R/mlqmm.R
In AntoineBbi/BQt: BQt: Bayesian Quantile regression for joint modeling
Defines functions
mlqmm
Documented in
mlqmm
#' \code{mlqmm} fits multiple linear quantile mixed model
#'
#' Function using JAGS to estimate a multivariate linear quantile mixed model assuming multivariate asymmetric Laplace
#' distribution for residual error.
#'
#' @param formFixed formula for fixed part of longitudinal submodel with response variable
#' @param formRandom formula for random part of longitudinal submodel without response variable
#' @param formGroup formula specifying the cluster variable (e.g. = ~ subject)
#' @param data dataset of observed variables
#' @param tau vector of quantiles to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped.
#' If more than one quantile is specified, rounding off to the 4th decimal must give non–duplicated values of \code{tau},
#' otherwise the execution is stopped.
#' @param corr_structure string specifying the correlation structure between $Y|W_{tau}$: "free", "middle" or "none".
#' If 'none', the dependendance is only caught by the common covariance matrix of all random effects;
#' if 'middle', the model assumes a correlation structure based on both a common correlation parameter and the distances between considered quantiles's orders;
#' if 'free", a specific correlation parameter is assumed for each multivariate responses.
#' @param RE_ind if TRUE, the random effects are assumed to be independent between different quantile.
#' Otherwise (FALSE by default), correlation between quantile (markers) is also caught through common covariance matrix of random effects.
#' @param n.chains the number of parallel chains for the model; default is 1.
#' @param n.iter integer specifying the total number of iterations; default is 10000
#' @param n.burnin integer specifying how many of n.iter to discard as burn-in ; default is 5000
#' @param n.thin integer specifying the thinning of the chains; default is 1
#' @param n.adapt integer specifying the number of iterations to use for adaptation; default is NULL
#' @param precision variance by default for vague prior distribution
#' @param save_jagsUI If TRUE (by default), the output of jagsUI package is return by the function
#' @param parallel see jagsUI::jags() function
#'
#'
#' @return A \code{BQt} object is a list with the following elements:
#' \describe{
#' \item{\code{mean}}{list of posterior mean for each parameter}
#' \item{\code{median}}{list of posterior median for each parameter}
#' \item{\code{modes}}{list of posterior mode for each parameter}
#' \item{\code{StErr}}{list of standard error for each parameter}
#' \item{\code{StDev}}{list of standard deviation for each parameter}
#' \item{\code{ICs}}{list of the credibility interval at 0.95 for each parameters excepted for covariance parameters in covariance matrix of random effects. Otherwise, use save_jagsUI=TRUE to have the associated quantiles.}
#' \item{\code{data}}{data included in argument}
#' \item{\code{sims.list}}{list of the MCMC chains of the parameters and random effects}
#' \item{\code{control}}{list of arguments giving details about the estimation}
#' \item{\code{random_effect}}{list for each quantile including both posterior mean and posterior standard deviation of subject-specific random effects}
#' \item{\code{out_jagsUI}}{only if \code{save_jagsUI=TRUE} in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standart deviation for each parameter and each random effect.
#' Moreover, this list also returns the MCMC draws, the Gelman and Rubin diagnostics (see output of jagsUI objects)}
#' }
#
#' @author Antoine Barbieri
#'
#' @import lqmm jagsUI
#'
#' @references Lea Petrella and Valentina Raponi (2019).
#' \emph{Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress}.
#' Journal of Multivariate Analysis, 173:70-84. doi: 10.1016/j.jmva.2019.02.008.
#'
#' @references Elisabeth Waldmann and Thomas Kneib (2015).
#' \emph{Bayesian bivariate quantile regression}.
#' Statistical Modelling, 15(4):326-344. doi: 10.1177/1471082X14551247.
#'
#' @export
#'
#' @examples
#'
#' \dontrun{
#' #---- Orthodont data from lqmm package
#' data("aids", package = "joineR")
#'
#' #---- Fit regression model for the first quartile
#' BQt_mQr <- mlqmm(formFixed = CD4 ~ obstime,
#' formRandom = ~ obstime,
#' formGroup = ~ id,
#' data = aids,
#' tau = c(0.25,0.5,0.75),
#' n.iter = 1000,
#' n.burnin = 500)
#'
#' #---- Get the estimated coefficients (posterior means)
#' BQt_mQr$mean
