rho = 0Dataset under Beta Distribution to simulate Small Area Estimation using Hierarchical Bayesian Method for Rao-Yu Model with rho = 0 This data is generated by these following steps:
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 \(\beta_{0}=\beta_{1}=\beta_{2}=2\)
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 \(\phi_{ij}\)~Gamma(1,0.5)
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
Auxiliary variables xdi1,xdi2, direct estimation y, area, period, and vardir are combined in a dataframe called dataPanel
dataPanelbetaA data frame with 100 rows and 6 variables:
Direct Estimation of y
Area (domain) of the data
Period (subdomain) of the data
Sampling Variance of y
Auxiliary variable of xdi1
Auxiliary variable of xdi2