PoissonGamma {saeHB}

Small Area Estimation using Hierarchical Bayesian under Poisson Gamma Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Poisson Distribution which it is parameter (\lambda) is assumed to be a Gamma distribution. The data is a count data, y = 1,2,3,...

Usage

PoissonGamma(
  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

##Load Dataset
library(CARBayesdata)
data(lipdata)
dataPoissonGamma <- lipdata
dataPoissonGammaNs <- lipdata
dataPoissonGammaNs$observed[c(2,9,15,23,40)] <- NA


##Compute Fitted Model
##observed ~ pcaff


## For data without any nonsampled area

formula = observed ~ pcaff
v= c(1,1)
c = c(0,0)
dat = dataPoissonGamma


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

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

## Do not using parameter coef and var.coef
saeHBPoissonGamma <- PoissonGamma(formula,data=dataPoissonGamma)



## For data with nonsampled area use dataPoissonGammaNs