#'
#' #---- Summary of output
#' summary(BQt_mQr)
#'
#' #---- Traces of somes parameters
#' traceplot(x = BQt_mQr$out_jagsUI,
#' parameters = c("beta", "sigma", "rho"))
#' }
mlqmm <- function(formFixed,
formRandom,
formGroup,
data,
tau,
corr_structure = "middle",
RE_ind = FALSE,
n.chains = 3,
n.iter = 10000,
n.burnin = 5000,
n.thin = 1,
n.adapt = NULL,
precision = 10,
save_jagsUI = TRUE,
parallel = FALSE){
# Stopping condition
if(prod(tau<1 & tau>0)!=1)
stop("'Tau' have to be a numerical vector with elements included between 0 and 1.\n")
if(length(tau)>3)
stop("'Tau' have to be a numerical vector with length lower than 4.\n")
if(sum(duplicated(tau))>0)
stop("'Tau' have to be a numerical vector with no duplicated quantiles.\n")
if(RE_ind && length(tau)==2){
cat("Until now, all random effects are assumed dependant when considering only two quantiles.\n")
RE_ind <- FALSE
}
if(RE_ind && corr_structure=="none"){
cat("WARNING: There is no correlation structure between quantiles in the specified model.\n")
}
#-- data management
tau <- sort(tau)
data_long <- data[unique(c(all.vars(formGroup),all.vars(formFixed),all.vars(formRandom)))]
y <- data_long[all.vars(formFixed)][, 1]
mfX <- model.frame(formFixed, data = data_long)
X <- model.matrix(formFixed, mfX)
mfU <- model.frame(formRandom, data = data_long)
U <- model.matrix(formRandom, mfU)
ncU = ncol(U)
id <- as.integer(data_long[all.vars(formGroup)][,1])
if(!("id" %in% colnames(data_long)))
data_long <- cbind(data_long, id = id)
offset <- as.vector(c(1, 1 + cumsum(tapply(id, id, length))))
I <- length(unique(id))
Q <- length(tau)
if(Q==2 & corr_structure=="middle")
corr_structure = "free"
# use lqmm function to initiated values
cat("Initiation of parameter values using lqmm package. \n")
tmp_model <- lqmm::lqmm(fixed = formFixed,
random = formRandom,
group = id,
tau = tau,
data = data_long)
# prior beta parameters
priorMean.beta <- t(coef(tmp_model))
priorTau.beta <- diag(rep(1/10,length(priorMean.beta[1, ])))
bis <- matrix(unlist(lqmm::ranef(tmp_model)), ncol = Q*ncU, byrow = F)
bis[abs(bis)<.0001] <- 0
init_sigma <- rep(1, Q)
for(qq in 1:Q){
init_sigma[qq] <- tmp_model[[qq]]$scale
}
initial.values <- list(b = bis,
beta = priorMean.beta,
sigma = init_sigma)
# list of data jags
jags.data <- list(y = matrix(rep(y,Q), ncol = Q, byrow = F),
X = X,
U = U,
tau = tau,
ncX = ncol(X),
ncU = ncol(U),
I = I,
Q = Q,
offset = offset,
priorMean.beta = priorMean.beta,
priorTau.beta = priorTau.beta,
priorA.sigma = 1/precision,
priorB.sigma = 1/precision
)
if(RE_ind){
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncU)),
priorK.Sigma2 = ncU,
mu0 = rep(0, ncU)
)
)
}else{
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncU*Q)),
priorK.Sigma2 = ncU*Q,
mu0 = rep(0, ncU*Q)
)
)
}
initial.values$prec.Sigma2 <- diag(1/unlist(lqmm::VarCorr(tmp_model)))
initial.values$prec.Sigma2[initial.values$prec.Sigma2 > 100] <- 100
# manage the correlation between quantile
if(corr_structure == "free"){
if(Q==3){
initial.values$rho12 <- 0.9
initial.values$rho13 <- 0.9
initial.values$rho23 <- 0.9
}else{
# Q=2
initial.values$rho <- 0.9
}
}
if(corr_structure == "middle"){
jags.data$d12 <- tau[2]-tau[1]
jags.data$d13 <- tau[3]-tau[1]
jags.data$d23 <- tau[3]-tau[2]
}
model <- switch(paste(corr_structure, Q, RE_ind, sep = "/"),
`free/3/FALSE` = jags_3mlqmm_f,
`middle/3/FALSE` = jags_3mlqmm_m,
`none/3/FALSE` = jags_3mlqmm_n,
`free/2/FALSE` = jags_2mlqmm_f,
`middle/2/FALSE` = jags_2mlqmm_f,
`none/2/FALSE` = jags_mlqmm_n,
`free/3/TRUE` = jags_3mlqmm_f_b,
`middle/3/TRUE` = jags_3mlqmm_m_b,
`none/3/TRUE` = jags_3mlqmm_n_b
)
# parameters to save in the sampling step
if(corr_structure == "free"){
if(Q==3){
parms_to_save <- c("beta", "sigma", "rho12", "rho13", "rho23")
}else{
# Q=2
parms_to_save <- c("beta", "sigma", "rho")
}
}
if(corr_structure == "middle"){
jags.data$d12 <- tau[2]-tau[1]
jags.data$d13 <- tau[3]-tau[1]
jags.data$d23 <- tau[3]-tau[2]
parms_to_save <- c("beta", "sigma", "rho")
}
if(corr_structure == "none")
parms_to_save <- c("beta", "sigma")
if(RE_ind && Q==3){
parms_to_save <- c(parms_to_save, "b1", "b2", "b3", "covariance.b1", "covariance.b2", "covariance.b3")
}else{
parms_to_save <- c(parms_to_save, "b", "covariance.b")
}
#---- write jags model in txt from R function
working.directory = getwd()
write.model.jags(model = model,
name_model = "jags_mlqmm",
intitled = file.path(working.directory, "JagsModel.txt"),
Data = jags.data)
#---- use JAGS sampler
