R/gpois.R
In joiceevangelista/saeHB.gpois: SAE using HB Method under Generalized Poisson Distribution
Defines functions
GPois
Documented in
GPois
#' @title Small Area Estimation Using Hierarchical Bayesian Method under Generalized Poisson Distribution
#'
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Generalized Poisson Distribution. The range of data is \eqn{0 < y < \infty}. Generalized Distribution model can be used to handle underdispersion and overdispersion in count data.
#'
#' @param formula Formula that describe the fitted model
#' @param iter.update Number of updates with default \code{3}
#' @param coef Regression coefficient for variable of interest \eqn{(y)}
#' @param var.coef Variance of coefficient
#' @param iter.mcmc Number of total iterations per chain with default \code{2000}
#' @param thin Thinning rate, must be a positive integer with default \code{1}
#' @param burn.in Number of iterations to discard at the beginning with default \code{1000}
#' @param tau.u Variance of random effect area for non-zero count of variable interest with default \code{1}
#' @param data The data frame
#'
#' @import stringr
#' @import coda
#' @import rjags
#' @import stats
#' @import grDevices
#' @import graphics
#'
#' @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 contains the estimated model coefficient}
#' \item{plot}{Trace, Density, Autocorrelation Function Plot of MCMC samples}
#'
#'@examples
#' ##For data without any non-sampled area
#' data(dataGPois) # Load dataset
#'
#' result <- GPois(y ~ x1 + x2, data = dataGPois)
#'
#' result$Est # Small Area mean estimates
#' result$refVar # Estimated random effect variances
#' result$coefficient # Estimated model coefficient
#'
#' # Load library 'coda' to execute the plot
#' # autocorr.plot(result$plot[[3]]) # Generate ACF Plot
#' # plot(result$plot[[3]]) # Generate Density and Trace Plot
#'
#' ## For data with non-sampled area use dataGPoisNs
#'
#' @export
GPois <- function(formula,iter.update=3, iter.mcmc=2000,
coef, var.coef, thin = 1, burn.in =1000, 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
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")
}
if (!any(is.na(formuladata[,1]))){
formuladata <- as.matrix(na.omit(formuladata))
x <- model.matrix(formula,data = as.data.frame(formuladata))
n <- nrow(formuladata)
mu.b = mu.b.value
tau.b = tau.b.value
tau.ua = tau.ub = a.var = 1
alpha.a = -1
alpha.b = 1
for (i in 1:iter.update){
dat <- list("Zeros" = rep(0, n), "C" = 10000, "n"= n, "nvar"= nvar, "y" = formuladata[,1], "x"=as.matrix(x[,-1]),
"mu.b"=mu.b, "tau.b"=tau.b, "tau.ua"=tau.ua, "tau.ub"=tau.ub, "alpha.a" = alpha.a, "alpha.b" = alpha.b)
inits <- list(u = rep(0, n),b = mu.b, tau.u =tau.u)
cat("model {
for (i in 1:n) {
Zeros[i] ~ dpois(Zeros.mean[i])
Zeros.mean[i] <- -L[i] + C
l1[i] <- log((1-alpha)*mu[i]) + (y[i]-1)*log((1-alpha)*mu[i] + alpha*y[i])
l2[i] <- (1-alpha)*mu[i] + alpha*y[i] + loggam(y[i] + 1)
L[i] <- l1[i] - l2[i]
log(mu[i]) <- b[1] + sum(b[2:nvar]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
alpha ~ dunif(alpha.a, alpha.b)
tau.u~dgamma(tau.ua, tau.ub)
a.var <- 1/tau.u
}", file="gpois.txt")
jags.m <- jags.model( file = "gpois.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("gpois.txt")
params <- c("mu","a.var","b", "tau.u", "alpha")
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$statistics[3:(nvar+2),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.ua = result_samps$statistics[3+nvar+n,1]^2/result_samps$statistics[3+nvar+n,2]^2
tau.ub = result_samps$statistics[3+nvar+n,1]/result_samps$statistics[3+nvar+n,2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(3:(nvar+2))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
