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R/meHBt.R
In saeHB.ME: Small Area Estimation with Measurement Error using Hierarchical Bayesian Method
Defines functions
meHBt
Documented in
meHBt
#' @title Small Area Estimation with Measurement Error using Hierarchical Bayesian Method under Student-t Distribution
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Normal Distribution when auxiliary variable is measured with error.
#' @param formula an object of class \code{\link[stats]{formula}} (or one that can be coerced to that class): a symbolic description of the model to be fitted. The variables included \code{formula} must have a length equal to the number of domains \code{m}. This formula can provide auxiliary variable either measured with error or combination between measured with \code{error} and \code{without error}. If the auxiliary variable are combination between \code{error} and \code{without error}, input the \code{error} variable first followed by \code{without error} variable.
#' @param vardir vector containing the \code{m} sampling variances of direct estimators for each domain. The values must be sorted as the \code{Y}.
#' @param var.x vector containing mean squared error of \code{X}. The values must be sorted as the \code{X}.
#' @param coef a vector contains prior initial value of Coefficient of Regression Model for fixed effect with default vector of \code{0} with the length of the number of regression coefficients.
#' @param var.coef a vector contains prior initial value of variance of Coefficient of Regression Model with default vector of \code{1} with the length of the number of regression coefficients.
#' @param tau.u prior initial value of inverse of Variance of area random effect with default \code{1}.
#' @param iter.update number of updates with default \code{3}.
#' @param iter.mcmc number of total iterations per chain with default \code{10000}.
#' @param thin thinning rate, must be a positive integer with default \code{2}.
#' @param burn.in number of iterations to discard at the beginning with default \code{2000}.
#' @param data the data frame.
#'
#' @return This function returns a list with the following objects:
#' \item{Est}{A vector with the values of Small Area mean Estimates using Hierarchical bayesian method }
#' \item{refVar}{Estimated random effect variances}
#' \item{coefficient}{A data frame with the estimated model coefficient}
#' \item{plot}{Trace, Dencity, Autocorrelation Function Plot of MCMC samples}
#'
#' @export meHBt
#'
#' @examples
#' ## Load dataset
#' data(dataTMEHB)
#'
#' \donttest{
#' ## Auxiliary variables only contains variable with error
#' example <- meHBt(Y~x1, vardir = "vardir",
#' var.x = c("v.x1"), iter.update = 3, iter.mcmc = 10000,
#' thin = 5, burn.in = 1000, data = dataTMEHB)
#'
#' ## Auxiliary variables contains variable with error and without error
#' example_mix <- meHBt(Y~x1+x2, vardir = "vardir",
#' var.x = c("v.x1"), iter.update = 3, iter.mcmc = 10000,
#' thin = 5, burn.in = 1000, data = dataTMEHB)
#' }
#' ## Create dataset with nonsampled area
#' dataTMEHBns <- dataTMEHB
#' dataTMEHBns[c(1,10,20,30),"Y"] <- NA
#'
#' ## For data with nonsampled area use dataTMEHBns
#'
meHBt <- function(formula, vardir, var.x, coef, var.coef,
iter.update=3, iter.mcmc=10000, thin = 2, tau.u = 1, burn.in =2000, data){
result <- list(Est = NA, refVar = NA, coefficient = NA,
plot=NA)
formuladata <- model.frame(formula, na.action = NULL, data)
n <- nrow(formuladata)
if (any(is.na(formuladata[,-1]))){
stop("Auxiliary Variables contains NA values.")