# if (!require("rjags"))
# stop("'rjags' is required.\n")
if(n.chains==3)
inits <- list(initial.values,
initial.values,
initial.values)
if(n.chains==2)
inits <- list(initial.values,
initial.values)
if(n.chains==1)
inits <- initial.values
# using jagsUI
out_jags = jagsUI::jags(data = jags.data,
parameters.to.save = parms_to_save,
model.file = "JagsModel.txt",
inits = inits,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
DIC = F)
file.remove(file.path(working.directory, "JagsModel.txt"))
#---- output building
#-- MCMClist management
#- arguments
out <- list(data = data)
out$control <- list(formFixed,
formRandom,
formGroup,
tau = tau,
corr_structure = corr_structure,
RE_ind = RE_ind,
call_function = "mlqmm",
I = I)
#- other outputs
# sims.list output
out$sims.list <- out_jags$sims.list
if(!is.null(out$sims.list$out))
out$sims.list$out <- NULL
if(!RE_ind){
out$sims.list$b <- NULL
}else{
out$sims.list$b1 <- out$sims.list$b2 <- out$sims.list$b3 <- NULL
}
# random effect output
random_effect <- vector("list", Q)
if(Q==3){
names(random_effect) <- c(paste("tau", 100*tau[1], sep=""),
paste("tau", 100*tau[2], sep=""),
paste("tau", 100*tau[3], sep=""))
}else{
names(random_effect) <- c(paste("tau", 100*tau[1], sep=""),
paste("tau", 100*tau[2], sep=""))
}
if(!RE_ind){
for(q in 1:Q){
random_effect[[q]] <- list(postMeans = out_jags$mean$b[, ((q-1)*ncU+1):(q*ncU)],
postSd = out_jags$sd$b[, ((q-1)*ncU+1):(q*ncU)])
colnames(random_effect[[q]]$postMeans) <- colnames(U)
colnames(random_effect[[q]]$postSd) <- colnames(U)
}
}else{
random_effect[[1]] <- list(postMeans = out_jags$mean$b1, postSd = out_jags$sd$b1)
random_effect[[2]] <- list(postMeans = out_jags$mean$b2, postSd = out_jags$sd$b2)
random_effect[[3]] <- list(postMeans = out_jags$mean$b3, postSd = out_jags$sd$b3)
colnames(random_effect[[1]]$postMeans) <-
colnames(random_effect[[2]]$postMeans) <-
colnames(random_effect[[3]]$postMeans) <- colnames(U)
colnames(random_effect[[1]]$postSd) <-
colnames(random_effect[[2]]$postSd) <-
colnames(random_effect[[3]]$postSd) <- colnames(U)
}
out$random_effect <- random_effect
# median : Posterior median of parameters
out$median <- out_jags$q50
if(!RE_ind){
out$median$b <- NULL
}else{
out$median$b1 <- out$median$b2 <- out$median$b3 <- NULL
}
# mean : Posterior mean of parameters
out$mean <- out_jags$mean
if(!RE_ind){
out$mean$b <- NULL
}else{
out$mean$b1 <- out$mean$b2 <- out$mean$b3 <- NULL
}
# # if inverse in jags doesn't run
# sims.list$covariance.b <- array(NA, dim = dim(jags_res$sims.list$prec.Sigma2))
# for(i in 1:dim(jags_res$sims.list$prec.Sigma2)[1]){
# sims.list$covariance.b[i, , ] <- solve(jags_res$sims.list$prec.Sigma2[i, , ])
# }
# out$sims.list$covariance.b = covariance.b
# modes of parameters
out$modes <- lapply(out$sims.list, function(x) {
m <- function(x) {
d <- density(x, bw = "nrd", adjust = 3, n = 1000)
d$x[which.max(d$y)]
}
if (is.matrix(x))
as.array(apply(x, 2, m))
else{
if(is.array(x))
apply(x, c(2,3), m)
else m(x)
}
})
# standard error of parameters
out$StErr <- lapply(out$sims.list, function(x) {
f <- function(x) {
acf.x <- drop(acf(x, lag.max = 0.4 * length(x), plot = FALSE)$acf)[-1]
acf.x <- acf.x[seq_len(rle(acf.x > 0)$lengths[1])]
ess <- length(x)/(1 + 2 * sum(acf.x))
sqrt(var(x)/ess)
}
if (is.matrix(x))
as.array(apply(x, 2, f))
else{
if(is.array(x))
apply(x, c(2,3), f)
else f(x)
}
})
# standard deviation of parameters
out$StDev <- out_jags$sd
if(!RE_ind){
out$StDev$b <- NULL
}else{
out$StDev$b1 <- out$StDev$b2 <- out$StDev$b3 <- NULL
}
# Rhat : Gelman & Rubin diagnostic
out$Rhat <- out_jags$Rhat
if(!RE_ind){
out$Rhat$b <- NULL
}else{
out$Rhat$b1 <- out$Rhat$b2 <- out$Rhat$b3 <- NULL
}
# names
colnames(out$mean$beta) <-
colnames(out$median$beta) <-
colnames(out$modes$beta) <-
colnames(out$StErr$beta) <-
colnames(out$Rhat$beta) <-
colnames(out$StDev$beta) <- colnames(X)
rownames(out$mean$beta) <-
rownames(out$median$beta) <-
rownames(out$modes$beta) <-
rownames(out$StErr$beta) <-
rownames(out$Rhat$beta) <-
rownames(out$StDev$beta) <- paste("tau", as.character(tau*100), sep = "")
rownames(out$mean$sigma) <-
rownames(out$median$sigma) <-
rownames(out$modes$sigma) <-
rownames(out$StErr$sigma) <-
rownames(out$Rhat$sigma) <-
rownames(out$StDev$sigma) <- paste("tau", as.character(tau*100), sep = "")
if(RE_ind){
colnames(out$mean$covariance.b1) <-
rownames(out$mean$covariance.b1) <-
colnames(out$median$covariance.b1) <-
rownames(out$median$covariance.b1) <-
colnames(out$modes$covariance.b1) <-
rownames(out$modes$covariance.b1) <-
