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R/Lognormal.R
In saeHB: Small Area Estimation using Hierarchical Bayesian Method
Defines functions
Lognormal
Documented in
Lognormal
#' @title Small Area Estimation using Hierarchical Bayesian under Lognormal Distribution
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Lognormal Distribution. The range of data is \eqn{(y > 0}
#' @param formula Formula that describe the fitted model
#' @param iter.update Number of updates with default \code{3}
#' @param iter.mcmc Number of total iterations per chain with default \code{10000}
#' @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 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 tau.u Prior initial value of inverse of Variance of area random effect with default \code{1}
#' @param data The data frame
#'
#' @return This function returns a list of 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 dataframe with the estimated model coefficient}
#' \item{plot}{Trace, Dencity, Autocorrelation Function Plot of MCMC samples}
#'
#' @export Lognormal
#'
#' @examples
#' \donttest{
#' ##Data Generation
#' set.seed(123)
#' m=30
#' x1=runif(m,0,1)
#' x2=runif(m,1,2)
#' x3=runif(m,2,3)
#' b0=b1=b2=b3=0.5
#' u=rnorm(m,0,1)
#' mu=b0 + b1*x1+b2*x2+b3*x3+u
#' sig=1
#' y=rlnorm(m,mu,sig)
#' E=exp(mu+1/2*sig^2)
#' vardir=exp(2*mu+sig^2)*(exp(sig^2)-1)
#' dataLognormal=as.data.frame(cbind(y,x1,x2,x3,vardir))
#' dataLognormalNs=dataLognormal
#' dataLognormalNs$y[c(3,14,22,29,30)] <- NA
#' dataLognormalNs$vardir[c(3,14,22,29,30)] <- NA
#'
#'
#' ##Compute Fitted Model
#' ##y ~ x1 +x2 +x3
#'
#'
#' ## For data without any nonsampled area
#'
#' formula = y ~ x1 +x2 +x3
#' v = c(1,1,1,1)
#' c= c(0,0,0,0)
#'
#'
#' ## Using parameter coef and var.coef
#' saeHBLognormal <- Lognormal(formula,coef=c,var.coef=v,iter.update=10,data=dataLognormal)
#'
#' saeHBLognormal$Est #Small Area mean Estimates
#' saeHBLognormal$refVar #Random effect variance
#' saeHBLognormal$coefficient #coefficient
#' #Load Library 'coda' to execute the plot
#' #autocorr.plot(saeHBLognormal$plot[[3]]) is used to generate ACF Plot
#' #plot(saeHBLognormal$plot[[3]]) is used to generate Density and trace plot
#'
#' ## Do not using parameter coef and var.coef
#' saeHBLognormal <- Lognormal(formula,data=dataLognormal)
#'
#'
#' ## For data with nonsampled area use dataLognormalNs
#'
#' }
#'
Lognormal <- function(formula,iter.update=3, iter.mcmc=10000, coef, var.coef, thin = 2, burn.in =2000, tau.u = 1, data){
result <- list(Est = NA, refVar = NA, coefficient = NA,
plot=NA)
formuladata <- model.frame(formula,data,na.action=NULL)
if (any(is.na(formuladata[,-1])))
stop("Auxiliary Variables contains NA values.")
