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R/ddp_quantiles.R
In growcurves: Bayesian Semi and Nonparametric Growth Curve Models that Additionally Include Multiple Membership Random Effects
Defines functions
ddp_quantiles
Documented in
ddp_quantiles
#' Produce quantile summaries of model posterior samples
#'
#' Inputs MCMC samples for model parameters and constructs c(2.5\%,50\%,97.5\%) quantile summaries.
#'
#' @param model.output A list vector of objects returned by MCMC sampling functions. e.g. mmCplusDpPost for \code{option = "mmcar"}.
#' @param dosemat An \code{P x (T+1)} \code{matrix} object that maps \code{subjects} to treatment dosages. The first column should be an
#' intercept column (filled with 1's).
#' @param Nfixed Number of total fixed effects, both time-based and nuisance.
#' @param Nrandom Number of total random effects, both time-based and nuisance, all grouped by subject.
#' @param Nsubject Number of unique subjects (on which repeated measures are observed).
#' @param typet A numeric vector of length equal to the number of treatments that contains the base distribution for each treatment.
#' \code{1 = "car"}, \code{2 = "mvn"}, \code{3 = "ind"}.
#' @return A list object containing quantile summaries for all sampled model parameters.
#' \item{deviance.summary}{vector of length 3 summarizing quantiles for model deviance.}
#' \item{beta.summary}{\code{Nfixed x 3} quantile summaries of model fixed effects.}
#' \item{alpha.summary}{quantile summary of model global intercept parameter.}
#' \item{theta.summary}{list object of length \code{Nrandom}, each cell containing a \code{n x 3} matrix of by-subject random effect parameter quantile summaries.}
#' \item{lambda.summary}{\code{Nrandom^2 x 3} quantile summaries of by-polynomial order precision parameters used in base distributions.}
#' \item{lambda.mean}{\code{Nrandom x Nrandom} posterior means of by-polynomial order precision parameters used in base distributions.}
#' \item{alphacar.summary}{\code{numcar x 3} quantile summaries of proper CAR strength of correlation parameters for CAR base distribution on subject-dose random effects, where numcar <= nty treatments.}
#' \item{taucar.summary}{\code{numcar x 3} quantile summaries of proper CAR precision parameters for CAR base distribution on subject-dose random effects, where numcar <= nty treatments.}
#' \item{dosetrt.summary}{list object of length \code{nty}, each cell containing a \code{Nsubject*(Nrandom*numt[m]) x 3} matrix of quantile summaries for subject-dose random effects.}
#' \item{dosetrt.mean}{list object of length \code{nty}, each cell containing a \code{Nsubject x (Nrandom*numt[m])} matrix of posterior mean values for subject-dose random effects.}
#' \item{pind.summary}{list object of length \code{numind}, each cell contains a \code{numt[m] x 3} matrix of quantile summaries for precision values under IND base distribution, where numind <= nty treatments.}
#' \item{pmvn.summary}{list object of length \code{nummvn}, each cell containing quantile summaries for precision parameters used for MVN base distribution on subject-dose random effects, where nummvn <= nty treatments.}
#' \item{pmvn.summary}{list object of length \code{nummvn}, each cell containing posterior mean for \code{numt[m] x numt[m]} matrix of precision parameters used for MVN base distribution on subject-dose random effects, where nummvn <= nty treatments.}
#' \item{doseint.summary}{list object of length \code{Nrandom}, each cell containing a \code{Nsubject x 3} matrix of quantile summaries for the intercept parameter in the subject-dose random effects.}
#' \item{taue.summary}{quantile summary for model error precision parameter.}
#' \item{M.summary}{quantile summary for number of DP posterior clusters formed.}
#' \item{Dbar}{Model fit statistics.}
#' \item{pD}{Model fit statistics.}
#' \item{pV}{Model fit statistics.}
#' \item{DIC}{Model fit statistics.}
#' \item{lpml}{Model fit statistics.}
#' @seealso \code{\link{dpgrowmm}}, \code{\link{dpgrow}}
#' @author Terrance Savitsky \email{tds151@@gmail.com}
#' @aliases ddp_quantiles
#' @export
ddp_quantiles = function(model.output, dosemat, Nfixed, Nrandom, Nsubject, typet)
{
##
## Input checks
##
stopifnot(ncol(model.output$Beta) == Nfixed)
stopifnot(ncol(model.output$Theta) == (Nrandom*Nsubject)) ## same dimensions and loading structure as B under MM models
stopifnot(length(model.output$DoseEffects) == (length(typet)) + 1)
##
## compose model fit statistics
##
pV = var(model.output$Deviance)/2
DIC = model.output$devres[1]
Dbar = model.output$devres[2]
Dhat = model.output$devres[3]
pD = model.output$devres[4]
lpml = model.output$lpml
##
## compose summaries for DDP effects
##
## Extract dimensions
nty <- length(model.output$DoseEffects) - 1 ## "-1" for the q intercept anova effects
## extract size for each treatment type
poscar <- which(typet == 1); numcar = length(poscar);
posmvn <- which(typet == 2); nummvn = length(posmvn); countmvn = 1;
posind <- which(typet == 3); numind = length(posind); countind = 1;