colnames(out$StErr$covariance.b1) <-
rownames(out$StErr$covariance.b1) <-
colnames(out$Rhat$covariance.b1) <-
rownames(out$Rhat$covariance.b1) <-
colnames(out$StDev$covariance.b1) <-
rownames(out$StDev$covariance.b1) <-
colnames(out$mean$covariance.b2) <-
rownames(out$mean$covariance.b2) <-
colnames(out$median$covariance.b2) <-
rownames(out$median$covariance.b2) <-
colnames(out$modes$covariance.b2) <-
rownames(out$modes$covariance.b2) <-
colnames(out$StErr$covariance.b2) <-
rownames(out$StErr$covariance.b2) <-
colnames(out$Rhat$covariance.b2) <-
rownames(out$Rhat$covariance.b2) <-
colnames(out$StDev$covariance.b2) <-
rownames(out$StDev$covariance.b2) <-
colnames(out$mean$covariance.b3) <-
rownames(out$mean$covariance.b3) <-
colnames(out$median$covariance.b3) <-
rownames(out$median$covariance.b3) <-
colnames(out$modes$covariance.b3) <-
rownames(out$modes$covariance.b3) <-
colnames(out$StErr$covariance.b3) <-
rownames(out$StErr$covariance.b3) <-
colnames(out$Rhat$covariance.b3) <-
rownames(out$Rhat$covariance.b3) <-
colnames(out$StDev$covariance.b3) <-
rownames(out$StDev$covariance.b3) <- colnames(U)
}else{
colnames(out$mean$covariance.b) <-
rownames(out$mean$covariance.b) <-
colnames(out$median$covariance.b) <-
rownames(out$median$covariance.b) <-
colnames(out$modes$covariance.b) <-
rownames(out$modes$covariance.b) <-
colnames(out$StErr$covariance.b) <-
rownames(out$StErr$covariance.b) <-
colnames(out$Rhat$covariance.b) <-
rownames(out$Rhat$covariance.b) <-
colnames(out$StDev$covariance.b) <-
rownames(out$StDev$covariance.b) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncU),
rep(colnames(U), Q),
sep = ".")
}
# credible intervalles
out$CIs$beta <- cbind(as.vector(t(out_jags$q2.5$beta)),
as.vector(t(out_jags$q97.5$beta)))
rownames(out$CIs$beta) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncol(X)),
rep(colnames(X), Q),
sep = ".")
out$CIs$sigma <- cbind(out_jags$q2.5$sigma,
out_jags$q97.5$sigma)
rownames(out$CIs$sigma) <- paste("tau", as.character(tau*100), sep = "")
if(corr_structure == "free"){
if(Q==3){
out$CIs$rho12 <- cbind(out_jags$q2.5$rho12,
out_jags$q97.5$rho12)
out$CIs$rho13 <- cbind(out_jags$q2.5$rho13,
out_jags$q97.5$rho13)
out$CIs$rho23 <- cbind(out_jags$q2.5$rho23,
out_jags$q97.5$rho23)
}else{
out$CIs$rho <- cbind(out_jags$q2.5$rho,
out_jags$q97.5$rho)
}
}
if(corr_structure == "middle"){
out$CIs$rho <- cbind(out_jags$q2.5$rho,
out_jags$q97.5$rho)
}
# only for diagonal elements of covariance matrix of random effects
if(RE_ind){
out$CIs$variances.b1 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b1)),
as.vector(diag(out_jags$q97.5$covariance.b1)))
out$CIs$variances.b2 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b2)),
as.vector(diag(out_jags$q97.5$covariance.b2)))
out$CIs$variances.b3 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b3)),
as.vector(diag(out_jags$q97.5$covariance.b3)))
rownames(out$CIs$variances.b1) <- rownames(out$CIs$variances.b2) <- rownames(out$CIs$variances.b3) <- colnames(U)
}else{
out$CIs$variances.b <- cbind(as.vector(diag(out_jags$q2.5$covariance.b)),
as.vector(diag(out_jags$q97.5$covariance.b)))
rownames(out$CIs$variances.b) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncol(U)),
rep(colnames(U), Q),
sep = ".")
}
# lapply(out$CIs, setNames, nm = c("2.5%", "97.5%"))
if(!RE_ind){
if(corr_structure == "free"){
if(Q==3){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho12) <-
colnames(out$CIs$rho13) <-
colnames(out$CIs$rho23) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}else{
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
}
if(corr_structure == "middle"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
if(corr_structure == "none"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
}else{
if(corr_structure == "free"){
if(Q==3){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho12) <-
colnames(out$CIs$rho13) <-
colnames(out$CIs$rho23) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}else{# not implemented yet...
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-c("2.5%", "97.5%")
}
}
if(corr_structure == "middle"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}
if(corr_structure == "none"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}
}
# save jags output if requires
if(save_jagsUI)
out$out_jagsUI <- out_jags
#---- End of the function defining the class and retruning the output
class(out) <- "BQt"
out
}
AntoineBbi/BQt documentation built on June 25, 2022, 3:32 p.m.
