat[, 1] * (1/x))))) + .grad <- array(0, c(length(.value), 1L), list(NULL, c("dose"))) # Changed from 'x' to 'dose' + .grad[, "dose"] <- -(.expr1 * (.expr8 * (.expr6 * (parmMat[, 1] * (1/dose))))) # Changed from 'x' to 'dose' .grad } } # Weibull2 if(identical(class(object$fct), "Weibull-2")){ - derivx <- function(x, parm) + derivx <- function(dose, parm) # Changed from 'x' to 'dose' { parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE) parmMat[, notFixed] <- parm .expr1 <- parmMat[, 3] - parmMat[, 2] - .expr6 <- exp(parmMat[, 1] * (log(x) - log(parmMat[, 4]))) + .expr6 <- exp(parmMat[, 1] * (log(dose) - log(parmMat[, 4]))) # Changed from 'x' to 'dose' .expr8 <- exp(-.expr6) .value <- parmMat[, 2] + .expr1 * (1 - .expr8) - .grad <- array(0, c(length(.value), 1L), list(NULL, c("x"))) - .grad[, "x"] <- .expr1 * (.expr8 * (.expr6 * (parmMat[, 1] * (1/x)))) + .grad <- array(0, c(length(.value), 1L), list(NULL, c("dose"))) # Changed from 'x' to 'dose' + .grad[, "dose"] <- .expr1 * (.expr8 * (.expr6 * (parmMat[, 1] * (1/dose)))) # Changed from 'x' to 'dose' .grad } } if(identical(class(object$fct), "Boltzmann")){ - derivx <- function(x, parm) + derivx <- function(dose, parm) # Changed from 'x' to 'dose' { parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE) parmMat[, notFixed] <- parm - temp1 <- exp(parmMat[, 1]*(x - parmMat[, 4])) + temp1 <- exp(parmMat[, 1]*(dose - parmMat[, 4])) # Changed from 'x' to 'dose' (-parmMat[, 5]*(parmMat[, 3] - parmMat[, 2])*temp1*parmMat[, 1])/((1 + temp1)^(parmMat[, 5] + 1)) } @@ -149,6 +146,6 @@ getFctDerivx <- function(object){ attr(dFct(dose, parmMat[, 1], parmMat[, 2], parmMat[, 3], parmMat[, 4]), "gradient") } } - + derivx -} +} \ No newline at end of file diff --git a/R/invBmd.R b/R/invBmd.R index 1cd2f49..13a1ca3 100644 --- a/R/invBmd.R +++ b/R/invBmd.R @@ -95,7 +95,7 @@ #' #' **Important considerations:** #' \itemize{ -#' \item The search range is limited to [0, extFactor × max(dose)] +#' \item The search range is limited to `[0, extFactor × max(dose)]` #' \item Hybrid definitions require careful specification of useSD and backg #' \item Function modification uses string manipulation and may be sensitive to model structure #' } @@ -695,7 +695,7 @@ invBmd <- function(object, bmr, level=0.9, slope, backgType="modelBased", # g1<-function(x){as.numeric(g(x, matrix(coef(object), 1, length(coef(object)))))} if(sandwich.vcov){ j1<-function(x){sqrt(as.vector(h(x, matrix(coef(object), 1, length(coef(object)))))%*% - sandwich(object)%*% + sandwich::sandwich(object)%*% as.vector(h(x, matrix(coef(object), 1, length(coef(object))))))} } else{ j1<-function(x){sqrt(as.vector(h(x, matrix(coef(object), 1, length(coef(object)))))%*% diff --git a/R/plot.drcHetVar.R b/R/plot.drcHetVar.R index 97c1d03..b979655 100644 --- a/R/plot.drcHetVar.R +++ b/R/plot.drcHetVar.R @@ -15,7 +15,8 @@ plot.drcHetVar <- function(x, ...){ } else { gridsize <- 300 } - + sigma0 <- NULL ## avoiding global binding issues + rm(list("sigma0")) # Add assertion of gridExtra if(!requireNamespace("gridExtra")){ stop('package "gridExtra" must be installed to plot drcHetVar object') diff --git a/R/plot.drcOrdinal.R b/R/plot.drcOrdinal.R index 6f48e9c..abbdde2 100644 --- a/R/plot.drcOrdinal.R +++ b/R/plot.drcOrdinal.R @@ -13,7 +13,12 @@ plot.drcOrdinal <- function(x, ...){ dots <- list(...) col_pal <- dots$col_pal xlim <- dots$xlim - + ## avoiding global binding of variables issues + name <- NULL + value <- NULL + dose <- NULL + prop <- NULL + rm(list=c("name", "value", "dose", "prop")) if(!requireNamespace("scales")){ stop('package "scales" must be installed to plot drcOrdinal object') } @@ -30,8 +35,8 @@ plot.drcOrdinal <- function(x, ...){ plotData <- tidyr::pivot_longer(object$data, cols = object$levels) %>% #-c(object$dose, object$weights)) %>% dplyr::mutate(dose = eval(parse(text=object$dose)), - cat = factor(name, levels = object$levels), - prop = value/eval(parse(text=object$weights))) + cat = factor(name, levels = object$levels), + prop = value/eval(parse(text=object$weights))) plot <- ggplot2::ggplot(plotData) + ggplot2::geom_col(aes(x = dose, y = prop, fill = cat), alpha = 0.5) + diff --git a/R/qplotDrc.R b/R/qplotDrc.R index 396e2ed..9428557 100644 --- a/R/qplotDrc.R +++ b/R/qplotDrc.R @@ -126,6 +126,12 @@ qplotDrc <- function(x, add = FALSE, level = NULL, type = c("average", "all", "b normal = FALSE, normRef = 1, confidence.level = 0.95){ object <- x type <- match.arg(type) + ### Avoiding global variable binding problems + normalizeLU <- NULL + Lower <- NULL + Upper <- NULL + y <- NULL + rm(list=(c("normalizeLU", "Lower", "Upper","y"))) ## Determining logarithmic scales if ((xtrans == "log") || (xtrans == "pseudo_log")) @@ -397,3 +403,9 @@ qplotDrc <- function(x, add = FALSE, level = NULL, type = c("average", "all", "b obsLayer = obsLayer) } } + + +getLU <- function(object){ + ## using the drc internal function + eval(parse(text = "drc:::getLU(object))")) +} diff --git a/man/BCa.Rd b/man/BCa.Rd index 93972cd..687d7a5 100644 --- a/man/BCa.Rd +++ b/man/BCa.Rd @@ -11,37 +11,29 @@ BCa(obs, data, bootSample, bootjack, level) \item{data}{data.frame or matrix; The original dataset from which bootstrap samples are drawn} -\item{bootSample}{numeric vector; Bootstrap replicates of the statistic. Must be of length R +\item{bootSample}{numeric vector; Bootstrap replicates of the statistic. Must be of length R where R is the number of bootstrap replicates} -\item{bootjack}{numeric vector; Jackknife replicates of the statistic. Must be of length n +\item{bootjack}{numeric vector; Jackknife replicates of the statistic. Must be of length n where n is the number of observations in data} -\item{level}{numeric; Confidence level between 0 and 1 (e.g., 0.95 for 95% confidence interval)} +\item{level}{numeric; Confidence level between 0 and 1 (e.g., 0.95 for 95\% confidence interval)} } \value{ A numeric vector of length 2 containing: \itemize{ - \item lower: The lower confidence limit - \item upper: The upper confidence limit +\item lower: The lower confidence limit +\item upper: The upper confidence limit } } \description{ -Computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. +This function calculates the BCa confidence interval for a given statistic using bootstrap and jackknife estimates. +} +\details{ +It computes the BCa confidence interval for a statistic using bootstrap and jackknife estimates. The BCa method adjusts for both bias and skewness in the bootstrap distribution and generally provides better coverage than standard bootstrap confidence intervals. } -\section{Warning}{ - -The function assumes that: -\itemize{ - \item The bootstrap samples are independent - \item The statistic of interest is smooth (continuously differentiable) - \item There are sufficient bootstrap replicates (typically >1000) - \item The jackknife values are properly computed -} -} - \examples{ \dontrun{ # Example with mean as the statistic @@ -62,12 +54,9 @@ BCa(obs_mean, data, boot_means, jack_means, 0.95) } \references{ -Efron, B. (1987). Better Bootstrap Confidence Intervals. +Efron, B. (1987). Better Bootstrap Confidence Intervals. \emph{Journal of the American Statistical Association}, 82(397), 171-185. DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. \emph{Statistical Science}, 11(3), 189-212. } -\seealso{ -\code{\link{quantile}} for the underlying quantile computation -} diff --git a/man/BIC.drcOrdinal.Rd b/man/BIC.drcOrdinal.Rd index db5254b..fe573d3 100644 --- a/man/BIC.drcOrdinal.Rd +++ b/man/BIC.drcOrdinal.Rd @@ -7,23 +7,23 @@ \method{BIC}{drcOrdinal}(object, ...) } \arguments{ -\item{object}{An object of class "drcOrdinal" containing fitted ordinal +\item{object}{An object of class "drcOrdinal" containing fitted ordinal dose-response models} \item{...