NegativeBinomial: Small Area Estimation using Hierarchical Bayesian under...

In saeHB: Small Area Estimation using Hierarchical Bayesian Method

Small Area Estimation using Hierarchical Bayesian under Negative Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Negative Binomial Distribution. The data is a number of the Bernoulli process. The negative binomial is used to overcome an over dispersion from the discrete model.

Usage

NegativeBinomial(
  formula,
  iter.update = 3,
  iter.mcmc = 10000,
  coef,
  var.coef,
  thin = 2,
  burn.in = 2000,
  tau.u = 1,
  data
)

Arguments

formula	Formula that describe the fitted model
iter.update	Number of updates with default 3
iter.mcmc	Number of total iterations per chain with default 10000
coef	a vector contains prior initial value of Coefficient of Regression Model for fixed effect with default vector of 0 with the length of the number of regression coefficients
var.coef	a vector contains prior initial value of variance of Coefficient of Regression Model with default vector of 1 with the length of the number of regression coefficients
thin	Thinning rate, must be a positive integer with default 2
burn.in	Number of iterations to discard at the beginning with default 2000
tau.u	Prior initial value of inverse of Variance of area random effect with default 1
data	The data frame

Value

This function returns a list of the following objects:

Est	A vector with the values of Small Area mean Estimates using Hierarchical bayesian method
refVar	Estimated random effect variances
coefficient	A dataframe with the estimated model coefficient
plot	Trace, Dencity, Autocorrelation Function Plot of MCMC samples

Examples

## Data Generation
set.seed(123)
library(MASS)
m <- 30
x <- runif(m, 0, 1)
b0 <- b1 <- 0.5
u <- rnorm(m, 0, 1)
Mu <- exp(b0 + b1 * x + u)
theta <- 1
y <- MASS::rnegbin(m, Mu, theta)
vardir <- Mu + Mu^2 / theta
dataNegativeBinomial <- as.data.frame(cbind(y, x, vardir))
dataNegativeBinomialNs <- dataNegativeBinomial
dataNegativeBinomialNs$y[c(3, 14, 22, 29, 30)] <- NA
dataNegativeBinomialNs$vardir[c(3, 14, 22, 29, 30)] <- NA


## Compute Fitted Model
## y ~ x


## For data without any nonsampled area

formula <- y ~ x
v <- c(1, 1)
c <- c(0, 0)
dat <- dataNegativeBinomial

## Using parameter coef and var.coef
saeHBNegbin <- NegativeBinomial(formula, coef = c, var.coef = v, iter.update = 10, data = dat)

saeHBNegbin$Est # Small Area mean Estimates
saeHBNegbin$refVar # Random effect variance
saeHBNegbin$coefficient # coefficient
# Load Library 'coda' to execute the plot
# autocorr.plot(saeHBNegbin$plot[[3]]) is used to generate ACF Plot
# plot(saeHBNegbin$plot[[3]]) is used to generate Density and trace plot

## Do not using parameter coef and var.coef
saeHBNegbin <- NegativeBinomial(formula, data = dat)



## For data with nonsampled area use dataNegativeBinomialNs

saeHB documentation built on Nov. 26, 2025, 5:06 p.m.