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Defines functions mlqmm
Documented in mlqmm
#' \code{mlqmm} fits multiple linear quantile mixed model
#'
#' Function using JAGS to estimate a multivariate linear quantile mixed model assuming multivariate asymmetric Laplace
#' distribution for residual error.
#'
#' @param formFixed formula for fixed part of longitudinal submodel with response variable
#' @param formRandom formula for random part of longitudinal submodel without response variable
#' @param formGroup formula specifying the cluster variable (e.g. = ~ subject)
#' @param data dataset of observed variables
#' @param tau vector of quantiles to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped.
#' If more than one quantile is specified, rounding off to the 4th decimal must give non–duplicated values of \code{tau},
#' otherwise the execution is stopped.
#' @param corr_structure string specifying the correlation structure between $Y|W_{tau}$: "free", "middle" or "none".
#' If 'none', the dependendance is only caught by the common covariance matrix of all random effects;
#' if 'middle', the model assumes a correlation structure based on both a common correlation parameter and the distances between considered quantiles's orders;
#' if 'free", a specific correlation parameter is assumed for each multivariate responses.
#' @param RE_ind if TRUE, the random effects are assumed to be independent between different quantile.
#' Otherwise (FALSE by default), correlation between quantile (markers) is also caught through common covariance matrix of random effects.
#' @param n.chains the number of parallel chains for the model; default is 1.
#' @param n.iter integer specifying the total number of iterations; default is 10000
#' @param n.burnin integer specifying how many of n.iter to discard as burn-in ; default is 5000
#' @param n.thin integer specifying the thinning of the chains; default is 1
#' @param n.adapt integer specifying the number of iterations to use for adaptation; default is NULL
#' @param precision variance by default for vague prior distribution
#' @param save_jagsUI If TRUE (by default), the output of jagsUI package is return by the function
#' @param parallel see jagsUI::jags() function
#'
#'
#' @return A \code{BQt} object is a list with the following elements:
#' \describe{
#' \item{\code{mean}}{list of posterior mean for each parameter}
#' \item{\code{median}}{list of posterior median for each parameter}
#' \item{\code{modes}}{list of posterior mode for each parameter}
#' \item{\code{StErr}}{list of standard error for each parameter}
#' \item{\code{StDev}}{list of standard deviation for each parameter}
#' \item{\code{ICs}}{list of the credibility interval at 0.95 for each parameters excepted for covariance parameters in covariance matrix of random effects. Otherwise, use save_jagsUI=TRUE to have the associated quantiles.}
#' \item{\code{data}}{data included in argument}
#' \item{\code{sims.list}}{list of the MCMC chains of the parameters and random effects}
#' \item{\code{control}}{list of arguments giving details about the estimation}
#' \item{\code{random_effect}}{list for each quantile including both posterior mean and posterior standard deviation of subject-specific random effects}
#' \item{\code{out_jagsUI}}{only if \code{save_jagsUI=TRUE} in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standart deviation for each parameter and each random effect.
#' Moreover, this list also returns the MCMC draws, the Gelman and Rubin diagnostics (see output of jagsUI objects)}
#' }
#
#' @author Antoine Barbieri
#'
#' @import lqmm jagsUI
#'
#' @references Lea Petrella and Valentina Raponi (2019).
#' \emph{Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress}.
#' Journal of Multivariate Analysis, 173:70-84. doi: 10.1016/j.jmva.2019.02.008.
#'
#' @references Elisabeth Waldmann and Thomas Kneib (2015).
#' \emph{Bayesian bivariate quantile regression}.
#' Statistical Modelling, 15(4):326-344. doi: 10.1177/1471082X14551247.
#'
#' @export
#'
#' @examples
#'
#' \dontrun{
#' #---- Orthodont data from lqmm package
#' data("aids", package = "joineR")
#'
#' #---- Fit regression model for the first quartile
#' BQt_mQr <- mlqmm(formFixed = CD4 ~ obstime,
#' formRandom = ~ obstime,
#' formGroup = ~ id,
#' data = aids,
#' tau = c(0.25,0.5,0.75),
#' n.iter = 1000,
#' n.burnin = 500)
#'
#' #---- Get the estimated coefficients (posterior means)
#' BQt_mQr$mean
#'
#' #---- Summary of output
#' summary(BQt_mQr)
#'
