dataBetaAr1 {saeHB.panel.beta}

Sample Data under Beta Distribution for Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model

Description

Dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian Method for Rao Yu Model This data is generated by these following steps:

1. Generate random effect area v, random effect for area i at time point j u, epsilon \epsilon, variance of ydi vardir, sampling error e, auxiliary xdi1 and xdi2

   • Set coefficient \beta_{0}=\beta_{1}=\beta_{2}=2 and \rho = -0,5

   • Generate random effect area v_{i}~N(0,1)

   • Generate auxiliary variable xdi1_{ij}~U(0,1)

   • Generate auxiliary variable xdi2_{ij}~U(0,1)

   • Generate epsilon \epsilon_{ij}~N(0,1)

   • Generate sampling error e_{ij}~N(0,vardir_{ij})

   • Generate \phi_{ij}~Gamma(1,0.5)

   • Calculate random effect for area i at time point j u_{ij}=\rho*u_{ij-1}+\epsilon_{ij}

   • Calculate \mu_{ij}=\frac{(\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}})}{(1+\exp{\beta_{0}+\beta_{1}xdi1_{ij}+\beta_{2}xdi2_{ij}+v_{i}+\epsilon_{ij}}})

   • Calculate A_{ij}=\mu_{ij}*\phi_{ij}

   • Calculate B_{ij}=(1-\mu_{ij})*\phi_{ij}

   • Generate ydi y_{ij}~Beta(A_{ij},B_{ij})

   • Calculate variance of ydi with vardir_{ij}=\frac{(A_{ij})(B_{ij})}{(A_{ij}+B_{ij})^2(A_{ij}+B_{ij}+1)}

   • Set area=20 and period=5

2. Auxiliary variables xdi1,xdi2, direct estimation y, area, period, and vardir are combined in a dataframe called dataAr1

Usage

dataBetaAr1

Format

A data frame with 100 rows and 6 variables:

ydi

Direct Estimation of y

area

Area (domain) of the data

period

Period (subdomain) of the data

vardir

Sampling Variance of y

xdi1

Auxiliary variable of xdi1

xdi2

Auxiliary variable of xdi2