Provides several functions and datasets for area level of Small Area Estimation under Spatial 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.
Arina Mana Sikana, Azka Ubaidillah
Arina Mana Sikana [email protected]
sar.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 < ∞)
You can install the development version of saeHB.spatial from
GitHub with:
# install.packages("devtools")
devtools::install_github("arinams/saeHB.spatial")This is a basic example of using sar.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 <- sar.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 modelSmall Area mean Estimates
result$EstEstimated model coefficient
result$coefficient
#> Mean SD 2.5% 25% 50% 75% 97.5%
#> b[0] 0.1700130 0.74079233 -1.3348037 -0.2860765 0.2121135 0.7049094 1.4542826
#> b[1] 1.4196559 0.40454428 0.6013067 1.1724748 1.4341555 1.6957986 2.1986285
#> b[2] 1.1204738 0.05961372 0.9999717 1.0827609 1.1224242 1.1628727 1.2381436
#> rho 0.8166122 0.09833086 0.5842319 0.7573845 0.8349576 0.8915150 0.9572931Estimated random effect variances
result$refVar
#> [1] 8.248286 8.064647 7.659618 7.500457 7.500457 7.659618 8.064647 8.248286
#> [9] 8.064647 7.777176 7.417112 7.278729 7.278729 7.417112 7.777176 8.064647
#> [17] 7.659618 7.417112 7.118359 7.005280 7.005280 7.118359 7.417112 7.659618
#> [25] 7.500457 7.278729 7.005280 6.904393 6.904393 7.005280 7.278729 7.500457
#> [33] 7.500457 7.278729 7.005280 6.904393 6.904393 7.005280 7.278729 7.500457
#> [41] 7.659618 7.417112 7.118359 7.005280 7.005280 7.118359 7.417112 7.659618
#> [49] 8.064647 7.777176 7.417112 7.278729 7.278729 7.417112 7.777176 8.064647
#> [57] 8.248286 8.064647 7.659618 7.500457 7.500457 7.659618 8.064647 8.248286- 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.