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:
Generate auxiliary variable
X_{ij1},X_{ij2}
, sampling errore_{ij}
,subarea random effectu_{ij}
, area random effectv_{i}
, and weight or proportions of unitw_{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}
andA=(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)
Direct estimation (
y_{ij}
), Auxiliary variablesX_{ij1}
,X_{ij2}
, vardir, codearea, and weightw_{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}