alpha=result_samps$statistics[2]
beta=result_samps$statistics[3:(nvar+2),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+3):(2+nvar+n),1:2]
Estimation=data.frame(mu)
Quantiles <- as.data.frame(result_samps$quantiles[1:(3+nvar+n),])
q_mu <- Quantiles[(nvar+3):(nvar+2+n),]
q_beta <- (Quantiles[3:(nvar+2),])
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.ua = tau.ub = a.var = 1
alpha.a = -1
alpha.b = 1
formuladata$idx <- rep(1:n)
data_sampled <- na.omit(formuladata)
data_nonsampled <- formuladata[-data_sampled$idx,]
r=data_nonsampled$idx
n1=nrow(data_sampled)
n2=nrow(data_nonsampled)
for (i in 1:iter.update){
dat <- list("Zeros" = rep(0, n1), "C" = 10000,"n1"= n1, "n2"=n2,"nvar"=nvar, "y_sampled" = data_sampled[,1],
"x_sampled"=as.matrix(data_sampled[,2:nvar]),
"x_nonsampled"=as.matrix(data_nonsampled[,2:nvar]),
"mu.b"=mu.b,"tau.b"=tau.b, "tau.ua"=tau.ua,"tau.ub"=tau.ub, "alpha.a" = alpha.a, "alpha.b" = alpha.b)
inits <- list(u = rep(0,n1), v = rep(0,n2), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:n1) {
Zeros[i] ~ dpois(Zeros.mean[i])
Zeros.mean[i] <- -L[i] + C
l1[i] <- log((1-alpha)*mu[i]) + (y_sampled[i]-1)*log((1-alpha)*mu[i] + alpha*y_sampled[i])
l2[i] <- (1-alpha)*mu[i] + alpha*y_sampled[i] + loggam(y_sampled[i] + 1)
L[i] <- l1[i] - l2[i]
log(mu[i]) <- b[1] + sum(b[2:nvar]*x_sampled[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
}
alpha ~ dunif(alpha.a, alpha.b)
tau.u~dgamma(tau.ua, tau.ub)
a.var <- 1/tau.u
for(j in 1:n2) {
v[j]~dnorm(0, tau.u)
log(mu.nonsampled[j]) <- mu.b[1] + sum(mu.b[2:nvar]*x_nonsampled[j,]) +v[j]
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
}", file="gpois.txt")
jags.m <- jags.model( file = "gpois.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("gpois.txt")
params <- c("mu","mu.nonsampled","a.var","b", "tau.u", "alpha")
samps <- coda.samples( jags.m, params, n.iter=iter.mcmc, thin=thin)
samps1 <- window(samps, start=burn.in+1, end=iter.mcmc)
result_samps=summary(samps1)
a.var=result_samps$statistics[1]
beta=result_samps$statistics[3:(nvar+2),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.ua = result_samps$statistics[3+nvar+n,1]^2/result_samps$statistics[3+nvar+n,2]^2
tau.ub = result_samps$statistics[3+nvar+n,1]/result_samps$statistics[3+nvar+n,2]^2
}
result_samps=summary(samps1)
b.varnames <- list()
for (i in 1:(nvar)) {
idx.b.varnames <- as.character(i-1)
b.varnames[i] <-str_replace_all(paste("b[",idx.b.varnames,"]"),pattern=" ", replacement="")
}
result_mcmc <- samps1[,c(3:(nvar+2))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
alpha=result_samps$statistics[2]
beta=result_samps$statistics[3:(nvar+2),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+3):(2+nvar+n1),1:2]
mu.nonsampled =result_samps$statistics[(3+nvar+n1):(2+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$quantiles[1:(3+nvar+n),])
q_beta <- (Quantiles[3:(nvar+2),])
q_mu <- (Quantiles[(nvar+3):(nvar+2+n1),])
q_mu.nonsampled <- (Quantiles[(3+nvar+n1):(2+nvar+n),])
q_Estimation <- matrix(0,n,5)
for (i in 1:5){
q_Estimation[r,i] <- q_mu.nonsampled[,i]
q_Estimation[-r,i] <- q_mu[,i]
}
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
Estimation <- data.frame(Estimation,q_Estimation)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
}
result$Est = Estimation
result$refVar = a.var
result$coefficient = beta
result$plot = list(graphics.off() ,par(mar=c(2,2,2,2)),
autocorr.plot(result_mcmc,col="brown2",lwd=2),
plot(result_mcmc,col="brown2",lwd=2))
return(result)
}
joiceevangelista/saeHB.gpois documentation built on June 15, 2022, 9:56 a.m.