## DoseEffects summary and mean matrix, the latter for plotting.
dosetrt.summary <- vector("list", nty)
dosetrt.mean <- vector("list", nty)
numt <- vector("numeric", nty)
## Precision parameters for base distribution treatments.
if( nummvn > 0 )
{
pmvn.summary <- vector("list", nummvn)
pmvn.mean <- vector("list", nummvn)
}
if( numind > 0 ) tauind.summary <- vector("list", numind)
if( numcar > 0 )
{
Alphacar <- model.output$CAR_Q[[1]] ## nkeep x numcar matrix
Taucar <- model.output$CAR_Q[[2]] ## nkeep x numcar matrix
mcmc.data = cbind(Alphacar, Taucar)
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
mcmc.summary = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high") and rows ordered as Deviance, Beta, ..
alphacar.summary = matrix(mcmc.summary[1:numcar,], numcar, 3) ## numcar x 3
taucar.summary = matrix(mcmc.summary[(numcar+1):(2*numcar),], numcar, 3) ## numcar x 3
}
start.labs = 2
for(m in 1:nty)
{
## DoseEffects summary and mean matrix, the latter for plotting.
numt[m] = ncol(model.output$DoseEffects[[m]]) / (Nsubject*Nrandom)
mcmc.data = model.output$DoseEffects[[m]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
## for dosetrt.summary[[m]], subject is slowest moving index, followed by polynomial order, followed by numt[m]
## <--> Nsubject*(Nrandom*numt[m]) x 1, index speed order: subject, order, dose
dosetrt.summary[[m]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high")
dosetrt.mean[[m]] = matrix(dosetrt.summary[[m]][,2], (Nrandom*numt[m]), Nsubject, byrow = FALSE) ## column 2 captures the means
dosetrt.mean[[m]] = t(dosetrt.mean[[m]]) ## Nsubject x (Nrandom*numt[m]) - will take row i to construct delta_i for plotting heat map
if( !is.null(colnames(dosemat)) ) ## assign colnames to dosetrt.mean[[m]] to anticipate plotting
{
end.labs = start.labs + numt[m] - 1
doselabs = colnames(dosemat)[start.labs:end.labs]
start.labs = end.labs + 1
colnames(dosetrt.mean[[m]]) = paste(rep(1:Nrandom, each = numt[m]), rep(doselabs, Nrandom), sep=".")
}else{ ## no colnames for dosemat
colnames(dosetrt.mean[[m]]) = paste(rep(1:Nrandom, each = numt[m]), rep(1:numt[m], Nrandom), sep=".") ## 1.1, 1.2, ...., 1.numt[m]
}
## Precision parameters for base distribution treatments.
if(typet[m] == 2) ## mvn
{
mcmc.data = model.output$Pmvn[[countmvn]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
pmvn.summary[[countmvn]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high))
pmvn.mean[[countmvn]] = matrix(pmvn.summary[[countmvn]][,2], numt[m], numt[m], byrow = FALSE) ## loading by column reverses vectorization in DDP.cpp
countmvn = countmvn + 1
}else{
if( typet[m] == 3 ) ## typet[m] == 3, ind
{
mcmc.data = model.output$Tauind[[countind]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
tauind.summary[[countind]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## numt[m] x 3
countind = countind + 1
}
}
}
##
## compose summaries for remaining model parameters
##
mcmc.data = cbind(model.output$Deviance,model.output$Beta,model.output$Alpha,model.output$Theta,model.output$Lambda,
model.output$Taue,model.output$M,model.output$DoseEffects[[nty+1]]) #nrow(mcmc.data) = n.keep
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
rm(mcmc.data) #free up memory
mcmc.summary = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high") and rows ordered as Deviance, Beta, ..
