dataBeta {saeHB.TF.beta}R Documentation

Simulated dataset Under Two Fold Subarea level model with Beta distribution.

Description

A dataset to simulate Small Area Estimation using Hierarchical Bayesian method under Two Fold Subarea level model with Beta distribution on variable interest.

This data is generated by these following steps:

  1. Generate auxiliary variable X_{ij1},X_{ij2}, sampling error e_{ij},subarea random effect u_{ij}, area random effect v_{i}, and weight or proportions of unit w_{ij}

    • Generate auxiliary variable on subarea level X_{ij1}~ U(0,1)

    • Generate auxiliary variable on subarea level X_{ij2}~N(0,1)

    • Setting coefficient \beta_{0}=\beta_{1}=\beta_{2} =0.5

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

    • Generate subarea random effect u_{ij}~N(0,1)

    • Calculate target parameter \mu_{ij}=\beta_{0} +\beta_{1}x_{ij1} +\beta_{2}x_{ij2}+v_{i}+u_{ij}

    • Generate constant for Beta parameter \pi_{ij}~ Gamma(1,0.5)

    • Calculate Beta parameter A=\mu_{ij}\pi_{ij} and A=(1-\mu_{ij})\pi_{ij}

    • Generate direct estimator y_{ij}~ Beta(A,B)

    • Generate weight on each subarea w_{ij}~U(0.2,0.7)

  2. Direct estimation (y_{ij}), Auxiliary variables X_{ij1},X_{ij2}, vardir, codearea, and weight w_{ij} are combined in a dataframe called dataBeta

Usage

dataBeta

Format

A data frame with 90 rows and 6 columns:

y

Direct estimation of subarea mean y_{ij}

X1

Auxiliary variable of X_{ij1}

X2

Auxiliary variable of X_{ij2}

codearea

Index that describes the code relating to area for each subarea

w

Unit proportion on each subarea or weight w_{ij}

vardir

Sampling variance of direct estimator y_{ij}


[Package saeHB.TF.beta version 0.1.0 Index]