sp.norm {saeHB.spatial} | R Documentation |
Synthetic Data for Small Area Estimation under Spatial Simultaneous Autoregressive (SAR) Model and Normal Distribution
Description
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
withu ~ N(0, I)
,I
is an identity matrix, andW
is proximity matrix. The auxiliary variables are generated byx1 ~ U(0, 1)
andx2 ~ N(10, 1)
. The parameters\beta_{0}, \beta_{1}, \beta_{2}
are set as 1 and\rho
as 0.7Generate variance of the direct estimators
\sigma^{2}_{e}
with\sigma^{2}_{e} ~ InvGamma(a, b)
. Sampling errore
is generated bye ~ N(0, \sigma^{2}_{e})
Calculate
\mu = \beta_{0} + \beta_{1}x1 + \beta_{2}x2 + u
. Calculate the direct estimators of\mu
, i.ey = \mu + e
Direct estimators
y
, auxiliary variablesx1, x2
, and variance of the direct estimators are combined in a data frame calledsp.norm
Usage
data(sp.norm)
Format
A data frame with 64 observations on the following 4 variables:
- y
Direct estimators for each region
- x1
Auxiliary variable of x1
- x2
Auxiliary variable of x2
- vardir
Sampling variance of the direct estimators for each region