}
X <- model.matrix(formula, data)
p <- dim(X)[2]
if(!missing(var.coef)){
if (length(var.coef) != p) {
stop("length of vector var.coef does not match the number of regression coefficients, the length must be ",
p)
}
tau.b <- 1/var.coef
} else {
tau.b <- 1/rep(1, p)
}
if(!missing(coef)){
if (length(coef) != p) {
stop("length of vector coef does not match the number of regression coefficients, the length must be ",
p)
}
mu.b <- coef
} else {
mu.b <- rep(0, p)
}
if (iter.update < 3){
stop("the number of iteration updates at least 3 times")
}
tau.a = tau.tb = tau.ua = tau.ub = tau.aa = tau.ab = tau.ba = tau.bb = phi.aa = phi.ab = phi.ba = phi.bb = 1
c <- data[, var.x]
c <- as.data.frame(c)
n_c <- dim(c)[2]
if(ncol(c) == 1){
names(c) = var.x
}
psi <- data[, vardir]
if (!any(is.na(formuladata[,1]))){
formuladata <- model.frame(formula, na.action = na.omit, data)
X <- model.matrix(formula, data)
y <- formuladata[,1]
m <- length(y)
if(n_c < p-1){
for (iter in 1:iter.update) {
dat <- list(m = m, y = y, Xme=as.matrix(formuladata[,2:(n_c+1)]), x=as.matrix(formuladata[,(n_c+2):p]),
mu.b = mu.b, p = p, var.x = c, n_c = n_c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb) # names list of numbers
inits <- list(u = rep(0,m), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m) {
y[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,]) + sum(b[(n_c+2):p]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(n_c)){
em[i,j] ~ dnorm(Xme[i,j],te[i,j])
}
for(I in 1:(n_c)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(n_c)){
te[i,k] <- 1/var.x[i,k]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa,phi.ab)
phi.b ~ dgamma(phi.ba,phi.bb)
tau.a ~ dgamma(tau.aa,tau.ab)
tau.tb ~ dgamma(tau.ba,tau.bb)
tau.u ~ dgamma(tau.ua, tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start = burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
else{
for (iter in 1:iter.update) {
dat <- list(m = m, y = y, x = as.matrix(formuladata[,2:p]), mu.b = mu.b, p = p, var.x = c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb) # names list of numbers
inits <- list(u = rep(0,m), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m) {
y[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,])+u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(p-1)){
em[i,j] ~ dnorm(x[i,j],te[i,j])
}
for(I in 1:(p-1)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(p-1)){
te[i,k] <- 1/var.x[i,k]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa,phi.ab)
phi.b ~ dgamma(phi.ba,phi.bb)
tau.a ~ dgamma(tau.aa,tau.ab)
tau.tb ~ dgamma(tau.ba,tau.bb)
tau.u ~ dgamma(tau.ua, tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start = burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(p)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(p+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(p+2):(1+p+m),1:2]
Estimation=data.frame(mu)
colnames(Estimation)=c("mean","sd")
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+p+m),])
q_beta <- (Quantiles[2:(p+1),])
q_Estimation <- (Quantiles[(p+2):(p+1+m),])
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
} else{
formuladata <- as.data.frame(formuladata)
X <- model.matrix(formula, data)
y <- formuladata[,1]
m <- length(y)
formuladata$idx <- rep(1:m)
formuladata[,2+p] <- psi
formuladata <- cbind(formuladata, c)
data_sampled <- na.omit(formuladata)
psi_sampled <- data_sampled[, 2+p]
c_sampled <- as.data.frame(data_sampled[, var.x])
data_nonsampled <- formuladata[-data_sampled$idx,]
c_nonsampled <- as.data.frame(data_nonsampled[, var.x])
r <- data_nonsampled$idx
m1 <- nrow(data_sampled)
m2 <- nrow(data_nonsampled)
if(n_c < p-1){
for (iter in 1:iter.update) {
dat <- list(m1 = m1, m2 = m2, y_sampled = data_sampled[,1],
Xme_sampled = as.matrix(data_sampled[,2:(n_c+1)]), Xme_nonsampled = as.matrix(data_nonsampled[,2:(n_c+1)]),
x_sampled = as.matrix(data_sampled[,(n_c+2):p]), x_nonsampled = as.matrix(data_nonsampled[,(n_c+2):p]),
mu.b = mu.b, p = p, n_c = n_c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb, var.x = c_sampled,
var.x.T = c_nonsampled) # names list of numbers