auxVar <- as.matrix(formuladata[,-1])
nvar <- ncol(auxVar) + 1
#formuladata <- data.frame(formuladata, n.samp = data[,n.samp])
if (!missing(var.coef)){
if( length(var.coef) != nvar ){
stop("length of vector var.coef does not match the number of regression coefficients, the length must be ",nvar)
}
tau.b.value = 1/var.coef
} else {
tau.b.value = 1/rep(1,nvar)
}
if (!missing(coef)){
if( length(coef) != nvar ){
stop("length of vector coef does not match the number of regression coefficients, the length must be ",nvar)
}
mu.b.value = coef
} else {
mu.b.value = rep(0,nvar)
}
if (iter.update < 3){
stop("the number of iteration updates at least 3 times")
}
#Fungsi Tersampel
if (!any(is.na(formuladata[,1]))){
formuladata <- as.matrix(na.omit(formuladata))
if (any(formuladata[,1]<=0)){
stop("response variable must be " ,formula[2], " > 0")
}
x <- model.matrix(formula,data = as.data.frame(formuladata))
n <- nrow(formuladata)
mu.b = mu.b.value
tau.b = tau.b.value
tau.aa=tau.ab=tau.ba=tau.bb=1
tau.ua=tau.ub=1
a.var=1
for (i in 1:iter.update){
dat <- list("n"= n, "nvar"= nvar, "y" = formuladata[,1], "x"=as.matrix(x[,-1]),
"mu.b"=mu.b, "tau.b"=tau.b,"tau.aa"=tau.aa,"tau.ab"=tau.ab,"tau.ba"=tau.ba,"tau.bb"=tau.bb,"tau.ua"=tau.ua,"tau.ub"=tau.ub)
inits <- list(u = rep(0,n),b = mu.b, tau.u =tau.u)
cat("model {
for (i in 1:n) {
y[i] ~ dlnorm(mu.ln[i],tau[i])
mu.ln[i] <- b[1] + sum(b[2:nvar]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
mu[i] <- exp(mu.ln[i])
tau[i] ~ dgamma(tau.a, tau.tb)
}
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
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="lognormal.txt")
jags.m <- jags.model(file = "lognormal.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("lognormal.txt")
params <- c("mu","a.var","b", "tau.u", "tau.a", "tau.tb")
samps <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps1 <- window(samps, start=burn.in+1, end=iter.mcmc)
result_samps=summary(samps1)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.aa = result_samps$statistics[(n+nvar+2),1]^2/result_samps$statistics[(n+nvar+2),2]^2
tau.ab = result_samps$statistics[(n+nvar+2),1]/result_samps$statistics[(n+nvar+2),2]^2
tau.ba = result_samps$statistics[(n+nvar+3),1]^2/result_samps$statistics[(n+nvar+3),2]^2
tau.bb = result_samps$statistics[(n+nvar+3),1]/result_samps$statistics[(n+nvar+3),2]^2
tau.ua = result_samps$statistics[(4+nvar+n),1]^2/result_samps$statistics[(4+nvar+n),2]^2
tau.ub = result_samps$statistics[(4+nvar+n),1]/result_samps$statistics[(4+nvar+n),2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(nvar+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+2):(1+nvar+n),1:2]
Estimation=data.frame(mu)
Quantiles <- as.data.frame(result_samps$quantiles[1:(3+nvar+n),])
q_mu <- Quantiles[(nvar+2):(nvar+1+n),]
q_beta <- (Quantiles[2:(nvar+1),])
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
Estimation <- data.frame(Estimation,q_mu)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
} else {
formuladata <- as.data.frame(formuladata)
x <- as.matrix(formuladata[,2:nvar])
n <- nrow(formuladata)
mu.b =mu.b.value
tau.b = tau.b.value
tau.aa=tau.ab=tau.ba=tau.bb=1
tau.ua=tau.ub=1
a.var=1
formuladata$idx <- rep(1:n)
data_sampled <- na.omit(formuladata)
if (any(data_sampled[,1]<=0)){
stop("response variable must be " ,formula[2], " > 0")}
data_nonsampled <- formuladata[-data_sampled$idx,]
r=data_nonsampled$idx
n1=nrow(data_sampled)
n2=nrow(data_nonsampled)
for (i in 1:iter.update){
dat <- list("n1"= n1, "n2"=n2,"nvar"=nvar, "y_sampled" = data_sampled[,1],
"x_sampled"=as.matrix(data_sampled[,2:nvar]),
"x_nonsampled"=as.matrix(data_nonsampled[,2:nvar]),
"mu.b"=mu.b,"tau.b"=tau.b,
"tau.aa"=tau.aa,"tau.ab"=tau.ab,"tau.ba"=tau.ba,"tau.bb"=tau.bb,
"tau.ua"=tau.ua,"tau.ub"=tau.ub)
inits <- list(u = rep(0,n1), v = rep(0,n2), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:n1) {
y_sampled[i] ~ dlnorm(mu.ln[i],tau[i])
mu.ln[i] <- b[1] + sum(b[2:nvar]*x_sampled[i,]) + u[i]
u[i] ~dnorm(0,tau.u)
mu[i] <- exp(mu.ln[i])
tau[i] ~ dgamma(tau.a, tau.tb)
}
for (j in 1:n2) {
v[j] ~dnorm(0,tau.u)
y_nonsampled[j] ~ dlnorm(mu.ln.nonsampled[j],tau.nonsampled[j])
mu.ln.nonsampled[j] <- mu.b[1] + sum(mu.b[2:nvar]*x_nonsampled[j,]) +v[j]
mu.nonsampled[j] <- exp(mu.ln.nonsampled[j])
tau.nonsampled[j] ~ dgamma(tau.a, tau.tb)
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
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="LogNormal.txt")
