NegativeBinomial {saeHB}

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=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