#' #---- Traces of somes parameters
#' traceplot(x = BQt_mQr$out_jagsUI,
#' parameters = c("beta", "sigma", "rho"))
#' }
mlqmm <- function(formFixed,
formRandom,
formGroup,
data,
tau,
corr_structure = "middle",
RE_ind = FALSE,
n.chains = 3,
n.iter = 10000,
n.burnin = 5000,
n.thin = 1,
n.adapt = NULL,
precision = 10,
save_jagsUI = TRUE,
parallel = FALSE){
# Stopping condition
if(prod(tau<1 & tau>0)!=1)
stop("'Tau' have to be a numerical vector with elements included between 0 and 1.\n")
if(length(tau)>3)
stop("'Tau' have to be a numerical vector with length lower than 4.\n")
if(sum(duplicated(tau))>0)
stop("'Tau' have to be a numerical vector with no duplicated quantiles.\n")
if(RE_ind && length(tau)==2){
cat("Until now, all random effects are assumed dependant when considering only two quantiles.\n")
RE_ind <- FALSE
}
if(RE_ind && corr_structure=="none"){
cat("WARNING: There is no correlation structure between quantiles in the specified model.\n")
}
#-- data management
tau <- sort(tau)
data_long <- data[unique(c(all.vars(formGroup),all.vars(formFixed),all.vars(formRandom)))]
y <- data_long[all.vars(formFixed)][, 1]
mfX <- model.frame(formFixed, data = data_long)
X <- model.matrix(formFixed, mfX)
mfU <- model.frame(formRandom, data = data_long)
U <- model.matrix(formRandom, mfU)
ncU = ncol(U)
id <- as.integer(data_long[all.vars(formGroup)][,1])
if(!("id" %in% colnames(data_long)))
data_long <- cbind(data_long, id = id)
offset <- as.vector(c(1, 1 + cumsum(tapply(id, id, length))))
I <- length(unique(id))
Q <- length(tau)
if(Q==2 & corr_structure=="middle")
corr_structure = "free"
# use lqmm function to initiated values
cat("Initiation of parameter values using lqmm package. \n")
tmp_model <- lqmm::lqmm(fixed = formFixed,
random = formRandom,
group = id,
tau = tau,
data = data_long)
# prior beta parameters
priorMean.beta <- t(coef(tmp_model))
priorTau.beta <- diag(rep(1/10,length(priorMean.beta[1, ])))
bis <- matrix(unlist(lqmm::ranef(tmp_model)), ncol = Q*ncU, byrow = F)
bis[abs(bis)<.0001] <- 0
init_sigma <- rep(1, Q)
for(qq in 1:Q){
init_sigma[qq] <- tmp_model[[qq]]$scale
}
initial.values <- list(b = bis,
beta = priorMean.beta,
sigma = init_sigma)
# list of data jags
jags.data <- list(y = matrix(rep(y,Q), ncol = Q, byrow = F),
X = X,
U = U,
tau = tau,
ncX = ncol(X),
ncU = ncol(U),
I = I,
Q = Q,
offset = offset,
priorMean.beta = priorMean.beta,
priorTau.beta = priorTau.beta,
priorA.sigma = 1/precision,
priorB.sigma = 1/precision
)
if(RE_ind){
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncU)),
priorK.Sigma2 = ncU,
mu0 = rep(0, ncU)
)
)
}else{
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncU*Q)),
priorK.Sigma2 = ncU*Q,
mu0 = rep(0, ncU*Q)
)
)
}
initial.values$prec.Sigma2 <- diag(1/unlist(lqmm::VarCorr(tmp_model)))
initial.values$prec.Sigma2[initial.values$prec.Sigma2 > 100] <- 100
# manage the correlation between quantile
if(corr_structure == "free"){
if(Q==3){
initial.values$rho12 <- 0.9
initial.values$rho13 <- 0.9
initial.values$rho23 <- 0.9
}else{
# Q=2
initial.values$rho <- 0.9
}
}
if(corr_structure == "middle"){
jags.data$d12 <- tau[2]-tau[1]
jags.data$d13 <- tau[3]-tau[1]
jags.data$d23 <- tau[3]-tau[2]
}
model <- switch(paste(corr_structure, Q, RE_ind, sep = "/"),
`free/3/FALSE` = jags_3mlqmm_f,
`middle/3/FALSE` = jags_3mlqmm_m,
`none/3/FALSE` = jags_3mlqmm_n,
`free/2/FALSE` = jags_2mlqmm_f,
`middle/2/FALSE` = jags_2mlqmm_f,
`none/2/FALSE` = jags_mlqmm_n,
`free/3/TRUE` = jags_3mlqmm_f_b,
`middle/3/TRUE` = jags_3mlqmm_m_b,
`none/3/TRUE` = jags_3mlqmm_n_b
)
# parameters to save in the sampling step
if(corr_structure == "free"){
if(Q==3){
parms_to_save <- c("beta", "sigma", "rho12", "rho13", "rho23")
}else{
# Q=2
parms_to_save <- c("beta", "sigma", "rho")
}
}
if(corr_structure == "middle"){
jags.data$d12 <- tau[2]-tau[1]
jags.data$d13 <- tau[3]-tau[1]
jags.data$d23 <- tau[3]-tau[2]
parms_to_save <- c("beta", "sigma", "rho")
}
if(corr_structure == "none")
parms_to_save <- c("beta", "sigma")
if(RE_ind && Q==3){
parms_to_save <- c(parms_to_save, "b1", "b2", "b3", "covariance.b1", "covariance.b2", "covariance.b3")
}else{
parms_to_save <- c(parms_to_save, "b", "covariance.b")
}
#---- write jags model in txt from R function
working.directory = getwd()
write.model.jags(model = model,
name_model = "jags_mlqmm",
intitled = file.path(working.directory, "JagsModel.txt"),
Data = jags.data)
#---- use JAGS sampler
# if (!require("rjags"))
# stop("'rjags' is required.\n")
if(n.chains==3)
inits <- list(initial.values,
initial.values,