inits <- list(u = rep(0,m1), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m1) {
y_sampled[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,]) + sum(b[(n_c+2):p]*x_sampled[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(n_c)){
em[i,j] ~ dnorm(Xme_sampled[i,j],te[i,j])
}
for(I in 1:(n_c)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(n_c)){
te[i,k] <- 1/var.x[i,k]
}
}
for(j in 1:m2){
y_nonsampled[j] ~ dt(mu.T[j], tau.T[j], phi.T[j])
mu.T[j]<- mu.b[1] + sum(kjk.T[j,]) + sum(mu.b[(n_c+2):p]*x_nonsampled[j,]) + v[j]
v[j]~dnorm(0,tau.u)
phi.T[j] ~ dgamma(phi.a, phi.b)
tau.T[j] ~ dgamma(tau.a, tau.tb)
for(J in 1:(n_c)){
em.T[j,J] ~ dnorm(Xme_nonsampled[j,J], te.T[j,J])
}
for(I in 1:(n_c)){
kjk.T[j,I] <- mu.b[I+1]*em.T[j,I]
}
for(G in 1:(n_c)){
te.T[j,G] <- 1/var.x.T[j,G]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa, phi.ab)
phi.b ~ dgamma(phi.ba, phi.bb)
tau.a ~ dgamma(tau.aa, tau.ab)
tau.tb ~ dgamma(tau.ba, tau.bb)
tau.u ~ dgamma(tau.ua,tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","mu.T","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start=burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
} else {
for (iter in 1:iter.update) {
dat <- list(m1 = m1, m2 = m2, y_sampled = data_sampled[,1],
x_sampled = as.matrix(data_sampled[,2:p]), x_nonsampled = as.matrix(data_nonsampled[,2:p]),
mu.b = mu.b, p = p,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb, var.x = c_sampled,
var.x.T = c_nonsampled) # names list of numbers
inits <- list(u = rep(0,m1), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m1) {
y_sampled[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,])+u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(p-1)){
em[i,j] ~ dnorm(x_sampled[i,j],te[i,j])
}
for(I in 1:(p-1)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(p-1)){
te[i,k] <- 1/var.x[i,k]
}
}
for(j in 1:m2){
y_nonsampled[j] ~ dt(mu.T[j], tau.T[j], phi.T[j])
mu.T[j]<- mu.b[1] + sum(kjk.T[j,])+v[j]
v[j]~dnorm(0,tau.u)
phi.T[j] ~ dgamma(phi.a, phi.b)
tau.T[j] ~ dgamma(tau.a, tau.tb)
for(J in 1:(p-1)){
em.T[j,J] ~ dnorm(x_nonsampled[j,J], te.T[j,J])
}
for(I in 1:(p-1)){
kjk.T[j,I] <- mu.b[I+1]*em.T[j,I]
}
for(G in 1:(p-1)){
te.T[j,G] <- 1/var.x.T[j,G]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa, phi.ab)
phi.b ~ dgamma(phi.ba, phi.bb)
tau.a ~ dgamma(tau.aa, tau.ab)
tau.tb ~ dgamma(tau.ba, tau.bb)
tau.u ~ dgamma(tau.ua,tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","mu.T","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start=burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(p)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(p+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var <- result_samps$statistics[1]
beta <- result_samps$statistics[2:(p+1),1:2]
rownames(beta) <- b.varnames
mu <- result_samps$statistics[(p+2):(1+p+m1),1:2]
mu.nonsampled <- result_samps$statistics[(2+p+m1):(1+p+m),1:2]
Estimation <- matrix(rep(0,m),nrow = m, ncol = 2)
Estimation[r,] <- mu.nonsampled
Estimation[-r,] <- mu
Estimation <- as.data.frame(Estimation)
colnames(Estimation) <- c("mean","sd")
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+p+m),])
q_beta <- (Quantiles[2:(p+1),])
q_mu <- (Quantiles[(p+2):(p+1+m1),])
q_mu.nonsampled <- (Quantiles[(2+p+m1):(1+p+m),])
q_Estimation <- matrix(0,m,5)
for (i in 1:5) {
q_Estimation[r,i] <- q_mu.nonsampled[,i]
q_Estimation[-r,i] <- q_mu[,i]
}
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
}
result$Est = cbind(Estimation, q_Estimation)
result$refVar = a.var
result$coefficient = beta
result$plot = list(graphics.off(),
par(mar=c(2,2,2,2)),
autocorr.plot(result_mcmc,col="brown2",lwd=2),
plot(result_mcmc,col="brown2",lwd=2))
on.exit(result)
return(result)
}
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Defines functions meHBt
Documented in meHBt
#' @title Small Area Estimation with Measurement Error using Hierarchical Bayesian Method under Student-t Distribution
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Normal Distribution when auxiliary variable is measured with error.