jags.m <- jags.model( file = "LogNormal.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("LogNormal.txt")
params <- c("mu","mu.nonsampled","a.var","b","tau.a","tau.tb","tau.u")
samps <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps1 <- window(samps, start=burn.in+1, end=iter.mcmc)
result_samps=summary(samps1)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.aa = result_samps$statistics[(n+nvar+2),1]^2/result_samps$statistics[(n+nvar+2),2]^2
tau.ab = result_samps$statistics[(n+nvar+2),1]/result_samps$statistics[(n+nvar+2),2]^2
tau.ba = result_samps$statistics[(n+nvar+3),1]^2/result_samps$statistics[(n+nvar+3),2]^2
tau.bb = result_samps$statistics[(n+nvar+3),1]/result_samps$statistics[(n+nvar+3),2]^2
tau.ua = result_samps$statistics[(4+nvar+n),1]^2/result_samps$statistics[(4+nvar+n),2]^2
tau.ub = result_samps$statistics[(4+nvar+n),1]/result_samps$statistics[(4+nvar+n),2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
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:(nvar+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+2):(1+nvar+n1),1:2]
mu.nonsampled =result_samps$statistics[(2+nvar+n1):(1+nvar+n),1:2]
Estimation=matrix(rep(0,n),n,2)
Estimation[r,]=mu.nonsampled
Estimation[-r,]=mu
Estimation = as.data.frame(Estimation)
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+nvar+n),])
q_beta <- (Quantiles[2:(nvar+1),])
q_mu <- (Quantiles[(nvar+2):(nvar+1+n1),])
q_mu.nonsampled <- (Quantiles[(2+nvar+n1):(1+nvar+n),])
q_Estimation <- matrix(0,n,5)
for (i in 1:5){
q_Estimation[r,i] <- q_mu.nonsampled[,i]
q_Estimation[-r,i] <- q_mu[,i]
}
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
Estimation <- data.frame(Estimation,q_Estimation)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
}
result$Est = 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))
return(result)
}
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Defines functions Lognormal
Documented in Lognormal
#' @title Small Area Estimation using Hierarchical Bayesian under Lognormal Distribution
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Lognormal Distribution. The range of data is \eqn{(y > 0}
#' @param formula Formula that describe the fitted model
#' @param iter.update Number of updates with default \code{3}
#' @param iter.mcmc Number of total iterations per chain with default \code{10000}
#' @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 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 tau.u Prior initial value of inverse of Variance of area random effect with default \code{1}
#' @param data The data frame
#'
#' @return This function returns a list of 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 dataframe with the estimated model coefficient}
#' \item{plot}{Trace, Dencity, Autocorrelation Function Plot of MCMC samples}
#'
#' @export Lognormal
#'
#' @examples
#' \donttest{
#' ##Data Generation
#' set.seed(123)
#' m=30
#' x1=runif(m,0,1)
#' x2=runif(m,1,2)
#' x3=runif(m,2,3)
#' b0=b1=b2=b3=0.5
#' u=rnorm(m,0,1)
#' mu=b0 + b1*x1+b2*x2+b3*x3+u
#' sig=1
#' y=rlnorm(m,mu,sig)
#' E=exp(mu+1/2*sig^2)
#' vardir=exp(2*mu+sig^2)*(exp(sig^2)-1)
#' dataLognormal=as.data.frame(cbind(y,x1,x2,x3,vardir))
#' dataLognormalNs=dataLognormal
#' dataLognormalNs$y[c(3,14,22,29,30)] <- NA
#' dataLognormalNs$vardir[c(3,14,22,29,30)] <- NA
#'
#'
#' ##Compute Fitted Model
#' ##y ~ x1 +x2 +x3
#'
#'
#' ## For data without any nonsampled area
#'
#' formula = y ~ x1 +x2 +x3
#' v = c(1,1,1,1)
#' c= c(0,0,0,0)
#'
#'
#' ## Using parameter coef and var.coef
#' saeHBLognormal <- Lognormal(formula,coef=c,var.coef=v,iter.update=10,data=dataLognormal)
#'
#' saeHBLognormal$Est #Small Area mean Estimates
#' saeHBLognormal$refVar #Random effect variance
#' saeHBLognormal$coefficient #coefficient
#' #Load Library 'coda' to execute the plot
#' #autocorr.plot(saeHBLognormal$plot[[3]]) is used to generate ACF Plot
#' #plot(saeHBLognormal$plot[[3]]) is used to generate Density and trace plot
#'
#' ## Do not using parameter coef and var.coef
#' saeHBLognormal <- Lognormal(formula,data=dataLognormal)
#'
#'
#' ## For data with nonsampled area use dataLognormalNs
#'
#' }
#'
Lognormal <- function(formula,iter.update=3, iter.mcmc=10000, coef, var.coef, thin = 2, burn.in =2000, tau.u = 1, data){
result <- list(Est = NA, refVar = NA, coefficient = NA,
plot=NA)
formuladata <- model.frame(formula,data,na.action=NULL)
if (any(is.na(formuladata[,-1])))
stop("Auxiliary Variables contains NA values.")