deviance.summary = mcmc.summary[1,];
beta.summary = mcmc.summary[2:(Nfixed+1),]
alpha.summary = mcmc.summary[(Nfixed+2),]
theta.summary = vector(mode = "list", length = Nrandom)
for(i in 1:Nrandom)
{
theta.summary[[i]] = mcmc.summary[(Nfixed+3+(i-1)*Nsubject):(Nfixed+2+i*Nsubject),]
}
Nrandom.2 = Nrandom^2
lambda.summary = mcmc.summary[(Nfixed+3+Nrandom*Nsubject):(Nfixed+2+Nrandom*Nsubject+Nrandom.2),]
taue.summary = mcmc.summary[(Nfixed+3+Nrandom*Nsubject+Nrandom.2),]
M.summary = mcmc.summary[(Nfixed+4+Nrandom*Nsubject+Nrandom.2),]
doseint.summary = vector(mode = "list", length = Nrandom)
for(i in 1:Nrandom)
{
doseint.summary[[i]] = mcmc.summary[(Nfixed+5+Nrandom*Nsubject+Nrandom.2+(i-1)*Nsubject):(Nfixed+4+Nrandom*Nsubject+Nrandom.2+i*Nsubject),]
}
## create lambda.mean (Nrandom x Nrandom)
lambda.mean = matrix(lambda.summary[,2], Nrandom, Nrandom, byrow = FALSE) ## reverse by column stacking into a vector
##
## return results
##
res <- list(deviance.summary = deviance.summary, beta.summary = beta.summary, alpha.summary = alpha.summary, theta.summary = theta.summary,
taue.summary = taue.summary, M.summary = M.summary, lambda.summary = lambda.summary, lambda.mean = lambda.mean,
dosetrt.summary = dosetrt.summary, dosetrt.mean = dosetrt.mean,
doseint.summary = doseint.summary, pV = pV, DIC = DIC, Dbar = Dbar, Dhat = Dhat, pD = pD, lpml = lpml)
if( numcar > 0 )
{
res$alphacar.summary <- alphacar.summary
res$taucar.summary <- taucar.summary
}
if( numind > 0 )
{
res$tauind.summary <- tauind.summary
}
if( nummvn > 0 )
{
res$pmvn.summary <- pmvn.summary
res$pmvn.mean <- pmvn.mean
}
return(res)
} ## end function ddp_quantiles.R
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Defines functions ddp_quantiles
Documented in ddp_quantiles
#' Produce quantile summaries of model posterior samples
#'
#' Inputs MCMC samples for model parameters and constructs c(2.5\%,50\%,97.5\%) quantile summaries.
#'
#' @param model.output A list vector of objects returned by MCMC sampling functions. e.g. mmCplusDpPost for \code{option = "mmcar"}.
#' @param dosemat An \code{P x (T+1)} \code{matrix} object that maps \code{subjects} to treatment dosages. The first column should be an
#' intercept column (filled with 1's).
#' @param Nfixed Number of total fixed effects, both time-based and nuisance.
#' @param Nrandom Number of total random effects, both time-based and nuisance, all grouped by subject.
#' @param Nsubject Number of unique subjects (on which repeated measures are observed).
#' @param typet A numeric vector of length equal to the number of treatments that contains the base distribution for each treatment.
#' \code{1 = "car"}, \code{2 = "mvn"}, \code{3 = "ind"}.
#' @return A list object containing quantile summaries for all sampled model parameters.