}{Additional arguments passed to the method. Currently supports: \itemize{ - \item \code{epsilon}: Small positive value to avoid log(0) in likelihood - calculations (default: 1e-16) +\item \code{epsilon}: Small positive value to avoid log(0) in likelihood +calculations (default: 1e-16) }} } \value{ A numeric value representing the BIC of the fitted ordinal dose-response model. - Lower values indicate better model fit when comparing models. +Lower values indicate better model fit when comparing models. } \description{ -S3 method to calculate the Bayesian Information Criterion (BIC) for fitted -ordinal dose-response models. This method extends the generic `BIC()` function -to handle `drcOrdinal` objects which contain multiple fitted dose-response models +S3 method to calculate the Bayesian Information Criterion (BIC) for fitted +ordinal dose-response models. This method extends the generic \code{BIC()} function +to handle \code{drcOrdinal} objects which contain multiple fitted dose-response models for different response categories. } \details{ @@ -31,33 +31,33 @@ The BIC is calculated using the standard formula: \deqn{BIC = k \log(n) - 2 \log(L)}{BIC = k * log(n) - 2 * log(L)} where: \itemize{ - \item \eqn{k}{k} is the total number of parameters across all models in the ordinal fit - \item \eqn{n}{n} is the total number of observations (sum of weights) - \item \eqn{L}{L} is the likelihood of the fitted model +\item \eqn{k}{k} is the total number of parameters across all models in the ordinal fit +\item \eqn{n}{n} is the total number of observations (sum of weights) +\item \eqn{L}{L} is the likelihood of the fitted model } -For ordinal dose-response models, the total number of parameters is the sum -of parameters from all individual models in the `drmList` component, and the +For ordinal dose-response models, the total number of parameters is the sum +of parameters from all individual models in the \code{drmList} component, and the sample size is calculated as the sum of weights in the data. -The `epsilon` parameter is used in the `logLik()` calculation to prevent +The \code{epsilon} parameter is used in the \code{logLik()} calculation to prevent numerical issues when probabilities approach zero. } \note{ -This method assumes that the `drcOrdinal` object contains: +This method assumes that the \code{drcOrdinal} object contains: \itemize{ - \item A `drmList` component with fitted dose-response models - \item A `data` component with the original data including weights - \item A `weights` component specifying the column name for observation weights +\item A \code{drmList} component with fitted dose-response models +\item A \code{data} component with the original data including weights +\item A \code{weights} component specifying the column name for observation weights } } \section{Model Comparison}{ BIC penalizes model complexity more heavily than AIC, making it useful for: \itemize{ - \item Comparing ordinal dose-response models with different numbers of parameters - \item Model selection in situations where simpler models are preferred - \item Avoiding overfitting in dose-response modeling +\item Comparing ordinal dose-response models with different numbers of parameters +\item Model selection in situations where simpler models are preferred +\item Avoiding overfitting in dose-response modeling } } diff --git a/man/MACurve.Rd b/man/MACurve.Rd index 38621d3..ef1d936 100644 --- a/man/MACurve.Rd +++ b/man/MACurve.Rd @@ -36,7 +36,7 @@ curves. } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bmd.Rd b/man/bmd.Rd index 6f9ba18..24fd0c1 100644 --- a/man/bmd.Rd +++ b/man/bmd.Rd @@ -164,7 +164,7 @@ response model fits } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bmdHetVar.Rd b/man/bmdHetVar.Rd index e5b50b3..b676ebd 100644 --- a/man/bmdHetVar.Rd +++ b/man/bmdHetVar.Rd @@ -98,7 +98,7 @@ level and/or the fitted values } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bmdHetVarMA.Rd b/man/bmdHetVarMA.Rd index b53eacd..7855ff4 100644 --- a/man/bmdHetVarMA.Rd +++ b/man/bmdHetVarMA.Rd @@ -99,7 +99,7 @@ the dose level and/or the fitted values } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bmdMA.Rd b/man/bmdMA.Rd index 2604e5c..f9d9f8d 100644 --- a/man/bmdMA.Rd +++ b/man/bmdMA.Rd @@ -179,7 +179,7 @@ averaging from a user-defined list of dose response model fits \details{ This package project is still under development. The aim to provide an R package calculating the benchmark dose (BMD) and the lower limit of the -corresponding 95\% confidence interval (BMDL) for continuous and quantal +corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response model based on the available definitions of the benchmark dose concepts. diff --git a/man/bmdMACurve.Rd b/man/bmdMACurve.Rd index 8c28308..9e446d9 100644 --- a/man/bmdMACurve.Rd +++ b/man/bmdMACurve.Rd @@ -7,76 +7,76 @@ bmdMACurve(modelList, modelWeights, bmrScaled0, searchInterval = "dataBased") } \arguments{ -\item{modelList}{list; A list of fitted dose-response models from which to compute -the model average. Each model should be a fitted object with components -including `fct`, `parmMat`, `dataList`, etc.} +\item{modelList}{list; A list of fitted dose-response models from which to compute +the model average. Each model should be a fitted object with components +including \code{fct}, \code{parmMat}, \code{dataList}, etc.} -\item{modelWeights}{numeric vector; Weights for model averaging, typically derived -from model selection criteria (e.g., AIC weights). Must sum to 1 and have -the same length as `modelList`} +\item{modelWeights}{numeric vector; Weights for model averaging, typically derived +from model selection criteria (e.g., AIC weights). Must sum to 1 and have +the same length as \code{modelList}} -\item{bmrScaled0}{numeric; The benchmark response level(s) for which to calculate -BMD. For single curves, a scalar value; for multiple curves, a vector with +\item{bmrScaled0}{numeric; The benchmark response level(s) for which to calculate +BMD. For single curves, a scalar value; for multiple curves, a vector with length equal to the number of curves} -\item{searchInterval}{character or numeric; Search interval for root finding. -If "dataBased" (default), uses data range with small lower bound adjustment. -If numeric, should be a vector of length 2 for single curves, or a matrix -with 2 columns for multiple curves specifying [lower, upper] bounds} +\item{searchInterval}{character or numeric; Search interval for root finding. +If "dataBased" (default), uses data range with small lower bound adjustment. +If numeric, should be a vector of length 2 for single curves, or a matrix +with 2 columns for multiple curves specifying \verb{[lower, upper]} bounds} } \value{ An object