auxVar <- as.matrix(formuladata[,-1])
nvar <- ncol(auxVar) + 1
#formuladata <- data.frame(formuladata, n.samp = data[,n.samp])
if (!missing(var.coef)){
if( length(var.coef) != nvar ){
stop("length of vector var.coef does not match the number of regression coefficients, the length must be ",nvar)
}
tau.b.value = 1/var.coef
} else {
tau.b.value = 1/rep(1,nvar)
}
if (!missing(coef)){
if( length(coef) != nvar ){
stop("length of vector coef does not match the number of regression coefficients, the length must be ",nvar)
}
mu.b.value = coef
} else {
mu.b.value = rep(0,nvar)
}
if (iter.update < 3){
stop("the number of iteration updates at least 3 times")
}
#Fungsi Tersampel
if (!any(is.na(formuladata[,1]))){
formuladata <- as.matrix(na.omit(formuladata))
if (any(formuladata[,1]<=0)){
stop("response variable must be " ,formula[2], " > 0")
}
x <- model.matrix(formula,data = as.data.frame(formuladata))
n <- nrow(formuladata)
mu.b = mu.b.value
tau.b = tau.b.value
tau.aa=tau.ab=tau.ba=tau.bb=1
tau.ua=tau.ub=1
a.var=1
for (i in 1:iter.update){
dat <- list("n"= n, "nvar"= nvar, "y" = formuladata[,1], "x"=as.matrix(x[,-1]),
"mu.b"=mu.b, "tau.b"=tau.b,"tau.aa"=tau.aa,"tau.ab"=tau.ab,"tau.ba"=tau.ba,"tau.bb"=tau.bb,"tau.ua"=tau.ua,"tau.ub"=tau.ub)
inits <- list(u = rep(0,n),b = mu.b, tau.u =tau.u)
cat("model {
for (i in 1:n) {
y[i] ~ dlnorm(mu.ln[i],tau[i])
mu.ln[i] <- b[1] + sum(b[2:nvar]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
mu[i] <- exp(mu.ln[i])
tau[i] ~ dgamma(tau.a, tau.tb)
}
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
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="lognormal.txt")
jags.m <- jags.model(file = "lognormal.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("lognormal.txt")
params <- c("mu","a.var","b", "tau.u", "tau.a", "tau.tb")
samps <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps1 <- window(samps, start=burn.in+1, end=iter.mcmc)
result_samps=summary(samps1)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.aa = result_samps$statistics[(n+nvar+2),1]^2/result_samps$statistics[(n+nvar+2),2]^2
tau.ab = result_samps$statistics[(n+nvar+2),1]/result_samps$statistics[(n+nvar+2),2]^2
tau.ba = result_samps$statistics[(n+nvar+3),1]^2/result_samps$statistics[(n+nvar+3),2]^2
tau.bb = result_samps$statistics[(n+nvar+3),1]/result_samps$statistics[(n+nvar+3),2]^2
tau.ua = result_samps$statistics[(4+nvar+n),1]^2/result_samps$statistics[(4+nvar+n),2]^2
tau.ub = result_samps$statistics[(4+nvar+n),1]/result_samps$statistics[(4+nvar+n),2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
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:(nvar+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+2):(1+nvar+n),1:2]
Estimation=data.frame(mu)
Quantiles <- as.data.frame(result_samps$quantiles[1:(3+nvar+n),])
q_mu <- Quantiles[(nvar+2):(nvar+1+n),]
q_beta <- (Quantiles[2:(nvar+1),])
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
Estimation <- data.frame(Estimation,q_mu)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
} else {
formuladata <- as.data.frame(formuladata)
x <- as.matrix(formuladata[,2:nvar])
n <- nrow(formuladata)
mu.b =mu.b.value
tau.b = tau.b.value
tau.aa=tau.ab=tau.ba=tau.bb=1
tau.ua=tau.ub=1