#' \item{deviance.summary}{vector of length 3 summarizing quantiles for model deviance.}
#' \item{beta.summary}{\code{Nfixed x 3} quantile summaries of model fixed effects.}
#' \item{alpha.summary}{quantile summary of model global intercept parameter.}
#' \item{theta.summary}{list object of length \code{Nrandom}, each cell containing a \code{n x 3} matrix of by-subject random effect parameter quantile summaries.}
#' \item{lambda.summary}{\code{Nrandom^2 x 3} quantile summaries of by-polynomial order precision parameters used in base distributions.}
#' \item{lambda.mean}{\code{Nrandom x Nrandom} posterior means of by-polynomial order precision parameters used in base distributions.}
#' \item{alphacar.summary}{\code{numcar x 3} quantile summaries of proper CAR strength of correlation parameters for CAR base distribution on subject-dose random effects, where numcar <= nty treatments.}
#' \item{taucar.summary}{\code{numcar x 3} quantile summaries of proper CAR precision parameters for CAR base distribution on subject-dose random effects, where numcar <= nty treatments.}
#' \item{dosetrt.summary}{list object of length \code{nty}, each cell containing a \code{Nsubject*(Nrandom*numt[m]) x 3} matrix of quantile summaries for subject-dose random effects.}
#' \item{dosetrt.mean}{list object of length \code{nty}, each cell containing a \code{Nsubject x (Nrandom*numt[m])} matrix of posterior mean values for subject-dose random effects.}
#' \item{pind.summary}{list object of length \code{numind}, each cell contains a \code{numt[m] x 3} matrix of quantile summaries for precision values under IND base distribution, where numind <= nty treatments.}
#' \item{pmvn.summary}{list object of length \code{nummvn}, each cell containing quantile summaries for precision parameters used for MVN base distribution on subject-dose random effects, where nummvn <= nty treatments.}
#' \item{pmvn.summary}{list object of length \code{nummvn}, each cell containing posterior mean for \code{numt[m] x numt[m]} matrix of precision parameters used for MVN base distribution on subject-dose random effects, where nummvn <= nty treatments.}
#' \item{doseint.summary}{list object of length \code{Nrandom}, each cell containing a \code{Nsubject x 3} matrix of quantile summaries for the intercept parameter in the subject-dose random effects.}
#' \item{taue.summary}{quantile summary for model error precision parameter.}
#' \item{M.summary}{quantile summary for number of DP posterior clusters formed.}
#' \item{Dbar}{Model fit statistics.}
#' \item{pD}{Model fit statistics.}
#' \item{pV}{Model fit statistics.}
#' \item{DIC}{Model fit statistics.}
#' \item{lpml}{Model fit statistics.}
#' @seealso \code{\link{dpgrowmm}}, \code{\link{dpgrow}}
#' @author Terrance Savitsky \email{tds151@@gmail.com}
#' @aliases ddp_quantiles
#' @export
ddp_quantiles = function(model.output, dosemat, Nfixed, Nrandom, Nsubject, typet)
{
##
## Input checks
##
stopifnot(ncol(model.output$Beta) == Nfixed)
stopifnot(ncol(model.output$Theta) == (Nrandom*Nsubject)) ## same dimensions and loading structure as B under MM models
stopifnot(length(model.output$DoseEffects) == (length(typet)) + 1)
##
## compose model fit statistics
##
pV = var(model.output$Deviance)/2
DIC = model.output$devres[1]
Dbar = model.output$devres[2]
Dhat = model.output$devres[3]
pD = model.output$devres[4]
lpml = model.output$lpml
##
## compose summaries for DDP effects
##
## Extract dimensions
nty <- length(model.output$DoseEffects) - 1 ## "-1" for the q intercept anova effects
## extract size for each treatment type
poscar <- which(typet == 1); numcar = length(poscar);
posmvn <- which(typet == 2); nummvn = length(posmvn); countmvn = 1;
posind <- which(typet == 3); numind = length(posind); countind = 1;
## DoseEffects summary and mean matrix, the latter for plotting.
dosetrt.summary <- vector("list", nty)
dosetrt.mean <- vector("list", nty)
numt <- vector("numeric", nty)
## Precision parameters for base distribution treatments.
if( nummvn > 0 )
{
pmvn.summary <- vector("list", nummvn)
pmvn.mean <- vector("list", nummvn)
}
if( numind > 0 ) tauind.summary <- vector("list", numind)
if( numcar > 0 )
{
Alphacar <- model.output$CAR_Q[[1]] ## nkeep x numcar matrix
Taucar <- model.output$CAR_Q[[2]] ## nkeep x numcar matrix
mcmc.data = cbind(Alphacar, Taucar)
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
mcmc.summary = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high") and rows ordered as Deviance, Beta, ..
alphacar.summary = matrix(mcmc.summary[1:numcar,], numcar, 3) ## numcar x 3
taucar.summary = matrix(mcmc.summary[(numcar+1):(2*numcar),], numcar, 3) ## numcar x 3
}
start.labs = 2
for(m in 1:nty)
{
## DoseEffects summary and mean matrix, the latter for plotting.
numt[m] = ncol(model.output$DoseEffects[[m]]) / (Nsubject*Nrandom)
mcmc.data = model.output$DoseEffects[[m]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
## for dosetrt.summary[[m]], subject is slowest moving index, followed by polynomial order, followed by numt[m]
## <--> Nsubject*(Nrandom*numt[m]) x 1, index speed order: subject, order, dose
dosetrt.summary[[m]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high")
dosetrt.mean[[m]] = matrix(dosetrt.summary[[m]][,2], (Nrandom*numt[m]), Nsubject, byrow = FALSE) ## column 2 captures the means
dosetrt.mean[[m]] = t(dosetrt.mean[[m]]) ## Nsubject x (Nrandom*numt[m]) - will take row i to construct delta_i for plotting heat map
if( !is.null(colnames(dosemat)) ) ## assign colnames to dosetrt.mean[[m]] to anticipate plotting
{
end.labs = start.labs + numt[m] - 1
doselabs = colnames(dosemat)[start.labs:end.labs]
start.labs = end.labs + 1
colnames(dosetrt.mean[[m]]) = paste(rep(1:Nrandom, each = numt[m]), rep(doselabs, Nrandom), sep=".")