of class "bmd" containing: \itemize{ - \item \strong{Results}: A matrix with BMD values. For single curves, a 1x1 matrix; - for multiple curves, an nx1 matrix where n is the number of curves - \item \strong{MACurve}: The model-averaged function used for BMD calculation. - For single curves, returns the combined function; for multiple curves, returns NULL +\item \strong{Results}: A matrix with BMD values. For single curves, a 1x1 matrix; +for multiple curves, an nx1 matrix where n is the number of curves +\item \strong{MACurve}: The model-averaged function used for BMD calculation. +For single curves, returns the combined function; for multiple curves, returns NULL } } \description{ -Helper function for `bmdMA` that computes Benchmark Dose (BMD) values using -model averaging. The function creates a weighted average of multiple dose-response +Helper function for \code{bmdMA} that computes Benchmark Dose (BMD) values using +model averaging. The function creates a weighted average of multiple dose-response models and finds the dose corresponding to a specified benchmark response level. } \details{ The function handles two scenarios: -**Single Curve Analysis:** +\strong{Single Curve Analysis:} Creates a weighted combination of model functions: \deqn{f_{MA}(x) = \sum_{i=1}^{m} w_i \cdot f_i(x)}{f_MA(x) = sum of w_i * f_i(x)} where \eqn{w_i}{w_i} are model weights and \eqn{f_i(x)}{f_i(x)} are individual model functions. -**Multiple Curve Analysis:** -Computes BMD separately for each curve using the same model averaging approach +\strong{Multiple Curve Analysis:} +Computes BMD separately for each curve using the same model averaging approach but applied to curve-specific data and parameters. The BMD is found by solving: \deqn{f_{MA}(BMD) = BMR}{f_MA(BMD) = BMR} using root finding algorithms. -**Model Function Construction:** +\strong{Model Function Construction:} The function dynamically constructs model functions by: \itemize{ - \item Extracting function templates from `mtList()` - \item Substituting fixed parameters and estimated coefficients - \item Handling special cases like Fractional Polynomial models - \item Creating weighted combinations of all models +\item Extracting function templates from \code{mtList()} +\item Substituting fixed parameters and estimated coefficients +\item Handling special cases like Fractional Polynomial models +\item Creating weighted combinations of all models } } \note{ -This is primarily an internal helper function for `bmdMA`. Direct usage requires -properly formatted model lists and weights. The function assumes all models in -`modelList` are compatible and fitted to the same dataset structure. +This is primarily an internal helper function for \code{bmdMA}. Direct usage requires +properly formatted model lists and weights. The function assumes all models in +\code{modelList} are compatible and fitted to the same dataset structure. } \section{Search Interval}{ -When `searchInterval = "dataBased"`: +When \code{searchInterval = "dataBased"}: \itemize{ - \item Lower bound: Second smallest dose value divided by 10,000 - \item Upper bound: Maximum dose value in the dataset +\item Lower bound: Second smallest dose value divided by 10,000 +\item Upper bound: Maximum dose value in the dataset } -Custom intervals can be provided to avoid convergence issues or focus on +Custom intervals can be provided to avoid convergence issues or focus on specific dose ranges of interest. } @@ -84,9 +84,9 @@ specific dose ranges of interest. The function supports various dose-response models including: \itemize{ - \item Standard 4-parameter and 5-parameter models - \item Fractional Polynomial models (special handling) - \item Models with fixed parameters +\item Standard 4-parameter and 5-parameter models +\item Fractional Polynomial models (special handling) +\item Models with fixed parameters } } diff --git a/man/bmdOrdinal.Rd b/man/bmdOrdinal.Rd index e9d89c2..b54ad74 100644 --- a/man/bmdOrdinal.Rd +++ b/man/bmdOrdinal.Rd @@ -111,7 +111,7 @@ dose response model fits } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous, quantal, quantal and ordinal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bmdOrdinalMA.Rd b/man/bmdOrdinalMA.Rd index 4cec746..6388b67 100644 --- a/man/bmdOrdinalMA.Rd +++ b/man/bmdOrdinalMA.Rd @@ -100,7 +100,7 @@ averaging from a user-defined list of ordinal dose-response model fits } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous, quantal, quantal and ordinal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/bootDataGen.Rd b/man/bootDataGen.Rd index 7fcfbf2..8f55b20 100644 --- a/man/bootDataGen.Rd +++ b/man/bootDataGen.Rd @@ -7,103 +7,103 @@ bootDataGen(object, R = 1000, bootType = "nonparametric", aggregated = TRUE) } \arguments{ -\item{object}{A fitted dose-response model object (typically from `drm()`) +\item{object}{A fitted dose-response model object (typically from \code{drm()}) containing the original data and model specifications} \item{R}{integer; Number of bootstrap replicates to generate (default: 1000)} \item{bootType}{character; Type of bootstrap resampling method. Options are: \itemize{ - \item \code{"nonparametric"}: Resamples observations within dose groups - \item \code{"parametric"}: Generates new data from fitted distributions - \item \code{"semiparametric"}: Uses fitted values plus resampled residuals +\item \code{"nonparametric"}: Resamples observations within dose groups +\item \code{"parametric"}: Generates new data from fitted distributions +\item \code{"semiparametric"}: Uses fitted values plus resampled residuals }} -\item{aggregated}{logical; For binomial data, whether to return aggregated +\item{aggregated}{logical; For binomial data, whether to return aggregated (summary) format or expanded (individual observation) format (default: TRUE)} } \value{ -A list of length R containing bootstrap datasets. Each element is a - data.frame with the same structure as the original data, containing: - \itemize{ - \item Dose variable (same name as original) - \item Response variable(s) (same name(s) as original) - \item For binomial data: number of successes and total observations - \item For multi-curve data: curve identifier (if present) - } +A list of length R containing bootstrap datasets. Each element is a +data.frame with the same structure as the original data, containing: +\itemize{ +\item Dose variable (same name as original) +\item Response variable(s) (same name(s) as original) +\item For binomial data: number of successes and total observations +\item For multi-curve data: curve identifier (if present) +} } \description{ -Helper function for `bmdBoot` that generates bootstrap datasets from fitted -dose-response models. Supports multiple bootstrap methods (nonparametric, -parametric, and semiparametric) and handles different response types +Helper function for \code{bmdBoot} that generates bootstrap datasets from fitted +dose-response models. Supports multiple bootstrap methods (nonparametric, +parametric, and semiparametric) and handles different response types (binomial, continuous, Poisson, negative binomial). } \details{ The function implements different bootstrap strategies based on data type and method: -**Nonparametric Bootstrap:** +\strong{Nonparametric