README.md

In saeHB.Spatial.Beta: Small Area Estimation Hierarchical Bayes for Spatial Beta Model

saeHB.Spatial.Beta

We designed this package to provide several functions for area-level small area estimation under Spatial Simultaneous Autoregressive (SAR) and Leroux Conditional Autoregressive (CAR) models, accommodating survey design effect (DEFF) adjustments, using hierarchical Bayesian (HB) method with Beta distribution for variables of interest. Some datasets simulated by a data generation are also provided. The rjags package is employed to obtain parameter estimates using Gibbs Sampling algorithm. Model-based estimators involve the HB estimators which include the mean estimation, the estimated model coefficients, the random effect, and the random effect variance. For the reference, see Rao and Molina (2015), Kubacki and Jedrzejczak (2016), Leroux et al. (2000), and Chung and Datta (2020).

Author

Boby Iwan, Cucu Sumarni

Maintainer

Boby Iwan [e-mail]

Functions

• betadeff_sar() Estimates small area means using a Spatial SAR Model under a Beta distribution, incorporating survey design effect (DEFF) adjustments.
• beta_sar() Estimates small area means using a Spatial SAR Model under a Beta distribution without DEFF adjustments, by estimating the unknown precision parameter.
• betadeff_lerouxcar() Estimates small area means using a Spatial Leroux CAR Model under a Beta distribution, incorporating survey design effect (DEFF) adjustments.
• beta_lerouxcar() Estimates small area means using a Spatial Leroux CAR Model under a Beta distribution without DEFF adjustments, by estimating the unknown precision parameter.
• betadeff_nonspatial() Estimates small area means using a Non-Spatial Model under a Beta distribution with Independent and Identically Distributed (IID) random effects, incorporating DEFF adjustments.
• beta_nonspatial() Estimates small area means using a Non-Spatial Model under a Beta distribution with IID random effects without DEFF adjustments, by estimating the unknown precision parameter.
• build_w() A utility function to construct spatial weights matrices (contiguity, distance, or kernel) required for spatial modeling.
• moran_test() A diagnostic function to perform Moran’s I test for spatial autocorrelation.

Installation

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

# install.packages("devtools")
devtools::install_github("BobyIwan/saeHB.Spatial.Beta")

Or, to include the vignette:

devtools::install_github("BobyIwan/saeHB.Spatial.Beta", build_vignettes = TRUE)

Example

This is a basic example of using the betadeff_sar() function to make an estimate based on synthetic data in this package:

library(saeHB.Spatial.Beta)

# Load dataset and proximity matrix
data(databeta)
data(weight_mat)

# Fitting the Spatial SAR model
model_sar_deff <- betadeff_sar(
  formula = y ~ x1 + x2,
  deff = "deff",
  n_i = "n_i",
  proxmat = weight_mat,
  data = databeta
)

Extract the mean estimation for the areas:

head(model_sar_deff$est)
#>        Estimate  Est.Error   l-95% CI  u-95% CI
#> mu[1] 0.8733168 0.04930364 0.76952538 0.9521954
#> mu[2] 0.6701813 0.08491170 0.51026583 0.8503483
#> mu[3] 0.5614027 0.06997444 0.42116653 0.6891348
#> mu[4] 0.2284165 0.06585628 0.11267368 0.3603505
#> mu[5] 0.2291424 0.07970595 0.09536724 0.3880149
#> mu[6] 0.9381786 0.02863821 0.87710262 0.9851179

Extract the estimated model coefficients:

model_sar_deff$coefficient
#>          Estimate  Est.Error  l-95% CI  u-95% CI     Rhat       ESS
#> beta[0] 1.7055337 0.11951894 1.4620974 1.9419599 1.149548  66.70198
#> beta[1] 0.6605003 0.10885851 0.4504252 0.8648356 1.286895 176.22281
#> beta[2] 0.8336673 0.08175262 0.6674418 0.9867496 1.018137 237.12147
#> rho     0.6909635 0.14591695 0.3733486 0.9296335 1.124197 689.47647

Extract the random effect for the areas:

