dataTwofold {saeHB.twofold} | R Documentation |
Simulated dataset Under Two Fold Subarea level model with Normal distribution.
Description
A dataset to simulate Small Area Estimation using Hierarchical Bayesian method under Two Fold Subarea level model with Normal distribution on variabel interest.
This data is generated by these following steps:
Generate sampling error
e_{ij}
,subarea random effectu_{ij}
, area random effectv_{i}
, auxiliary variabelx_{ij1},x_{ij2}
, and weight or proportions of unitw_{ij}
Generate subarea random effect
u_{ij}
~N(0,8)
Generate area random effect
v_{i}
~N(0,8)
Generate auxilary variabel on subarea level
x_{ij1}
~U(0,1)
Generate auxilary variabel on subarea level
x_{ij2}
~N(10,1)
Generate unit proportion on each subarea
w_{ij}
~U(10,20)
Generate sampling error
e_{ij}
~N(0,\sigma^{2}_{e})
where\sigma^{2}_{e}
~IG(1,1)
is a variance of direct estimatorSetting coefficient
\beta_{0}=\beta_{1}=\beta_{2} =1
Calculate target parameter
\mu_{ij}=\beta_{0} +\beta_{1}x_{ij1} +\beta_{2}x_{ij2}+v_{i}+u_{ij}
Calculate direct estimator
y_{ij}=\mu_{ij}+e_{ij}
Auxiliary variables
x_{ij1}
,x_{ij2}
, direct estimation (y_{ij}
) ,vardir, and weightw_{ij}
are combined in a dataframe called dataTwofold
Usage
dataTwofold
Format
A data frame with 90 rows and 6 columns:
- y
Direct estimation of subarea mean
y_{ij}
- x1
Auxiliary variabel of
x_{ij1}
- x2
Auxiliary variabel of
x_{ij2}
- codearea
Index that describes the code relating to warea for each subarea
- w
Unit proportion on each subarea or weight
w_{ij}
- vardir
Sampling variance of direct estimator
y_{ij}