Bootstrap:} \itemize{ - \item \strong{Binomial}: Expands binomial data to individual observations, - resamples within dose groups, then optionally re-aggregates - \item \strong{Continuous/Count}: Resamples observations within dose groups - from the original dataset +\item \strong{Binomial}: Expands binomial data to individual observations, +resamples within dose groups, then optionally re-aggregates +\item \strong{Continuous/Count}: Resamples observations within dose groups +from the original dataset } -**Parametric Bootstrap:** +\strong{Parametric Bootstrap:} \itemize{ - \item \strong{Binomial}: Generates new binomial observations using estimated - success probabilities, with continuity correction (adds 0.25/0.5) for - boundary cases - \item \strong{Continuous}: Generates normal random variables using - dose-specific means and standard deviations from original data +\item \strong{Binomial}: Generates new binomial observations using estimated +success probabilities, with continuity correction (adds 0.25/0.5) for +boundary cases +\item \strong{Continuous}: Generates normal random variables using +dose-specific means and standard deviations from original data } -**Semiparametric Bootstrap:** +\strong{Semiparametric Bootstrap:} \itemize{ - \item \strong{Continuous only}: Uses fitted values plus resampled residuals - \item \strong{Binomial}: Not supported (throws error) +\item \strong{Continuous only}: Uses fitted values plus resampled residuals +\item \strong{Binomial}: Not supported (throws error) } } \note{ -This is an internal helper function for `bmdBoot`. It assumes the input object -has the standard structure from `drm()` fitting, including components like -`data`, `origData`, `call`, `type`, etc. +This is an internal helper function for \code{bmdBoot}. It assumes the input object +has the standard structure from \code{drm()} fitting, including components like +\code{data}, \code{origData}, \code{call}, \code{type}, etc. -**Important considerations:** +\strong{Important considerations:} \itemize{ - \item Semiparametric bootstrap requires model residuals and fitted values - \item Parametric bootstrap assumes distributional assumptions are met - \item Large R values may require substantial memory for complex datasets +\item Semiparametric bootstrap requires model residuals and fitted values +\item Parametric bootstrap assumes distributional assumptions are met +\item Large R values may require substantial memory for complex datasets } } \section{Data Type Handling}{ -**Binomial Data:** +\strong{Binomial Data:} \itemize{ - \item Handles both aggregated (n successes out of N trials) and expanded formats - \item Preserves dose group structure during resampling - \item Applies continuity correction in parametric bootstrap +\item Handles both aggregated (n successes out of N trials) and expanded formats +\item Preserves dose group structure during resampling +\item Applies continuity correction in parametric bootstrap } -**Continuous Data:** +\strong{Continuous Data:} \itemize{ - \item Maintains dose group structure - \item Preserves within-group variability patterns - \item Uses original data (`origData`) when available +\item Maintains dose group structure +\item Preserves within-group variability patterns +\item Uses original data (\code{origData}) when available } -**Count Data (Poisson/Negative Binomial):** +\strong{Count Data (Poisson/Negative Binomial):} \itemize{ - \item Treated similarly to continuous data for nonparametric bootstrap - \item Resamples within dose groups +\item Treated similarly to continuous data for nonparametric bootstrap +\item Resamples within dose groups } } \section{Multi-curve Support}{ -The function handles multi-curve dose-response data by preserving curve -identifiers during bootstrap resampling, ensuring that the bootstrap samples +The function handles multi-curve dose-response data by preserving curve +identifiers during bootstrap resampling, ensuring that the bootstrap samples maintain the original experimental structure. } diff --git a/man/bootDataGenOrdinal.Rd b/man/bootDataGenOrdinal.Rd index c5cf24d..a8b1371 100644 --- a/man/bootDataGenOrdinal.Rd +++ b/man/bootDataGenOrdinal.Rd @@ -11,91 +11,91 @@ bootDataGenOrdinal( ) } \arguments{ -\item{object}{A fitted ordinal dose-response model object containing the original +\item{object}{A fitted ordinal dose-response model object containing the original data, model specifications, response levels, and fitted parameters} \item{R}{integer; Number of bootstrap replicates to generate (default: 500)} \item{bootType}{character; Type of bootstrap resampling method. Options are: \itemize{ - \item \code{"nonparametric"}: Resamples individual observations within dose groups - \item \code{"parametric"}: Generates new observations using estimated category probabilities - \item \code{"model"}: Generates observations using fitted model probabilities - \item \code{"hierarchical"}: Hierarchical resampling accounting for block structure +\item \code{"nonparametric"}: Resamples individual observations within dose groups +\item \code{"parametric"}: Generates new observations using estimated category probabilities +\item \code{"model"}: Generates observations using fitted model probabilities +\item \code{"hierarchical"}: Hierarchical resampling accounting for block structure }} } \value{ -A list of length R containing bootstrap datasets. Each element is a - data.frame with the same structure as the original ordinal data, containing: - \itemize{ - \item Dose variable (same name as original) - \item Count columns for each response category - \item For hierarchical: block identifier and total counts - \item All columns from original data structure preserved - } +A list of length R containing bootstrap datasets. Each element is a +data.frame with the same structure as the original ordinal data, containing: +\itemize{ +\item Dose variable (same name as original) +\item Count columns for each response category +\item For hierarchical: block identifier and total counts +\item All columns from original data structure preserved +} } \description{ -Helper function for `bmdOrdinal` and `bmdOrdinalMA` that generates bootstrap -datasets from fitted ordinal dose-response models. Supports multiple bootstrap +Helper function for \code{bmdOrdinal} and \code{bmdOrdinalMA} that generates bootstrap +datasets from fitted ordinal dose-response models. Supports multiple bootstrap methods tailored for ordinal response data with different resampling strategies. } \details{ The function implements four distinct bootstrap strategies for ordinal data: -**Nonparametric Bootstrap:** +\strong{Nonparametric Bootstrap:} \itemize{ - \item Expands ordinal data to individual observations - \item Resamples observations within each original data row - \item Maintains the empirical distribution within dose groups - \item Most conservative approach, makes no distributional assumptions +\item Expands ordinal data to individual observations +\item Resamples observations within each original data row +\item Maintains the empirical distribution within dose groups +\item Most conservative approach, makes no distributional assumptions } -**Parametric Bootstrap:** +\strong{Parametric Bootstrap:} \itemize{ - \item Estimates