a.var=1
formuladata$idx <- rep(1:n)
data_sampled <- na.omit(formuladata)
if (any(data_sampled[,1]<=0)){
stop("response variable must be " ,formula[2], " > 0")}
data_nonsampled <- formuladata[-data_sampled$idx,]
r=data_nonsampled$idx
n1=nrow(data_sampled)
n2=nrow(data_nonsampled)
for (i in 1:iter.update){
dat <- list("n1"= n1, "n2"=n2,"nvar"=nvar, "y_sampled" = data_sampled[,1],
"x_sampled"=as.matrix(data_sampled[,2:nvar]),
"x_nonsampled"=as.matrix(data_nonsampled[,2:nvar]),
"mu.b"=mu.b,"tau.b"=tau.b,
"tau.aa"=tau.aa,"tau.ab"=tau.ab,"tau.ba"=tau.ba,"tau.bb"=tau.bb,
"tau.ua"=tau.ua,"tau.ub"=tau.ub)
inits <- list(u = rep(0,n1), v = rep(0,n2), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:n1) {
y_sampled[i] ~ dlnorm(mu.ln[i],tau[i])
mu.ln[i] <- b[1] + sum(b[2:nvar]*x_sampled[i,]) + u[i]
u[i] ~dnorm(0,tau.u)
mu[i] <- exp(mu.ln[i])
tau[i] ~ dgamma(tau.a, tau.tb)
}
for (j in 1:n2) {
v[j] ~dnorm(0,tau.u)
y_nonsampled[j] ~ dlnorm(mu.ln.nonsampled[j],tau.nonsampled[j])
mu.ln.nonsampled[j] <- mu.b[1] + sum(mu.b[2:nvar]*x_nonsampled[j,]) +v[j]
mu.nonsampled[j] <- exp(mu.ln.nonsampled[j])
tau.nonsampled[j] ~ dgamma(tau.a, tau.tb)
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
tau.a ~ dgamma(tau.aa, tau.ab)
tau.tb ~ dgamma(tau.ba, tau.bb)
tau.u ~ dgamma(tau.ua, tau.ub)
a.var <- 1 / tau.u
}", file="LogNormal.txt")
jags.m <- jags.model( file = "LogNormal.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("LogNormal.txt")
params <- c("mu","mu.nonsampled","a.var","b","tau.a","tau.tb","tau.u")
samps <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps1 <- window(samps, start=burn.in+1, end=iter.mcmc)
result_samps=summary(samps1)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.aa = result_samps$statistics[(n+nvar+2),1]^2/result_samps$statistics[(n+nvar+2),2]^2
tau.ab = result_samps$statistics[(n+nvar+2),1]/result_samps$statistics[(n+nvar+2),2]^2
tau.ba = result_samps$statistics[(n+nvar+3),1]^2/result_samps$statistics[(n+nvar+3),2]^2
tau.bb = result_samps$statistics[(n+nvar+3),1]/result_samps$statistics[(n+nvar+3),2]^2
tau.ua = result_samps$statistics[(4+nvar+n),1]^2/result_samps$statistics[(4+nvar+n),2]^2
tau.ub = result_samps$statistics[(4+nvar+n),1]/result_samps$statistics[(4+nvar+n),2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(2:(nvar+1))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
beta=result_samps$statistics[2:(nvar+1),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+2):(1+nvar+n1),1:2]
mu.nonsampled =result_samps$statistics[(2+nvar+n1):(1+nvar+n),1:2]
Estimation=matrix(rep(0,n),n,2)
Estimation[r,]=mu.nonsampled
Estimation[-r,]=mu
Estimation = as.data.frame(Estimation)
Quantiles <- as.data.frame(result_samps$quantiles[1:(2+nvar+n),])
q_beta <- (Quantiles[2:(nvar+1),])
q_mu <- (Quantiles[(nvar+2):(nvar+1+n1),])
q_mu.nonsampled <- (Quantiles[(2+nvar+n1):(1+nvar+n),])
q_Estimation <- matrix(0,n,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)
Estimation <- data.frame(Estimation,q_Estimation)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
}
result$Est = Estimation
result$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))
return(result)
}
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