Synthetic data of 64 regions to simulate Small Area Estimation under Spatial SAR Model and Normal Distribution using Hierarchical Bayesian Method
This data is generated by these following steps:
Generate sampling random area effect \(v = (I - \rho W)^{-1}u\) with \(u ~ N(0, I)\), \(I\) is an identity matrix, and \(W\) is proximity matrix. The auxiliary variables are generated by \(x1 ~ U(0, 1)\) and \(x2 ~ N(10, 1)\). The parameters \(\beta_{0}, \beta_{1}, \beta_{2}\) are set as 1 and \(\rho\) as 0.7
Generate variance of the direct estimators \(\sigma^{2}_{e}\) with \(\sigma^{2}_{e} ~ InvGamma(a, b)\). Sampling error \(e\) is generated by \(e ~ N(0, \sigma^{2}_{e})\)
Calculate \(\mu = \beta_{0} + \beta_{1}x1 + \beta_{2}x2 + u\). Calculate the direct estimators of \(\mu\), i.e \(y = \mu + e\)
Direct estimators \(y\), auxiliary variables \(x1, x2\), and variance of the direct estimators are combined in a data frame called sp.norm
data(sp.norm)A data frame with 64 observations on the following 4 variables:
Direct estimators for each region
Auxiliary variable of x1
Auxiliary variable of x2
Sampling variance of the direct estimators for each region