saeHB.ZIB (version 0.1.1)

dataZIB: Sample Data for Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial Distribution

Description

Dataset to simulate Small Area Estimation using Hierarchical Bayesian Method under Zero-Inflated Binomial distribution

This data is generated by these following steps:

1. Generate sampling random area effect u.Z and u.nZ with \((u.Z ~ N(0,1))\) and \((u.nZ ~ N(0,1))\). The auxilary variabels are generated by Uniform distribution with \((x1 ~ U(0,1))\) and \((x2 ~ U(1,5))\). The coefficient parameters \(\alpha0, \alpha1, \alpha2, \beta0, \beta1, \beta2\) are set as 0.

2. Calculate \(logit(p)=\alpha0 + \alpha1 * x1+ \alpha2 * x2 + u.Z\) and \(logit(\pi)=\beta0 + \beta1 * x1 +\beta2 * x2 + u.nZ\)

3. Generate number of sample with \(n.samp ~ U(10,30)\)

4. Generate \(delta ~ bernoulli(p)\) and \(y_star ~ binomial(s, \pi)\)

5. calculate \(y = delta*y_star\)

6. Calculate variance of direct estimates (vardir) with \(var (y) = (1-p)*s*pi*(1-\pi*(1-p*s))\)

7. Auxilary variables x1, x2, direct estimation \((y)\), vardir, and s are combined in a dataframe called dataZIB

Usage

data(dataZIB)

Format

A data frame with 64 observations on the following 4 variables:

y

Direct Estimation of y

X1

Auxiliary variable of x1

X2

Auxiliary variable of x2

vardir

sampling variance of y

s

number of sample