#' @param formula an object of class \code{\link[stats]{formula}} (or one that can be coerced to that class): a symbolic description of the model to be fitted. The variables included \code{formula} must have a length equal to the number of domains \code{m}. This formula can provide auxiliary variable either measured with error or combination between measured with \code{error} and \code{without error}. If the auxiliary variable are combination between \code{error} and \code{without error}, input the \code{error} variable first followed by \code{without error} variable.
#' @param vardir vector containing the \code{m} sampling variances of direct estimators for each domain. The values must be sorted as the \code{Y}.
#' @param var.x vector containing mean squared error of \code{X}. The values must be sorted as the \code{X}.
#' @param coef a vector contains prior initial value of Coefficient of Regression Model for fixed effect with default vector of \code{0} with the length of the number of regression coefficients.
#' @param var.coef a vector contains prior initial value of variance of Coefficient of Regression Model with default vector of \code{1} with the length of the number of regression coefficients.
#' @param tau.u prior initial value of inverse of Variance of area random effect with default \code{1}.
#' @param iter.update number of updates with default \code{3}.
#' @param iter.mcmc number of total iterations per chain with default \code{10000}.
#' @param thin thinning rate, must be a positive integer with default \code{2}.
#' @param burn.in number of iterations to discard at the beginning with default \code{2000}.
#' @param data the data frame.
#'
#' @return This function returns a list with the following objects:
#' \item{Est}{A vector with the values of Small Area mean Estimates using Hierarchical bayesian method }
#' \item{refVar}{Estimated random effect variances}
#' \item{coefficient}{A data frame with the estimated model coefficient}
#' \item{plot}{Trace, Dencity, Autocorrelation Function Plot of MCMC samples}
#'
#' @export meHBt
#'
#' @examples
#' ## Load dataset
#' data(dataTMEHB)
#'
#' \donttest{
#' ## Auxiliary variables only contains variable with error
#' example <- meHBt(Y~x1, vardir = "vardir",
#' var.x = c("v.x1"), iter.update = 3, iter.mcmc = 10000,
#' thin = 5, burn.in = 1000, data = dataTMEHB)
#'
#' ## Auxiliary variables contains variable with error and without error
#' example_mix <- meHBt(Y~x1+x2, vardir = "vardir",
#' var.x = c("v.x1"), iter.update = 3, iter.mcmc = 10000,
#' thin = 5, burn.in = 1000, data = dataTMEHB)
#' }
#' ## Create dataset with nonsampled area
#' dataTMEHBns <- dataTMEHB
#' dataTMEHBns[c(1,10,20,30),"Y"] <- NA
#'
#' ## For data with nonsampled area use dataTMEHBns
#'
meHBt <- function(formula, vardir, var.x, coef, var.coef,
iter.update=3, iter.mcmc=10000, thin = 2, tau.u = 1, burn.in =2000, data){
result <- list(Est = NA, refVar = NA, coefficient = NA,
plot=NA)
formuladata <- model.frame(formula, na.action = NULL, data)
n <- nrow(formuladata)
if (any(is.na(formuladata[,-1]))){
stop("Auxiliary Variables contains NA values.")