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Defines functions GPois
Documented in GPois
#' @title Small Area Estimation Using Hierarchical Bayesian Method under Generalized Poisson Distribution
#'
#' @description This function is implemented to variable of interest \eqn{(y)} that assumed to be a Generalized Poisson Distribution. The range of data is \eqn{0 < y < \infty}. Generalized Distribution model can be used to handle underdispersion and overdispersion in count data.
#'
#' @param formula Formula that describe the fitted model
#' @param iter.update Number of updates with default \code{3}
#' @param coef Regression coefficient for variable of interest \eqn{(y)}
#' @param var.coef Variance of coefficient
#' @param iter.mcmc Number of total iterations per chain with default \code{2000}
#' @param thin Thinning rate, must be a positive integer with default \code{1}
#' @param burn.in Number of iterations to discard at the beginning with default \code{1000}
#' @param tau.u Variance of random effect area for non-zero count of variable interest with default \code{1}
#' @param data The data frame
#'
#' @import stringr
#' @import coda
#' @import rjags
#' @import stats
#' @import grDevices
#' @import graphics
#'
#' @return This function returns a list of the following objects:
#' \item{Est}{A vector with the values of Small Area mean Estimates using Hierarchical Bayesian method}
#' \item{refVar}{Estimated random effect variances}
#' \item{coefficient}{A dataframe contains the estimated model coefficient}
#' \item{plot}{Trace, Density, Autocorrelation Function Plot of MCMC samples}
#'
#'@examples
#' ##For data without any non-sampled area
#' data(dataGPois) # Load dataset
#'
#' result <- GPois(y ~ x1 + x2, data = dataGPois)
#'
#' result$Est # Small Area mean estimates
#' result$refVar # Estimated random effect variances
#' result$coefficient # Estimated model coefficient
#'
#' # Load library 'coda' to execute the plot
#' # autocorr.plot(result$plot[[3]]) # Generate ACF Plot
#' # plot(result$plot[[3]]) # Generate Density and Trace Plot
#'
#' ## For data with non-sampled area use dataGPoisNs
#'
#' @export
GPois <- function(formula,iter.update=3, iter.mcmc=2000,
coef, var.coef, thin = 1, burn.in =1000, 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
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")
}
if (!any(is.na(formuladata[,1]))){
formuladata <- as.matrix(na.omit(formuladata))
x <- model.matrix(formula,data = as.data.frame(formuladata))
n <- nrow(formuladata)
mu.b = mu.b.value
tau.b = tau.b.value
tau.ua = tau.ub = a.var = 1
alpha.a = -1
alpha.b = 1
for (i in 1:iter.update){
dat <- list("Zeros" = rep(0, n), "C" = 10000, "n"= n, "nvar"= nvar, "y" = formuladata[,1], "x"=as.matrix(x[,-1]),
"mu.b"=mu.b, "tau.b"=tau.b, "tau.ua"=tau.ua, "tau.ub"=tau.ub, "alpha.a" = alpha.a, "alpha.b" = alpha.b)
inits <- list(u = rep(0, n),b = mu.b, tau.u =tau.u)
cat("model {
for (i in 1:n) {
Zeros[i] ~ dpois(Zeros.mean[i])
Zeros.mean[i] <- -L[i] + C
l1[i] <- log((1-alpha)*mu[i]) + (y[i]-1)*log((1-alpha)*mu[i] + alpha*y[i])
l2[i] <- (1-alpha)*mu[i] + alpha*y[i] + loggam(y[i] + 1)
L[i] <- l1[i] - l2[i]
log(mu[i]) <- b[1] + sum(b[2:nvar]*x[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
alpha ~ dunif(alpha.a, alpha.b)
tau.u~dgamma(tau.ua, tau.ub)
a.var <- 1/tau.u
}", file="gpois.txt")
jags.m <- jags.model( file = "gpois.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("gpois.txt")