initial.values)
if(n.chains==2)
inits <- list(initial.values,
initial.values)
if(n.chains==1)
inits <- initial.values
# using jagsUI
out_jags = jagsUI::jags(data = jags.data,
parameters.to.save = parms_to_save,
model.file = "JagsModel.txt",
inits = inits,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
DIC = F)
file.remove(file.path(working.directory, "JagsModel.txt"))
#---- output building
#-- MCMClist management
#- arguments
out <- list(data = data)
out$control <- list(formFixed,
formRandom,
formGroup,
tau = tau,
corr_structure = corr_structure,
RE_ind = RE_ind,
call_function = "mlqmm",
I = I)
#- other outputs
# sims.list output
out$sims.list <- out_jags$sims.list
if(!is.null(out$sims.list$out))
out$sims.list$out <- NULL
if(!RE_ind){
out$sims.list$b <- NULL
}else{
out$sims.list$b1 <- out$sims.list$b2 <- out$sims.list$b3 <- NULL
}
# random effect output
random_effect <- vector("list", Q)
if(Q==3){
names(random_effect) <- c(paste("tau", 100*tau[1], sep=""),
paste("tau", 100*tau[2], sep=""),
paste("tau", 100*tau[3], sep=""))
}else{
names(random_effect) <- c(paste("tau", 100*tau[1], sep=""),
paste("tau", 100*tau[2], sep=""))
}
if(!RE_ind){
for(q in 1:Q){
random_effect[[q]] <- list(postMeans = out_jags$mean$b[, ((q-1)*ncU+1):(q*ncU)],
postSd = out_jags$sd$b[, ((q-1)*ncU+1):(q*ncU)])
colnames(random_effect[[q]]$postMeans) <- colnames(U)
colnames(random_effect[[q]]$postSd) <- colnames(U)
}
}else{
random_effect[[1]] <- list(postMeans = out_jags$mean$b1, postSd = out_jags$sd$b1)
random_effect[[2]] <- list(postMeans = out_jags$mean$b2, postSd = out_jags$sd$b2)
random_effect[[3]] <- list(postMeans = out_jags$mean$b3, postSd = out_jags$sd$b3)
colnames(random_effect[[1]]$postMeans) <-
colnames(random_effect[[2]]$postMeans) <-
colnames(random_effect[[3]]$postMeans) <- colnames(U)
colnames(random_effect[[1]]$postSd) <-
colnames(random_effect[[2]]$postSd) <-
colnames(random_effect[[3]]$postSd) <- colnames(U)
}
out$random_effect <- random_effect
# median : Posterior median of parameters
out$median <- out_jags$q50
if(!RE_ind){
out$median$b <- NULL
}else{
out$median$b1 <- out$median$b2 <- out$median$b3 <- NULL
}
# mean : Posterior mean of parameters
out$mean <- out_jags$mean
if(!RE_ind){
out$mean$b <- NULL
}else{
out$mean$b1 <- out$mean$b2 <- out$mean$b3 <- NULL
}
# # if inverse in jags doesn't run
# sims.list$covariance.b <- array(NA, dim = dim(jags_res$sims.list$prec.Sigma2))
# for(i in 1:dim(jags_res$sims.list$prec.Sigma2)[1]){
# sims.list$covariance.b[i, , ] <- solve(jags_res$sims.list$prec.Sigma2[i, , ])
# }
# out$sims.list$covariance.b = covariance.b
# modes of parameters
out$modes <- lapply(out$sims.list, function(x) {
m <- function(x) {
d <- density(x, bw = "nrd", adjust = 3, n = 1000)
d$x[which.max(d$y)]
}
if (is.matrix(x))
as.array(apply(x, 2, m))
else{
if(is.array(x))
apply(x, c(2,3), m)
else m(x)
}
})
# standard error of parameters
out$StErr <- lapply(out$sims.list, function(x) {
f <- function(x) {
acf.x <- drop(acf(x, lag.max = 0.4 * length(x), plot = FALSE)$acf)[-1]
acf.x <- acf.x[seq_len(rle(acf.x > 0)$lengths[1])]
ess <- length(x)/(1 + 2 * sum(acf.x))
sqrt(var(x)/ess)
}
if (is.matrix(x))
as.array(apply(x, 2, f))
else{
if(is.array(x))
apply(x, c(2,3), f)
else f(x)
}
})
# standard deviation of parameters
out$StDev <- out_jags$sd
if(!RE_ind){
out$StDev$b <- NULL
}else{
out$StDev$b1 <- out$StDev$b2 <- out$StDev$b3 <- NULL
}
# Rhat : Gelman & Rubin diagnostic
out$Rhat <- out_jags$Rhat
if(!RE_ind){
out$Rhat$b <- NULL
}else{
out$Rhat$b1 <- out$Rhat$b2 <- out$Rhat$b3 <- NULL
}
# names
colnames(out$mean$beta) <-
colnames(out$median$beta) <-
colnames(out$modes$beta) <-
colnames(out$StErr$beta) <-
colnames(out$Rhat$beta) <-
colnames(out$StDev$beta) <- colnames(X)
rownames(out$mean$beta) <-
rownames(out$median$beta) <-
rownames(out$modes$beta) <-
rownames(out$StErr$beta) <-
rownames(out$Rhat$beta) <-
rownames(out$StDev$beta) <- paste("tau", as.character(tau*100), sep = "")
rownames(out$mean$sigma) <-
rownames(out$median$sigma) <-
rownames(out$modes$sigma) <-
rownames(out$StErr$sigma) <-
rownames(out$Rhat$sigma) <-
rownames(out$StDev$sigma) <- paste("tau", as.character(tau*100), sep = "")
if(RE_ind){
colnames(out$mean$covariance.b1) <-
rownames(out$mean$covariance.b1) <-
colnames(out$median$covariance.b1) <-
rownames(out$median$covariance.b1) <-
colnames(out$modes$covariance.b1) <-
rownames(out$modes$covariance.b1) <-
colnames(out$StErr$covariance.b1) <-
rownames(out$StErr$covariance.b1) <-
colnames(out$Rhat$covariance.b1) <-
rownames(out$Rhat$covariance.b1) <-