}
X <- model.matrix(formula, data)
p <- dim(X)[2]
if(!missing(var.coef)){
if (length(var.coef) != p) {
stop("length of vector var.coef does not match the number of regression coefficients, the length must be ",
p)
}
tau.b <- 1/var.coef
} else {
tau.b <- 1/rep(1, p)
}
if(!missing(coef)){
if (length(coef) != p) {
stop("length of vector coef does not match the number of regression coefficients, the length must be ",
p)
}
mu.b <- coef
} else {
mu.b <- rep(0, p)
}
if (iter.update < 3){
stop("the number of iteration updates at least 3 times")
}
tau.a = tau.tb = tau.ua = tau.ub = tau.aa = tau.ab = tau.ba = tau.bb = phi.aa = phi.ab = phi.ba = phi.bb = 1
c <- data[, var.x]
c <- as.data.frame(c)
n_c <- dim(c)[2]
if(ncol(c) == 1){
names(c) = var.x
}
psi <- data[, vardir]
if (!any(is.na(formuladata[,1]))){
formuladata <- model.frame(formula, na.action = na.omit, data)
X <- model.matrix(formula, data)
y <- formuladata[,1]
m <- length(y)
if(n_c < p-1){
for (iter in 1:iter.update) {
dat <- list(m = m, y = y, Xme=as.matrix(formuladata[,2:(n_c+1)]), x=as.matrix(formuladata[,(n_c+2):p]),
mu.b = mu.b, p = p, var.x = c, n_c = n_c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb) # names list of numbers
inits <- list(u = rep(0,m), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m) {
y[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,]) + sum(b[(n_c+2):p]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(n_c)){
em[i,j] ~ dnorm(Xme[i,j],te[i,j])
}
for(I in 1:(n_c)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(n_c)){
te[i,k] <- 1/var.x[i,k]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa,phi.ab)
phi.b ~ dgamma(phi.ba,phi.bb)
tau.a ~ dgamma(tau.aa,tau.ab)
tau.tb ~ dgamma(tau.ba,tau.bb)
tau.u ~ dgamma(tau.ua, tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start = burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
else{
for (iter in 1:iter.update) {
dat <- list(m = m, y = y, x = as.matrix(formuladata[,2:p]), mu.b = mu.b, p = p, var.x = c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb) # names list of numbers
inits <- list(u = rep(0,m), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m) {
y[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,])+u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(p-1)){
em[i,j] ~ dnorm(x[i,j],te[i,j])
}
for(I in 1:(p-1)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(p-1)){
te[i,k] <- 1/var.x[i,k]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa,phi.ab)
phi.b ~ dgamma(phi.ba,phi.bb)
tau.a ~ dgamma(tau.aa,tau.ab)
tau.tb ~ dgamma(tau.ba,tau.bb)
tau.u ~ dgamma(tau.ua, tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start = burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(p)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(p+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(p+2):(1+p+m),1:2]
Estimation=data.frame(mu)
colnames(Estimation)=c("mean","sd")
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+p+m),])
q_beta <- (Quantiles[2:(p+1),])
q_Estimation <- (Quantiles[(p+2):(p+1+m),])
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
} else{
