saeHB.spatial

Provides several functions and datasets for area level of Small Area Estimation under Spatial SAR Model using Hierarchical Bayesian (HB) Method. Model-based estimators include the HB estimators based on a Spatial Fay-Herriot model with univariate normal distribution for variable of interest.The ‘rjags’ package is employed to obtain parameter estimates. For the reference, see Rao and Molina (2015) doi:10.1002/9781118735855.

Author

Arina Mana Sikana, Azka Ubaidillah

Maintaner

Arina Mana Sikana sikanaradrianan@gmail.com

Function

• spatial.normal() This function gives small area estimator under Spatial SAR Model and is implemented to variable of interest (y) that assumed to be a Normal Distribution. The range of data is (-∞ < y < ∞)

Installation

You can install the development version of saeHB.spatial from GitHub with:

# install.packages("devtools")
devtools::install_github("arinams/saeHB.spatial")

Example

This is a basic example of using spatial.normal() function to make an estimate based on synthetic data in this package

library(saeHB.spatial)

## For data without any non-sampled area
data(sp.norm)       # Load dataset
data(prox.mat)      # Load proximity Matrix

## For data with non-sampled area use sp.normNs

## Fitting model
result <- spatial.normal(y ~ x1 + x2, "vardir", prox.mat, data = sp.norm)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 64
#>    Unobserved stochastic nodes: 6
#>    Total graph size: 8989
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 64
#>    Unobserved stochastic nodes: 6
#>    Total graph size: 8989
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 64
#>    Unobserved stochastic nodes: 6
#>    Total graph size: 8989
#> 
#> Initializing model

Small Area mean Estimates

result$Est

Estimated model coefficient

result$coefficient

Estimated random effect variances

result$refVar
#>  [1] 3.374605 3.210616 2.883059 2.772039 2.772039 2.883059 3.210616 3.374605
#>  [9] 3.210616 2.944840 2.664411 2.571676 2.571676 2.664411 2.944840 3.210616
#> [17] 2.883059 2.664411 2.434569 2.360292 2.360292 2.434569 2.664411 2.883059
#> [25] 2.772039 2.571676 2.360292 2.294087 2.294087 2.360292 2.571676 2.772039
#> [33] 2.772039 2.571676 2.360292 2.294087 2.294087 2.360292 2.571676 2.772039
#> [41] 2.883059 2.664411 2.434569 2.360292 2.360292 2.434569 2.664411 2.883059
#> [49] 3.210616 2.944840 2.664411 2.571676 2.571676 2.664411 2.944840 3.210616
#> [57] 3.374605 3.210616 2.883059 2.772039 2.772039 2.883059 3.210616 3.374605

References

• Rao, J.N.K & Molina. (2015). Small Area Estimation 2nd Edition. New Jersey: John Wiley and Sons, Inc. doi:10.1002/9781118735855.
• J. Kubacki and A. Jedrzejczak. (2016). Small Area Estimation of Income Under Spatial SAR Model. Statistics in Transition New Series, Vol. 17, No. 3, pp. 365–390. <doi: 10.21307/stattrans-2016-028>.
• H. C. Chung and G. S. Datta. (2020). Bayesian Hierarchical Spatial Models for Small Area Estimation. Research Report Series. Washington, D.C.: U.S. Census Bureau.