category probabilities from original data - \item Applies continuity correction for boundary cases: - \deqn{p_{corrected} = \frac{1/K^2}{n + 1/K} \text{ when } p = 0}{p_corrected = (1/K^2)/(n + 1/K) when p = 0} - \deqn{p_{corrected} = \frac{n + 1/K^2}{n + 1/K} \text{ when } p = 1}{p_corrected = (n + 1/K^2)/(n + 1/K) when p = 1} - where K is the number of response categories and n is the sample size - \item Generates new observations using multinomial sampling +\item Estimates category probabilities from original data +\item Applies continuity correction for boundary cases: +\deqn{p_{corrected} = \frac{1/K^2}{n + 1/K} \text{ when } p = 0}{p_corrected = (1/K^2)/(n + 1/K) when p = 0} +\deqn{p_{corrected} = \frac{n + 1/K^2}{n + 1/K} \text{ when } p = 1}{p_corrected = (n + 1/K^2)/(n + 1/K) when p = 1} +where K is the number of response categories and n is the sample size +\item Generates new observations using multinomial sampling } -**Model-Based Bootstrap:** +\strong{Model-Based Bootstrap:} \itemize{ - \item Uses fitted model probabilities (\code{object$pFun}) for each dose - \item Generates observations directly from the fitted dose-response relationship - \item Assumes the fitted model accurately represents the true relationship +\item Uses fitted model probabilities (\code{object$pFun}) for each dose +\item Generates observations directly from the fitted dose-response relationship +\item Assumes the fitted model accurately represents the true relationship } -**Hierarchical Bootstrap:** +\strong{Hierarchical Bootstrap:} \itemize{ - \item Accounts for block/cluster structure in the data - \item Requires \code{object$blocks} to be specified - \item Uses weighted resampling within dose groups - \item Maintains hierarchical correlation structure +\item Accounts for block/cluster structure in the data +\item Requires \code{object$blocks} to be specified +\item Uses weighted resampling within dose groups +\item Maintains hierarchical correlation structure } } \note{ -This is an internal helper function for ordinal BMD bootstrap procedures. It assumes -the input object has the standard structure from ordinal dose-response fitting, +This is an internal helper function for ordinal BMD bootstrap procedures. It assumes +the input object has the standard structure from ordinal dose-response fitting, including components like \code{data}, \code{levels}, \code{dose}, \code{pFun}, etc. -**Method Selection Guidelines:** +\strong{Method Selection Guidelines:} \itemize{ - \item Use \code{"nonparametric"} for robust, assumption-free bootstrap - \item Use \code{"parametric"} when sample sizes are small - \item Use \code{"model"} to assess model-based uncertainty - \item Use \code{"hierarchical"} for clustered/blocked experimental designs +\item Use \code{"nonparametric"} for robust, assumption-free bootstrap +\item Use \code{"parametric"} when sample sizes are small +\item Use \code{"model"} to assess model-based uncertainty +\item Use \code{"hierarchical"} for clustered/blocked experimental designs } } \section{Data Processing}{ The function uses several data manipulation steps: \itemize{ - \item \strong{Expansion}: Converts aggregated ordinal data to individual observations - \item \strong{Resampling}: Applies the specified bootstrap method - \item \strong{Aggregation}: Converts back to count format using \code{reshape2::dcast} - \item \strong{Completion}: Ensures all response categories are present (fills with 0 if missing) +\item \strong{Expansion}: Converts aggregated ordinal data to individual observations +\item \strong{Resampling}: Applies the specified bootstrap method +\item \strong{Aggregation}: Converts back to count format using \code{reshape2::dcast} +\item \strong{Completion}: Ensures all response categories are present (fills with 0 if missing) } } @@ -103,9 +103,9 @@ The function uses several data manipulation steps: This function requires the following packages: \itemize{ - \item \code{reshape2}: For data reshaping operations - \item \code{dplyr}: For data manipulation (hierarchical bootstrap only) - \item \code{tidyr}: For data tidying operations (hierarchical bootstrap only) +\item \code{reshape2}: For data reshaping operations +\item \code{dplyr}: For data manipulation (hierarchical bootstrap only) +\item \code{tidyr}: For data tidying operations (hierarchical bootstrap only) } The function will stop with an informative error if required packages are not installed. @@ -113,8 +113,8 @@ The function will stop with an informative error if required packages are not in \section{Continuity Correction}{ -For parametric bootstrap, when category probabilities are 0 or 1, a continuity -correction is applied to prevent degenerate sampling. This ensures all categories +For parametric bootstrap, when category probabilities are 0 or 1, a continuity +correction is applied to prevent degenerate sampling. This ensures all categories have some probability of being selected, improving bootstrap stability. } diff --git a/man/coef.drcHetVar.Rd b/man/coef.drcHetVar.Rd index 7789ae3..abe4516 100644 --- a/man/coef.drcHetVar.Rd +++ b/man/coef.drcHetVar.Rd @@ -7,7 +7,7 @@ \method{coef}{drcHetVar}(object, ...) } \arguments{ -\item{object}{An object of class "drcHetVar" containing a fitted heteroscedastic +\item{object}{An object of class "drcHetVar" containing a fitted heteroscedastic dose-response model with separate curve and variance parameters} \item{...}{Additional arguments (currently unused but included for S3 method consistency)} @@ -15,40 +15,40 @@ dose-response model with separate curve and variance parameters} \value{ A named numeric vector containing all model parameters: \itemize{ - \item Curve parameters with names prefixed by "Curve:" - \item Variance parameters with names prefixed by "Sigma:" +\item Curve parameters with names prefixed by "Curve:" +\item Variance parameters with names prefixed by "Sigma:" } } \description{ S3 method to extract coefficients from fitted heteroscedastic dose-response models. -This method extends the generic `coef()` function to handle `drcHetVar` objects, +This method extends the generic \code{coef()} function to handle \code{drcHetVar} objects, which contain both dose-response curve parameters and variance model parameters. } \details{ Heteroscedastic dose-response models fit two components simultaneously: \itemize{ - \item \strong{Curve parameters}: Describe the dose-response relationship - (e.g., slope, inflection point, asymptotes) - \item \strong{Variance parameters}: Model how the response variance changes - with dose or fitted values +\item \strong{Curve parameters}: Describe the dose-response relationship +(e.g., slope, inflection point, asymptotes) +\item \strong{Variance parameters}: Model how the response variance changes +with dose or fitted values } -This method combines both parameter sets into a single named vector for easy -access and interpretation. Parameter names are prefixed to distinguish between +This method combines both parameter sets into a single named vector for easy +access and interpretation. Parameter names are prefixed to distinguish between the two model components: \itemize{ - \item \code{"Curve:"} prefix for dose-response curve parameters - \item \code{"Sigma:"} prefix for variance