formuladata <- as.data.frame(formuladata)
X <- model.matrix(formula, data)
y <- formuladata[,1]
m <- length(y)
formuladata$idx <- rep(1:m)
formuladata[,2+p] <- psi
formuladata <- cbind(formuladata, c)
data_sampled <- na.omit(formuladata)
psi_sampled <- data_sampled[, 2+p]
c_sampled <- as.data.frame(data_sampled[, var.x])
data_nonsampled <- formuladata[-data_sampled$idx,]
c_nonsampled <- as.data.frame(data_nonsampled[, var.x])
r <- data_nonsampled$idx
m1 <- nrow(data_sampled)
m2 <- nrow(data_nonsampled)
if(n_c < p-1){
for (iter in 1:iter.update) {
dat <- list(m1 = m1, m2 = m2, y_sampled = data_sampled[,1],
Xme_sampled = as.matrix(data_sampled[,2:(n_c+1)]), Xme_nonsampled = as.matrix(data_nonsampled[,2:(n_c+1)]),
x_sampled = as.matrix(data_sampled[,(n_c+2):p]), x_nonsampled = as.matrix(data_nonsampled[,(n_c+2):p]),
mu.b = mu.b, p = p, n_c = n_c,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb, var.x = c_sampled,
var.x.T = c_nonsampled) # names list of numbers
inits <- list(u = rep(0,m1), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m1) {
y_sampled[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,]) + sum(b[(n_c+2):p]*x_sampled[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(n_c)){
em[i,j] ~ dnorm(Xme_sampled[i,j],te[i,j])
}
for(I in 1:(n_c)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(n_c)){
te[i,k] <- 1/var.x[i,k]
}
}
for(j in 1:m2){
y_nonsampled[j] ~ dt(mu.T[j], tau.T[j], phi.T[j])
mu.T[j]<- mu.b[1] + sum(kjk.T[j,]) + sum(mu.b[(n_c+2):p]*x_nonsampled[j,]) + v[j]
v[j]~dnorm(0,tau.u)
phi.T[j] ~ dgamma(phi.a, phi.b)
tau.T[j] ~ dgamma(tau.a, tau.tb)
for(J in 1:(n_c)){
em.T[j,J] ~ dnorm(Xme_nonsampled[j,J], te.T[j,J])
}
for(I in 1:(n_c)){
kjk.T[j,I] <- mu.b[I+1]*em.T[j,I]
}
for(G in 1:(n_c)){
te.T[j,G] <- 1/var.x.T[j,G]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa, phi.ab)
phi.b ~ dgamma(phi.ba, phi.bb)
tau.a ~ dgamma(tau.aa, tau.ab)
tau.tb ~ dgamma(tau.ba, tau.bb)
tau.u ~ dgamma(tau.ua,tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","mu.T","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start=burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
} else {
for (iter in 1:iter.update) {
dat <- list(m1 = m1, m2 = m2, y_sampled = data_sampled[,1],
x_sampled = as.matrix(data_sampled[,2:p]), x_nonsampled = as.matrix(data_nonsampled[,2:p]),
mu.b = mu.b, p = p,
tau.b = tau.b,
tau.ua = tau.ua, tau.ub = tau.ub, tau.aa = tau.aa,
tau.ab = tau.ab, tau.ba = tau.ba, tau.bb = tau.bb,
phi.aa = phi.aa, phi.ab = phi.ab, phi.ba = phi.ba,
phi.bb = phi.bb, var.x = c_sampled,
var.x.T = c_nonsampled) # names list of numbers
inits <- list(u = rep(0,m1), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:m1) {
y_sampled[i] ~ dt(mu[i],tau[i],phi[i])
mu[i] <- b[1] + sum(kjk[i,])+u[i]
u[i] ~ dnorm(0,tau.u)
phi[i] ~ dgamma(phi.a, phi.b)
tau[i] ~ dgamma(tau.a, tau.tb)
for (j in 1:(p-1)){
em[i,j] ~ dnorm(x_sampled[i,j],te[i,j])
}
for(I in 1:(p-1)){
kjk[i,I] <- b[I+1]*em[i,I]
}
for (k in 1:(p-1)){
te[i,k] <- 1/var.x[i,k]
}
}
for(j in 1:m2){
y_nonsampled[j] ~ dt(mu.T[j], tau.T[j], phi.T[j])
mu.T[j]<- mu.b[1] + sum(kjk.T[j,])+v[j]