colnames(out$StDev$covariance.b1) <-
rownames(out$StDev$covariance.b1) <-
colnames(out$mean$covariance.b2) <-
rownames(out$mean$covariance.b2) <-
colnames(out$median$covariance.b2) <-
rownames(out$median$covariance.b2) <-
colnames(out$modes$covariance.b2) <-
rownames(out$modes$covariance.b2) <-
colnames(out$StErr$covariance.b2) <-
rownames(out$StErr$covariance.b2) <-
colnames(out$Rhat$covariance.b2) <-
rownames(out$Rhat$covariance.b2) <-
colnames(out$StDev$covariance.b2) <-
rownames(out$StDev$covariance.b2) <-
colnames(out$mean$covariance.b3) <-
rownames(out$mean$covariance.b3) <-
colnames(out$median$covariance.b3) <-
rownames(out$median$covariance.b3) <-
colnames(out$modes$covariance.b3) <-
rownames(out$modes$covariance.b3) <-
colnames(out$StErr$covariance.b3) <-
rownames(out$StErr$covariance.b3) <-
colnames(out$Rhat$covariance.b3) <-
rownames(out$Rhat$covariance.b3) <-
colnames(out$StDev$covariance.b3) <-
rownames(out$StDev$covariance.b3) <- colnames(U)
}else{
colnames(out$mean$covariance.b) <-
rownames(out$mean$covariance.b) <-
colnames(out$median$covariance.b) <-
rownames(out$median$covariance.b) <-
colnames(out$modes$covariance.b) <-
rownames(out$modes$covariance.b) <-
colnames(out$StErr$covariance.b) <-
rownames(out$StErr$covariance.b) <-
colnames(out$Rhat$covariance.b) <-
rownames(out$Rhat$covariance.b) <-
colnames(out$StDev$covariance.b) <-
rownames(out$StDev$covariance.b) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncU),
rep(colnames(U), Q),
sep = ".")
}
# credible intervalles
out$CIs$beta <- cbind(as.vector(t(out_jags$q2.5$beta)),
as.vector(t(out_jags$q97.5$beta)))
rownames(out$CIs$beta) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncol(X)),
rep(colnames(X), Q),
sep = ".")
out$CIs$sigma <- cbind(out_jags$q2.5$sigma,
out_jags$q97.5$sigma)
rownames(out$CIs$sigma) <- paste("tau", as.character(tau*100), sep = "")
if(corr_structure == "free"){
if(Q==3){
out$CIs$rho12 <- cbind(out_jags$q2.5$rho12,
out_jags$q97.5$rho12)
out$CIs$rho13 <- cbind(out_jags$q2.5$rho13,
out_jags$q97.5$rho13)
out$CIs$rho23 <- cbind(out_jags$q2.5$rho23,
out_jags$q97.5$rho23)
}else{
out$CIs$rho <- cbind(out_jags$q2.5$rho,
out_jags$q97.5$rho)
}
}
if(corr_structure == "middle"){
out$CIs$rho <- cbind(out_jags$q2.5$rho,
out_jags$q97.5$rho)
}
# only for diagonal elements of covariance matrix of random effects
if(RE_ind){
out$CIs$variances.b1 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b1)),
as.vector(diag(out_jags$q97.5$covariance.b1)))
out$CIs$variances.b2 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b2)),
as.vector(diag(out_jags$q97.5$covariance.b2)))
out$CIs$variances.b3 <- cbind(as.vector(diag(out_jags$q2.5$covariance.b3)),
as.vector(diag(out_jags$q97.5$covariance.b3)))
rownames(out$CIs$variances.b1) <- rownames(out$CIs$variances.b2) <- rownames(out$CIs$variances.b3) <- colnames(U)
}else{
out$CIs$variances.b <- cbind(as.vector(diag(out_jags$q2.5$covariance.b)),
as.vector(diag(out_jags$q97.5$covariance.b)))
rownames(out$CIs$variances.b) <- paste(rep(paste("tau", as.character(tau*100), sep = ""),
each = ncol(U)),
rep(colnames(U), Q),
sep = ".")
}
# lapply(out$CIs, setNames, nm = c("2.5%", "97.5%"))
if(!RE_ind){
if(corr_structure == "free"){
if(Q==3){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho12) <-
colnames(out$CIs$rho13) <-
colnames(out$CIs$rho23) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}else{
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
}
if(corr_structure == "middle"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
if(corr_structure == "none"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
}
}else{
if(corr_structure == "free"){
if(Q==3){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho12) <-
colnames(out$CIs$rho13) <-
colnames(out$CIs$rho23) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}else{# not implemented yet...
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-c("2.5%", "97.5%")
}
}
if(corr_structure == "middle"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$rho) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}
if(corr_structure == "none"){
colnames(out$CIs$beta) <-
colnames(out$CIs$sigma) <-
colnames(out$CIs$variances.b1) <-
colnames(out$CIs$variances.b2) <-
colnames(out$CIs$variances.b3) <- c("2.5%", "97.5%")
}
}
# save jags output if requires
if(save_jagsUI)
out$out_jagsUI <- out_jags
#---- End of the function defining the class and retruning the output
class(out) <- "BQt"
out
}
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