model parameters +\item \code{"Curve:"} prefix for dose-response curve parameters +\item \code{"Sigma:"} prefix for variance model parameters } } \note{ -This method assumes the `drcHetVar` object contains: +This method assumes the \code{drcHetVar} object contains: \itemize{ - \item \code{curvePar}: Named vector of curve parameters - \item \code{sigmaPar}: Named vector of variance parameters +\item \code{curvePar}: Named vector of curve parameters +\item \code{sigmaPar}: Named vector of variance parameters } -The original parameter names from the fitting procedure are preserved but +The original parameter names from the fitting procedure are preserved but prefixed for clarity. } \examples{ diff --git a/man/drmHetVar.Rd b/man/drmHetVar.Rd index 364446e..2783fe5 100644 --- a/man/drmHetVar.Rd +++ b/man/drmHetVar.Rd @@ -42,7 +42,7 @@ level. } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/drmMMRE.Rd b/man/drmMMRE.Rd index 4f7875f..11b5639 100644 --- a/man/drmMMRE.Rd +++ b/man/drmMMRE.Rd @@ -39,7 +39,7 @@ Fits a meta-analytic hierarchical dose-response model. } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/drmOrdinal.Rd b/man/drmOrdinal.Rd index 5339e71..1ba0018 100644 --- a/man/drmOrdinal.Rd +++ b/man/drmOrdinal.Rd @@ -58,9 +58,6 @@ guthionS.LL <- drmOrdinal(levels = c("alive", "moribund", "dead"), weights = "to plot(guthionS.LL, xlim = c(15,55)) # uses ggplot -} -\references{ -# ADD REFERENCES } \author{ Signe M. Jensen and Jens Riis Baalkilde diff --git a/man/expandBinomial.Rd b/man/expandBinomial.Rd index 5cea692..786998c 100644 --- a/man/expandBinomial.Rd +++ b/man/expandBinomial.Rd @@ -29,7 +29,7 @@ Utility function for expanding binomial data } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. } diff --git a/man/getStackingWeights.Rd b/man/getStackingWeights.Rd index 2ee0ade..9a067c5 100644 --- a/man/getStackingWeights.Rd +++ b/man/getStackingWeights.Rd @@ -21,7 +21,7 @@ Computing stacking weights. } \details{ The aim to provide an R package calculating the benchmark dose (BMD) and the -lower limit of the corresponding 95\% confidence interval (BMDL) for +lower limit of the corresponding 95\\% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts. diff --git a/man/invBmd.Rd b/man/invBmd.Rd index 7c4138c..f149ddc 100644 --- a/man/invBmd.Rd +++ b/man/invBmd.Rd @@ -26,7 +26,7 @@ derivatives, coefficients, and data information} \item{level}{numeric; Confidence level for BMD confidence intervals (default: 0.9)} -\item{slope}{character; Direction of dose-response relationship, either +\item{slope}{character; Direction of dose-response relationship, either "increasing" or "decreasing"} \item{backgType}{character; Type of background response calculation. Options include: @@ -41,13 +41,13 @@ Default: NA} \item{def}{character; BMD definition type. Options include: \itemize{ - \item "additional"/"added": Additional risk over background - \item "excess": Excess risk over background - \item "relative": Relative change from background - \item "extra": Extra risk (between background and maximum) - \item "hybridAdd": Hybrid additional risk using statistical criteria - \item "hybridExc": Hybrid excess risk using statistical criteria - \item "point": Point estimate (not supported for inverse regression) +\item "additional"/"added": Additional risk over background +\item "excess": Excess risk over background +\item "relative": Relative change from background +\item "extra": Extra risk (between background and maximum) +\item "hybridAdd": Hybrid additional risk using statistical criteria +\item "hybridExc": Hybrid excess risk using statistical criteria +\item "point": Point estimate (not supported for inverse regression) }} \item{useSD}{numeric; Standard deviation value used in hybrid definitions} @@ -58,17 +58,17 @@ for robust standard errors (default: FALSE)} \value{ A matrix with 1 row and 3 columns: \itemize{ - \item \strong{BMD}: Benchmark dose estimate - \item \strong{BMDL}: Lower confidence limit for BMD - \item \strong{BMDU}: Upper confidence limit for BMD +\item \strong{BMD}: Benchmark dose estimate +\item \strong{BMDL}: Lower confidence limit for BMD +\item \strong{BMDU}: Upper confidence limit for BMD } If root finding fails for confidence limits, BMDL is set to 0 and BMDU to Inf. } \description{ -Helper function for `bmd` that calculates Benchmark Dose (BMD) and confidence -intervals using inverse regression. This function handles multiple BMD definitions -and background response types by dynamically modifying the dose-response function +Helper function for \code{bmd} that calculates Benchmark Dose (BMD) and confidence +intervals using inverse regression. This function handles multiple BMD definitions +and background response types by dynamically modifying the dose-response function and its derivatives to solve for the dose corresponding to a specified benchmark response. } \details{ @@ -76,42 +76,42 @@ The function implements inverse regression by solving: \deqn{f(BMD) = BMR}{f(BMD) = BMR} where f is the transformed dose-response function based on the specified definition. -**BMD Definitions:** +\strong{BMD Definitions:} -**Additional Risk:** \deqn{f(x) = |f_0(0) - f_0(x)|}{f(x) = |f_0(0) - f_0(x)|} +\strong{Additional Risk:} \deqn{f(x) = |f_0(0) - f_0(x)|}{f(x) = |f_0(0) - f_0(x)|} -**Excess Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} (decreasing) +\strong{Excess Risk:} \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} (decreasing) \deqn{f(x) = \frac{f_0(x) - f_0(0)}{1 - f_0(0)}}{f(x) = (f_0(x) - f_0(0))/(1 - f_0(0))} (increasing) -**Relative Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} +\strong{Relative Risk:} \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{f_0(0)}}{f(x) = |f_0(0) - f_0(x)|/f_0(0)} -**Extra Risk:** \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{|f_0(0) - f_0(\infty)|}}{f(x) = |f_0(0) - f_0(x)|/|f_0(0) - f_0(infinity)|} +\strong{Extra Risk:} \deqn{f(x) = \frac{|f_0(0) - f_0(x)|}{|f_0(0) - f_0(\infty)|}}{f(x) = |f_0(0) - f_0(x)|/|f_0(0) - f_0(infinity)|} -**Hybrid Definitions:** Use normal distribution probabilities: +\strong{Hybrid Definitions:} Use normal distribution probabilities: \deqn{f(x) = \Phi\left(\frac{f_0(0) - k \cdot SD - f_0(x)}{SD}\right) - (1-\Phi(k))}{f(x) = Phi((f_0(0) - k*SD - f_0(x))/SD) - (1-Phi(k))} where k is the number of standard deviations (default: 2). } \note{ -This is an internal helper function for BMD calculation. It assumes the input -object has the standard structure from dose-response model fitting, including -components like `fct`, `dataList`, `type`, etc. +This is an internal helper function for BMD calculation. It assumes the input +object has the standard structure from dose-response model fitting, including +components like \code{fct}, \code{dataList}, \code{type}, etc. -**Important considerations:** +\strong{Important considerations:} \itemize{ - \item The search range is limited to [0, extFactor × max(dose)] - \item Hybrid definitions require careful specification of useSD and backg - \item Function modification uses string manipulation and may be sensitive to model structure +\item The search range is limited to \verb{[0, extFactor × max(dose)]} +\item Hybrid definitions require careful specification of useSD and backg +\item