model_sar_deff$randeff
#>          Estimate Est.Error    l-95% CI   u-95% CI
#> v[1]   0.02976288 0.4913420 -0.81082629  1.0627591
#> v[2]  -0.48294515 0.4130690 -1.26231341  0.4176781
#> v[3]  -1.45769631 0.2796486 -2.00757022 -0.9495101
#> v[4]  -2.22277069 0.3881942 -3.03673421 -1.5279135
#> v[5]  -1.64869564 0.4580919 -2.58002521 -0.9115122
#> v[6]  -0.62490246 0.5151320 -1.42893550  0.6018907
#> v[7]  -1.31435972 0.3882503 -2.19447057 -0.5504201
#> v[8]  -0.59620167 0.4450396 -1.39301122  0.3173124
#> v[9]  -0.95142395 0.5666047 -1.97008703  0.1204738
#> v[10] -1.86188398 0.5945596 -2.89386412 -0.5135673
#> v[11] -0.63652811 0.5225169 -1.83768964  0.2488411
#> v[12] -0.90714526 0.6641371 -1.96549002  0.5444394
#> v[13] -0.02096918 0.4392347 -0.68315270  0.9051771
#> v[14] -0.45119582 0.3669391 -1.17877921  0.2616308
#> v[15] -0.45713340 0.3477433 -1.13515648  0.3267205
#> v[16] -0.78596192 0.4795931 -1.66931806  0.1213205
#> v[17]  0.50418771 0.6097966 -0.49833501  1.8635032
#> v[18]  0.27799928 0.5841174 -0.84562838  1.2239715
#> v[19]  1.11034886 0.3616849  0.55680893  1.9703014
#> v[20] -1.49159085 0.3551025 -2.29804991 -0.7811928
#> v[21] -1.09415346 0.6454870 -2.32510864  0.1760261
#> v[22] -0.27706199 0.3827362 -0.98308670  0.5526622
#> v[23]  0.21086216 0.5909151 -1.05375351  1.4838056
#> v[24]  1.47451757 0.6029423  0.38350864  2.9469047
#> v[25]  1.05609850 0.6278718  0.03317434  2.2172461
#> v[26]  0.33959270 0.4502330 -0.51380065  1.1474950
#> v[27]  0.14925259 0.4689303 -0.87424837  1.0693728
#> v[28]  0.22145721 0.6168820 -1.02130464  1.5324451
#> v[29]  0.96589620 0.5730657  0.07019757  2.3534697
#> v[30]  1.45079715 0.4512189  0.61843455  2.4450905
#> v[31]  0.10774431 0.6070810 -0.99013546  1.2600864
#> v[32]  0.67029354 0.9085850 -0.90793803  2.1876036
#> v[33]  1.19490972 0.5864462  0.05177372  2.3811276
#> v[34]  0.82487094 0.5193530 -0.19980381  1.7372592
#> v[35]  0.82003029 0.6997081 -0.20605962  2.5197002
#> v[36]  1.75099923 0.5749532  0.62416400  2.6853996

Extract the random effect variance for the areas:

model_sar_deff$refvar
#>           Estimate Est.Error  l-95% CI u-95% CI
#> a.var[1]  2.338106  4.781148 0.8432360 7.458702
#> a.var[2]  2.263956  4.788653 0.8277110 7.304105
#> a.var[3]  2.102129  4.732050 0.7882035 6.808402
#> a.var[4]  2.102129  4.732050 0.7882035 6.808402
#> a.var[5]  2.263956  4.788653 0.8277110 7.304105
#> a.var[6]  2.338106  4.781148 0.8432360 7.458702
#> a.var[7]  2.263956  4.788653 0.8277110 7.304105
#> a.var[8]  2.211989  4.828332 0.8111973 7.250767
#> a.var[9]  2.053250  4.772112 0.7767535 6.703232
#> a.var[10] 2.053250  4.772112 0.7767535 6.703232
#> a.var[11] 2.211989  4.828332 0.8111973 7.250767
#> a.var[12] 2.263956  4.788653 0.8277110 7.304105
#> a.var[13] 2.102129  4.732050 0.7882035 6.808402
#> a.var[14] 2.053250  4.772112 0.7767535 6.703232
#> a.var[15] 1.927767  4.732744 0.7612544 6.192884
#> a.var[16] 1.927767  4.732744 0.7612544 6.192884
#> a.var[17] 2.053250  4.772112 0.7767535 6.703232
#> a.var[18] 2.102129  4.732050 0.7882035 6.808402
#> a.var[19] 2.102129  4.732050 0.7882035 6.808402
#> a.var[20] 2.053250  4.772112 0.7767535 6.703232
#> a.var[21] 1.927767  4.732744 0.7612544 6.192884
#> a.var[22] 1.927767  4.732744 0.7612544 6.192884
#> a.var[23] 2.053250  4.772112 0.7767535 6.703232
#> a.var[24] 2.102129  4.732050 0.7882035 6.808402
#> a.var[25] 2.263956  4.788653 0.8277110 7.304105
#> a.var[26] 2.211989  4.828332 0.8111973 7.250767
#> a.var[27] 2.053250  4.772112 0.7767535 6.703232
#> a.var[28] 2.053250  4.772112 0.7767535 6.703232
#> a.var[29] 2.211989  4.828332 0.8111973 7.250767
#> a.var[30] 2.263956  4.788653 0.8277110 7.304105
#> a.var[31] 2.338106  4.781148 0.8432360 7.458702
#> a.var[32] 2.263956  4.788653 0.8277110 7.304105
#> a.var[33] 2.102129  4.732050 0.7882035 6.808402
#> a.var[34] 2.102129  4.732050 0.7882035 6.808402
#> a.var[35] 2.263956  4.788653 0.8277110 7.304105
#> a.var[36] 2.338106  4.781148 0.8432360 7.458702

References

• Rao, J. N. K., & Molina, I. (2015). Small Area Estimation (2nd Edition). New Jersey: John Wiley and Sons, Inc. .
• Kubacki, J., & Jedrzejczak, A. (2016). Small Area Estimation of Income Under Spatial SAR Model. Statistics in Transition New Series, Vol. 17, No. 3, pp. 365–390. .
• Leroux, B. G., Lei, X., & Breslow, N. (2000). Estimation of Disease Rates in Small Areas: A New Mixed Model for Spatial Dependence. In M. E. Halloran & D. Berry (Eds.), Statistical Models in Epidemiology, the Environment, and Clinical Trials (Vol. 116, pp. 179–191). New York: Springer. .
• Chung, H. C., & Datta, G. S. (2020). Bayesian Hierarchical Spatial Models for Small Area Estimation. Research Report Series. Washington, D.C.: U.S. Census Bureau.

saeHB.Spatial.Beta documentation built on July 1, 2026, 5:07 p.m.