}else{ ## no colnames for dosemat
colnames(dosetrt.mean[[m]]) = paste(rep(1:Nrandom, each = numt[m]), rep(1:numt[m], Nrandom), sep=".") ## 1.1, 1.2, ...., 1.numt[m]
}
## Precision parameters for base distribution treatments.
if(typet[m] == 2) ## mvn
{
mcmc.data = model.output$Pmvn[[countmvn]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
pmvn.summary[[countmvn]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high))
pmvn.mean[[countmvn]] = matrix(pmvn.summary[[countmvn]][,2], numt[m], numt[m], byrow = FALSE) ## loading by column reverses vectorization in DDP.cpp
countmvn = countmvn + 1
}else{
if( typet[m] == 3 ) ## typet[m] == 3, ind
{
mcmc.data = model.output$Tauind[[countind]]
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
tauind.summary[[countind]] = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## numt[m] x 3
countind = countind + 1
}
}
}
##
## compose summaries for remaining model parameters
##
mcmc.data = cbind(model.output$Deviance,model.output$Beta,model.output$Alpha,model.output$Theta,model.output$Lambda,
model.output$Taue,model.output$M,model.output$DoseEffects[[nty+1]]) #nrow(mcmc.data) = n.keep
mcmc.mean = colMeans(mcmc.data)
mcmc.low = apply(mcmc.data,2,function(x){quantile(x,probs = 0.025)})
mcmc.high = apply(mcmc.data,2,function(x){quantile(x,probs = 0.975)})
rm(mcmc.data) #free up memory
mcmc.summary = t(rbind(mcmc.low,mcmc.mean,mcmc.high)) ## transpose to 3 columns for c("mcmc.low","mcmc.mean","mcmc.high") and rows ordered as Deviance, Beta, ..
deviance.summary = mcmc.summary[1,];
beta.summary = mcmc.summary[2:(Nfixed+1),]
alpha.summary = mcmc.summary[(Nfixed+2),]
theta.summary = vector(mode = "list", length = Nrandom)
for(i in 1:Nrandom)
{
theta.summary[[i]] = mcmc.summary[(Nfixed+3+(i-1)*Nsubject):(Nfixed+2+i*Nsubject),]
}
Nrandom.2 = Nrandom^2
lambda.summary = mcmc.summary[(Nfixed+3+Nrandom*Nsubject):(Nfixed+2+Nrandom*Nsubject+Nrandom.2),]
taue.summary = mcmc.summary[(Nfixed+3+Nrandom*Nsubject+Nrandom.2),]
M.summary = mcmc.summary[(Nfixed+4+Nrandom*Nsubject+Nrandom.2),]
doseint.summary = vector(mode = "list", length = Nrandom)
for(i in 1:Nrandom)
{
doseint.summary[[i]] = mcmc.summary[(Nfixed+5+Nrandom*Nsubject+Nrandom.2+(i-1)*Nsubject):(Nfixed+4+Nrandom*Nsubject+Nrandom.2+i*Nsubject),]
}
## create lambda.mean (Nrandom x Nrandom)
lambda.mean = matrix(lambda.summary[,2], Nrandom, Nrandom, byrow = FALSE) ## reverse by column stacking into a vector
##
## return results
##
res <- list(deviance.summary = deviance.summary, beta.summary = beta.summary, alpha.summary = alpha.summary, theta.summary = theta.summary,
taue.summary = taue.summary, M.summary = M.summary, lambda.summary = lambda.summary, lambda.mean = lambda.mean,
dosetrt.summary = dosetrt.summary, dosetrt.mean = dosetrt.mean,
doseint.summary = doseint.summary, pV = pV, DIC = DIC, Dbar = Dbar, Dhat = Dhat, pD = pD, lpml = lpml)
if( numcar > 0 )
{
res$alphacar.summary <- alphacar.summary
res$taucar.summary <- taucar.summary
}
if( numind > 0 )
{
res$tauind.summary <- tauind.summary
}
if( nummvn > 0 )
{
res$pmvn.summary <- pmvn.summary
res$pmvn.mean <- pmvn.mean
}
return(res)
} ## end function ddp_quantiles.R
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