params <- c("mu","a.var","b", "tau.u", "alpha")
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[3:(nvar+2),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.ua = result_samps$statistics[3+nvar+n,1]^2/result_samps$statistics[3+nvar+n,2]^2
tau.ub = result_samps$statistics[3+nvar+n,1]/result_samps$statistics[3+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(3:(nvar+2))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
alpha=result_samps$statistics[2]
beta=result_samps$statistics[3:(nvar+2),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+3):(2+nvar+n),1:2]
Estimation=data.frame(mu)
Quantiles <- as.data.frame(result_samps$quantiles[1:(3+nvar+n),])
q_mu <- Quantiles[(nvar+3):(nvar+2+n),]
q_beta <- (Quantiles[3:(nvar+2),])
rownames(q_beta) <- b.varnames
beta <- cbind(beta,q_beta)
Estimation <- data.frame(Estimation,q_mu)
colnames(Estimation) <- c("MEAN","SD","2.5%","25%","50%","75%","97.5%")
} else {
formuladata <- as.data.frame(formuladata)
x <- as.matrix(formuladata[,2:nvar])
n <- nrow(formuladata)
mu.b =mu.b.value
tau.b = tau.b.value
tau.ua = tau.ub = a.var = 1
alpha.a = -1
alpha.b = 1
formuladata$idx <- rep(1:n)
data_sampled <- na.omit(formuladata)
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("Zeros" = rep(0, n1), "C" = 10000,"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.ua"=tau.ua,"tau.ub"=tau.ub, "alpha.a" = alpha.a, "alpha.b" = alpha.b)
inits <- list(u = rep(0,n1), v = rep(0,n2), b = mu.b, tau.u = tau.u)
cat("model {
for (i in 1:n1) {
Zeros[i] ~ dpois(Zeros.mean[i])
Zeros.mean[i] <- -L[i] + C
l1[i] <- log((1-alpha)*mu[i]) + (y_sampled[i]-1)*log((1-alpha)*mu[i] + alpha*y_sampled[i])
l2[i] <- (1-alpha)*mu[i] + alpha*y_sampled[i] + loggam(y_sampled[i] + 1)
L[i] <- l1[i] - l2[i]
log(mu[i]) <- b[1] + sum(b[2:nvar]*x_sampled[i,]) + u[i]
u[i] ~ dnorm(0,tau.u)
}
alpha ~ dunif(alpha.a, alpha.b)
tau.u~dgamma(tau.ua, tau.ub)
a.var <- 1/tau.u
for(j in 1:n2) {
v[j]~dnorm(0, tau.u)
log(mu.nonsampled[j]) <- mu.b[1] + sum(mu.b[2:nvar]*x_nonsampled[j,]) +v[j]
}
# prior
for (k in 1:nvar){
b[k] ~ dnorm(mu.b[k],tau.b[k])
}
}", file="gpois.txt")
jags.m <- jags.model( file = "gpois.txt", data=dat, inits=inits, n.chains=1, n.adapt=500 )
file.remove("gpois.txt")
params <- c("mu","mu.nonsampled","a.var","b", "tau.u", "alpha")
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[3:(nvar+2),1:2]
for (i in 1:nvar){
mu.b[i] = beta[i,1]
tau.b[i] = 1/(beta[i,2]^2)
}
tau.ua = result_samps$statistics[3+nvar+n,1]^2/result_samps$statistics[3+nvar+n,2]^2
tau.ub = result_samps$statistics[3+nvar+n,1]/result_samps$statistics[3+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(3:(nvar+2))]
colnames(result_mcmc[[1]]) <- b.varnames
a.var=result_samps$statistics[1]
alpha=result_samps$statistics[2]
beta=result_samps$statistics[3:(nvar+2),1:2]
rownames(beta) <- b.varnames
mu=result_samps$statistics[(nvar+3):(2+nvar+n1),1:2]
mu.nonsampled =result_samps$statistics[(3+nvar+n1):(2+nvar+n),1:2]
Estimation=matrix(rep(0,n),n,2)
Estimation[r,]=mu.nonsampled
Estimation[-r,]=mu
Estimation = as.data.frame(Estimation)
Quantiles <- as.data.frame(result_samps$quantiles[1:(3+nvar+n),])
q_beta <- (Quantiles[3:(nvar+2),])
q_mu <- (Quantiles[(nvar+3):(nvar+2+n1),])
q_mu.nonsampled <- (Quantiles[(3+nvar+n1):(2+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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