Function modification uses string manipulation and may be sensitive to model structure } } \section{Function Modification}{ -The function dynamically modifies the model's derivative function to account +The function dynamically modifies the model's derivative function to account for different BMD definitions by: \itemize{ - \item Parsing the derivative function body - \item Adding appropriate transformation terms - \item Handling parameter indexing for fixed vs. estimated parameters - \item Supporting both 4-parameter and 5-parameter models +\item Parsing the derivative function body +\item Adding appropriate transformation terms +\item Handling parameter indexing for fixed vs. estimated parameters +\item Supporting both 4-parameter and 5-parameter models } } @@ -121,7 +121,7 @@ Confidence intervals are calculated using the delta method: \deqn{CI = BMD \pm t_{\alpha/2} \sqrt{h(BMD)^T \Sigma h(BMD)}}{CI = BMD +/- t * sqrt(h(BMD)' * Sigma * h(BMD))} where h(BMD) is the gradient vector and Σ is the variance-covariance matrix. -For continuous data, t-distribution quantiles are used; for other data types, +For continuous data, t-distribution quantiles are used; for other data types, normal distribution quantiles are used. } @@ -129,10 +129,10 @@ normal distribution quantiles are used. The function includes several error checks: \itemize{ - \item Stops if "point" definition is used (not supported) - \item Stops if hybrid definitions are used without appropriate backgType - \item Stops if no background value is provided when required - \item Stops if no solution exists for the specified BMR +\item Stops if "point" definition is used (not supported) +\item Stops if hybrid definitions are used without appropriate backgType +\item Stops if no background value is provided when required +\item Stops if no solution exists for the specified BMR } } From 470d341f986ec75e48ceb00195f4e283d3c5d7b9 Mon Sep 17 00:00:00 2001 From: Zhenglei Gao Date: Mon, 14 Jul 2025 11:32:27 +0200 Subject: [PATCH 14/17] fixed rm list issue, has still calling ::: notes --- R/plot.drcHetVar.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/plot.drcHetVar.R b/R/plot.drcHetVar.R index b979655..3f2ad6c 100644 --- a/R/plot.drcHetVar.R +++ b/R/plot.drcHetVar.R @@ -16,7 +16,7 @@ plot.drcHetVar <- function(x, ...){ gridsize <- 300 } sigma0 <- NULL ## avoiding global binding issues - rm(list("sigma0")) + rm(list="sigma0") # Add assertion of gridExtra if(!requireNamespace("gridExtra")){ stop('package "gridExtra" must be installed to plot drcHetVar object') From 4529a8781dbe04089a8ab9f16d774988e147d51d Mon Sep 17 00:00:00 2001 From: Jens Riis Baalkilde Date: Thu, 31 Jul 2025 10:03:54 +0200 Subject: [PATCH 15/17] Imported internal functions from drc package to prevent ::: notes --- .DS_Store | Bin 8196 -> 8196 bytes R/EDhelper.R | 46 ++++++++++++++++++++++++++++++++++++++++++++++ R/absToRel.R | 15 +++++++++++++++ R/bmd.R | 4 ++-- R/bmd.edfct.R | 24 ++++++++++++++---------- R/confint.basic.R | 32 ++++++++++++++++++++++++++++++++ R/invBmd.R | 2 +- 7 files changed, 110 insertions(+), 13 deletions(-) create mode 100644 R/EDhelper.R create mode 100644 R/absToRel.R create mode 100644 R/confint.basic.R diff --git a/.DS_Store b/.DS_Store index d90517d684082b12140488642c7b1f03a8103523..2fbfc34126d464f972416c45c4f87d09f46913a4 100644 GIT binary patch delta 14 VcmZp1XmQw3Da>fLxk|W;2LLBJ1kwNi delta 16 XcmZp1XmQw3DLmOt$Yt|hVRs$?HE;#W diff --git a/R/EDhelper.R b/R/EDhelper.R new file mode 100644 index 0000000..155fa20 --- /dev/null +++ b/R/EDhelper.R @@ -0,0 +1,46 @@ +# HELPER FUNCTION BORROWED FROM DRC PACKAGE + +"EDhelper" <- function(parmVec, respl, reference, typeCalc, cond = TRUE) +{ + ## Works for log-logistic type dose-response models + + ## Converting absolute to relative + if (typeCalc == "absolute") + { + p <- 100 * ((parmVec[3] - respl) / (parmVec[3] - parmVec[2])) +# typeCalc <- "relative" + } else { + p <- respl + } + ## Swapping p for an increasing curve + if (cond) + { + if ((typeCalc == "relative") && (parmVec[1] < 0) && (reference == "control")) + { + p <- 100 - p + } + } else { + if ((typeCalc == "relative") && (reference == "control")) + { + p <- 100 - p + } + } + p +} + +## Used for FP models +"EDhelper2" <- function(parmVec, respl, reference, typeCalc, increasing) +{ + ## Converting absolute to relative + if (typeCalc == "absolute") + { + p <- 100 * (1 - (parmVec[3] - respl) / (parmVec[3] - parmVec[2])) + + } else { + + if (increasing) {p <- respl} else {p <- 100 - respl} + } + + p +} + diff --git a/R/absToRel.R b/R/absToRel.R new file mode 100644 index 0000000..a3ff6dd --- /dev/null +++ b/R/absToRel.R @@ -0,0 +1,15 @@ +# HELPER FUNCTION BORROWED FROM DRC PACKAGE + +"absToRel" <- function(parmVec, respl, typeCalc) +{ + ## Converting absolute to relative + if (typeCalc == "absolute") + { + p <- 100 * ((parmVec[3] - respl) / (parmVec[3] - parmVec[2])) + } else { + p <- respl + } + + p +} + diff --git a/R/bmd.R b/R/bmd.R index 3ce060b..a7011e8 100644 --- a/R/bmd.R +++ b/R/bmd.R @@ -92,7 +92,7 @@ bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", " if(inherits(object, "drcMMRE")){ intMat <- matrix(qnorm(c((1-level)/2, 1-(1-level)/2), mean = bmdVal, sd = bmdSEVal), ncol = 2) } else { - intMat <- drc:::confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), + intMat <- confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), level = level, object$"type", df.residual(object), FALSE) } } else if(interval == "inv"){ @@ -178,7 +178,7 @@ bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", " bmdSEVal <- sqrt(dBmdVal %*% varCov %*% dBmdVal) if(interval == "delta"){ - intMat <- drc:::confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), + intMat <- confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), level = level, object$"type", df.residual(object), FALSE) } diff --git a/R/bmd.edfct.R b/R/bmd.edfct.R index e518b85..3205dc4 100644 --- a/R/bmd.edfct.R +++ b/R/bmd.edfct.R @@ -12,7 +12,7 @@ bmd.edfct <- function(object){ edfct <- function(parm, respl, reference, type, ...) { parmVec[notFixed] <- parm - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) tempVal <- log((100-p)/100) EDp <- parmVec[4]*(exp(-tempVal/parmVec[5])-1)^(1/parmVec[1]) @@ -35,7 +35,7 @@ bmd.edfct <- function(object){ { parmVec[notFixed] <- parm - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) tempVal <- log((100-p)/100) EDp <- exp(parmVec[4])*(exp(-tempVal/parmVec[5])-1)^(1/parmVec[1]) @@ -61,7 +61,7 @@ bmd.edfct <- function(object){ edfct <- function(parm, respl, reference, type, ...) { parmVec[notFixed] <- parm - p <- drc:::absToRel(parmVec, respl, type) + p <- absToRel(parmVec, respl, type) ## Reversing p if (identical(type, "absolute")) @@ -105,7 +105,7 @@ bmd.edfct <- function(object){ edfct <- function(parm, respl, reference, type, ...) # function(parm, p, reference, type, ...) { parmVec[notFixed] <- parm - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) tempVal <- log(-log((100-p)/100)) EDp <- exp(tempVal/parmVec[1] + log(parmVec[4])) @@ -128,7 +128,7 @@ bmd.edfct <- function(object){ { parmVec[notFixed] <- parm - p <- drc:::absToRel(parmVec, respl, type) + p <- absToRel(parmVec, respl, type) ## Reversing p if ( (parmVec[1] > 0) && (reference == "control") && (type == "relative") ) @@ -154,7 +154,7 @@ bmd.edfct <- function(object){ edfct <- function(parm, respl, reference, type, ...) { parmVec[notFixed] <- parm - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) # if (parmVec[1] > 0) # { @@ -201,11 +201,11 @@ bmd.edfct <- function(object){ interval <- c(lower, upper) parmVec[notFixed] <- parm - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) tempVal <- (100-p)/100 edfct0 <- function(parmVec){ - p <- drc:::EDhelper(parmVec, respl, reference, type) + p <- EDhelper(parmVec, respl, reference, type) tempVal <- (100-p)/100 helpEqn <- function(dose) @@ -240,12 +240,16 @@ bmd.edfct <- function(object){ } if(identical(class(object$fct), "fp-logistic")){ + if(!requireNamespace("numDeriv")){ + stop('package "numDeriv" must be installed to use FPL models') + } + p1 <- as.numeric(unlist(strsplit(object$fct$name, split = "[,()]+"))[2]) p2 <- as.numeric(unlist(strsplit(object$fct$name, split = "[,()]+"))[3]) edfct <- function(parm, respl, reference, type, loged = FALSE, ...) { parmVec[notFixed] <- parm - p <- drc:::EDhelper2(parmVec, respl, reference, type, parmVec[1] > 0) + p <- EDhelper2(parmVec, respl, reference, type, parmVec[1] > 0) invfp <- function(resp, b, e) { @@ -260,7 +264,7 @@ bmd.edfct <- function(object){ EDfct0 <- function(par) { - p <- drc:::EDhelper2(par, respl, reference, type, par[1] > 0) + p <- EDhelper2(par, respl, reference, type, par[1] > 0) invfp(log((100-p)/p), par[1], par[4]) } diff --git a/R/confint.basic.R b/R/confint.basic.R new file mode 100644 index 0000000..b9c24f3 --- /dev/null +++ b/R/confint.basic.R @@ -0,0 +1,32 @@ +# HELPER FUNCTION BORROWED FROM DRC PACKAGE +# Defining basic function for providing confidence intervals + +"confint.basic" <- function(estMat, level, intType, dfres, formatting = TRUE) +{ + alphah <- (1 - level)/2 + # if (type == "u") {two <- qnorm(1 - alphah)} + # if (type == "t") {two <- qt(1 - alphah, df.residual(object))} + tailPercentile <- switch(intType, + binomial = qnorm(1 - alphah), + continuous = qt(1 - alphah, dfres), + event = qnorm(1 - alphah), + Poisson = qnorm(1 - alphah), + negbin1 = qnorm(1 - alphah), + negbin2 = qnorm(1 - alphah)) + + estVec <- estMat[, 1] + halfLength <- tailPercentile * estMat[, 2] + confMat <- matrix(c(estVec - halfLength, estVec + halfLength), ncol = 2) + + ## Formatting matrix + if (formatting) + { + colnames(confMat) <- c(paste(format(100 * alphah), "%", sep = " "), paste(format(100*(1 - alphah)), "%", sep = " ")) + rownames(confMat) <- rownames(estMat) + } + + return(confMat) +} + + + diff --git a/R/invBmd.R b/R/invBmd.R index e213a3f..84306d3 100644 --- a/R/invBmd.R +++ b/R/invBmd.R @@ -559,7 +559,7 @@ invBmd <- function(object, bmr, level=0.9, slope, backgType="modelBased", # g1<-function(x){as.numeric(g(x, matrix(coef(object), 1, length(coef(object)))))} if(sandwich.vcov){ j1<-function(x){sqrt(as.vector(h(x, matrix(coef(object), 1, length(coef(object)))))%*% - sandwich(object)%*% + sandwich::sandwich(object)%*% as.vector(h(x, matrix(coef(object), 1, length(coef(object))))))} } else{ j1<-function(x){sqrt(as.vector(h(x, matrix(coef(object), 1, length(coef(object)))))%*% From 3331cc0b2ff30300b9d4acf961ceb0c69d6e8cb4 Mon Sep 17 00:00:00 2001 From: Jens Riis Baalkilde Date: Thu, 31 Jul 2025 13:36:49 +0200 Subject: [PATCH 16/17] Changed confint.basic to confint_basic to avoid S3 mixup. --- R/bmd.R | 4 ++-- R/{confint.basic.R => confint_basic.R} | 3 ++- 2 files changed, 4 insertions(+), 3 deletions(-) rename R/{confint.basic.R => confint_basic.R} (87%) diff --git a/R/bmd.R b/R/bmd.R index a141673..f591cdb 100644 --- a/R/bmd.R +++ b/R/bmd.R @@ -265,7 +265,7 @@ bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", " if(inherits(object, "drcMMRE")){ intMat <- matrix(qnorm(c((1-level)/2, 1-(1-level)/2), mean = bmdVal, sd = bmdSEVal), ncol = 2) } else { - intMat <- confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), + intMat <- confint_basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), level = level, object$"type", df.residual(object), FALSE) } } else if(interval == "inv"){ @@ -351,7 +351,7 @@ bmd<-function(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", " bmdSEVal <- sqrt(dBmdVal %*% varCov %*% dBmdVal) if(interval == "delta"){ - intMat <- confint.basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), + intMat <- confint_basic(matrix(c(bmdVal, bmdSEVal), ncol = 2), level = level, object$"type", df.residual(object), FALSE) } diff --git a/R/confint.basic.R b/R/confint_basic.R similarity index 87% rename from R/confint.basic.R rename to R/confint_basic.R index b9c24f3..ad94c6d 100644 --- a/R/confint.basic.R +++ b/R/confint_basic.R @@ -1,7 +1,8 @@ # HELPER FUNCTION BORROWED FROM DRC PACKAGE +# Name in drc package: confint.basic - changed to confint_basic to avoid S3 mixup # Defining basic function for providing confidence intervals -"confint.basic" <- function(estMat, level, intType, dfres, formatting = TRUE) +"confint_basic" <- function(estMat, level, intType, dfres, formatting = TRUE) { alphah <- (1 - level)/2 # if (type == "u") {two <- qnorm(1 - alphah)} From 7d29748df9824b8503efaddbfa8a653e802fdd38 Mon Sep 17 00:00:00 2001 From: JensBaalkilde <122888295+JensBaalkilde@users.noreply.github.com> Date: Mon, 25 Aug 2025 13:24:56 +0200 Subject: [PATCH 17/17] Update version to 2.7.4 --- DESCRIPTION | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/DESCRIPTION b/DESCRIPTION index 7d80581..8c49cea 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: bmd Type: Package Title: Benchmark dose estimation for dose-response data -Version: 2.7.3 +Version: 2.7.4 Date: 2025-03-24 Author: Signe M.Jensen, Christian Ritz and Jens Riis Baalkilde Maintainer: Signe M. Jensen

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    +

    BMD: Benchmark Dose Modeling

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    +

    A package for benchmark dose modeling in toxicology and risk assessment

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    Developed by Signe M. Jensen.

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    + +
    +

    Site built with pkgdown 2.1.0.

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    + +

    • +
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    +
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    Authors and Citation

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    + + +
    • +

      Signe M. Jensen. Maintainer. +

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      • +
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    Citation

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    Jensen, S. M., Kluxen, F. M., Streibig, J. C., Cedergreen, N., & Ritz, C. (2020) bmd: an R package for benchmark dose estimation PeerJ, 8, e10557

    + 
    @Article{,
+  title = {bmd: an R package for benchmark dose estimation},
+  author = {S. M. Jensen and F. M. Kluxen and J. C. Streibig and N. Cedergreen and C. Ritz},
+  journal = {PeerJ},
+  volume = {8},
+  pages = {e10557},
+  year = {2020},
+  publisher = {PeerJ Inc.},
+}
    + +
    + +
    + + + +
    +

    Developed by Signe M. Jensen.

    +
    + +
    +

    Site built with pkgdown 2.1.0.

    +
    + +

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