v[j]~dnorm(0,tau.u)
phi.T[j] ~ dgamma(phi.a, phi.b)
tau.T[j] ~ dgamma(tau.a, tau.tb)
for(J in 1:(p-1)){
em.T[j,J] ~ dnorm(x_nonsampled[j,J], te.T[j,J])
}
for(I in 1:(p-1)){
kjk.T[j,I] <- mu.b[I+1]*em.T[j,I]
}
for(G in 1:(p-1)){
te.T[j,G] <- 1/var.x.T[j,G]
}
}
for (l in 1:p){
b[l]~dnorm(mu.b[l], tau.b[l])
}
phi.a ~ dgamma(phi.aa, phi.ab)
phi.b ~ dgamma(phi.ba, phi.bb)
tau.a ~ dgamma(tau.aa, tau.ab)
tau.tb ~ dgamma(tau.ba, tau.bb)
tau.u ~ dgamma(tau.ua,tau.ub)
a.var <- 1 / tau.u
}", file="TME.txt")
jags.m <- jags.model( file = "TME.txt", data=dat, inits=inits, n.chains=1, n.adapt=500)
file.remove("TME.txt")
params <- c("mu","mu.T","a.var","b", "phi.a","phi.b", "tau.a","tau.tb","tau.u")
samps1 <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps11 <- window(samps1, start=burn.in + 1, end=iter.mcmc)
result_samps=summary(samps11)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(p+1),1:2]
for (i in 1:p){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
phi.aa = result_samps$statistics[2+p+m,1]^2/result_samps$statistics[2+p+m,2]^2
phi.ab = result_samps$statistics[2+p+m,1]/result_samps$statistics[2+p+m,2]^2
phi.ba = result_samps$statistics[(m + p + 3),1]^2/result_samps$statistics[(m + p + 3),2]^2
phi.bb = result_samps$statistics[(m + p + 3),1]/result_samps$statistics[(m + p + 3), 2]^2
tau.aa = result_samps$statistics[(4 + p + m),1]^2/result_samps$statistics[(4 + p + m),2]^2
tau.ab = result_samps$statistics[(4 + p + m),1]/result_samps$statistics[(4 + p + m), 2]^2
tau.ba = result_samps$statistics[(m + p + 5),1]^2/result_samps$statistics[(m + p + 5),2]^2
tau.bb = result_samps$statistics[(m + p + 5),1]/result_samps$statistics[(m + p + 5), 2]^2
tau.ua = result_samps$statistics[(6 + p + m),1]^2/result_samps$statistics[(6 + p + m),2]^2
tau.ub = result_samps$statistics[(6 + p + m),1]/result_samps$statistics[(6 + p + m), 2]^2
}
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(p)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(p+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var <- result_samps$statistics[1]
beta <- result_samps$statistics[2:(p+1),1:2]
rownames(beta) <- b.varnames
mu <- result_samps$statistics[(p+2):(1+p+m1),1:2]
mu.nonsampled <- result_samps$statistics[(2+p+m1):(1+p+m),1:2]
Estimation <- matrix(rep(0,m),nrow = m, ncol = 2)
Estimation[r,] <- mu.nonsampled
Estimation[-r,] <- mu
Estimation <- as.data.frame(Estimation)
colnames(Estimation) <- c("mean","sd")
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+p+m),])
q_beta <- (Quantiles[2:(p+1),])
q_mu <- (Quantiles[(p+2):(p+1+m1),])
q_mu.nonsampled <- (Quantiles[(2+p+m1):(1+p+m),])
q_Estimation <- matrix(0,m,5)
for (i in 1:5) {
q_Estimation[r,i] <- q_mu.nonsampled[,i]
q_Estimation[-r,i] <- q_mu[,i]
}
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
}
result$Est = cbind(Estimation, q_Estimation)
result$refVar = a.var
result$coefficient = beta
result$plot = list(graphics.off(),
par(mar=c(2,2,2,2)),
autocorr.plot(result_mcmc,col="brown2",lwd=2),
plot(result_mcmc,col="brown2",lwd=2))
on.exit(result)
return(result)
}
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