saeHB (version 0.2.3)

NegativeBinomial: 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
)

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

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

Examples

# \donttest{
## 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
# }