ziBinomial {saeHB.ZIB}

Small Area Estimation using Hierarchical Bayesian under Zero Inflated Binomial Distribution

Description

This function is implemented to variable of interest (y) that assumed to be a Zero Inflated Binomial Distribution. The range of data is (0 < y < \infty). This model can be used to handle overdispersion caused by excess zero in data.

Usage

ziBinomial(
  formula,
  n.samp,
  iter.update = 3,
  iter.mcmc = 10000,
  coef.nonzero,
  var.coef.nonzero,
  coef.zero,
  var.coef.zero,
  thin = 2,
  burn.in = 2000,
  tau.u.nZ = 1,
  data
)

Arguments

formula

Formula that describe the fitted model

n.samp

Number of sample in each area

iter.update

Number of updates with default 3

iter.mcmc

Number of total iterations per chain with default 2000

coef.nonzero

Optional argument for mean on coefficient's prior distribution or \beta's prior distribution which value is non-zero

var.coef.nonzero

Optional argument for the variances of the prior distribution of the model coefficients (\beta)

coef.zero

Optional argument for mean on coefficient's prior distribution or \alpha's prior distribution which value is non-zero

var.coef.zero

Optional argument for the variances of the prior distribution of the model coefficients (\alpha)

thin

Thinning rate, must be a positive integer with default 1

burn.in

Number of iterations to discard at the beginning with default 1000

tau.u.nZ

Variance of random effect area for non-zero of variable interest (y) 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_alpha

Trace, Density, Autocorrelation Function Plot of MCMC samples

plot_beta

Trace, Density, Autocorrelation Function Plot of MCMC samples

Examples

#Compute Fitted Model
 y ~ X1 +X2

# For data without any nonsampled area
# Load Dataset
  data(dataZIB)
  saeHB.ZIB <- ziBinomial(formula = y~X1+X2, "s", iter.update=3, iter.mcmc = 1000,
                burn.in = 200,data = dataZIB)
#the setting of iter.update, iter.mcmc, and burn.in in this example
#is considered to make the example execution time be faster.
#Result
saeHB.ZIB$Est                                    #Small Area mean Estimates
saeHB.ZIB$Est$SD                                 #Standard deviation of Small Area Mean Estimates
saeHB.ZIB$refVar                                 #refVar
saeHB.ZIB$coefficient                            #coefficient
#Load Library 'coda' to execute the plot
#autocorr.plot(saeHB.ZIB$plot_alpha[[3]]) is used to   #ACF Plot for alpha
#autocorr.plot(saeHB.ZIB$plot_beta[[3]]) is used to    #ACF Plot for beta
#plot(saeHB.ZIB$plot_alpha[[3]]) is used to            #Dencity and trace plot for alpha
#plot(saeHB.ZIB$plot_beta[[3]]) is used to             #Dencity and trace plot for beta