datasaeT {msaeHB} | R Documentation |
Dataset to simulate Small Area Estimation using Hierarchical Bayesian Method under Multivariate T distribution
This data is generated by these following steps:
Generate sampling error e
, random effect u
, and auxiliary variables X1 X2
.
For sampling error e
, we set e_{d}
is multivariate T distributed where the vector of noncentrality parameters is zero, scale matrix V_{ed} = (\sigma_{dij})_{i,j=1,2,3}
, with \sigma_{ii}
~ InvGamma(a, b)
and \rho_{e}
= 0.5, and degree of freedom df
~ InvGamma(a, b)
.
For random effect u
, we set u
~ N_{3}(0, V_{u})
.
For auxiliary variables X1 and X2
, we set X1
~ UNIF(1,2)
and X2
~ UNIF(1, 10)
.
Calculate direct estimation Y1 Y2 and Y3
, where Y_{i}
= X * \beta + u_{i} + e_{i}
. We take \beta_{1} = 1
and \beta_{2} = 1
.
Auxiliary variables X1 X2
, direct estimation Y1 Y2 Y3
, and sampling variance-covariance v1 v2 v3 v12 v13 v23
are combined into a dataframe called datasaeT
datasaeT
A data frame with 30 rows and 11 variables:
Auxiliary variable of X1
Auxiliary variable of X2
Direct Estimation of Y1
Direct Estimation of Y2
Direct Estimation of Y3
Sampling Variance of Y1
Sampling Covariance of Y1 and Y2
Sampling Covariance of Y1 and Y3
Sampling Variance of Y2
Sampling Covariance of Y2 and Y3
Sampling Variance of Y3