saeHB.panel.beta

Several functions are provided for small area estimation at the area level using the hierarchical bayesian (HB) method with panel data under beta distribution for variable interest. This package also provides a dataset produced by data generation. The ‘rjags’ package is employed to obtain parameter estimates. Model-based estimators involve the HB estimators, which include the mean and the variation of the mean. For the reference, see Rao and Molina (2015, ISBN:978-1-118-73578-7).

Author

Dian Rahmawati Salis, Azka Ubaidillah

Maintaner

Dian Rahmawati Salis dianrahmawatisalis03@gmail.com

Function

• RaoYuAr1.beta() This function gives estimation of y using Hierarchical Bayesian Rao Yu Model under Beta distribution
• Panel.beta() This function gives estimation of y using Hierarchical Bayesian Rao Yu Model under Beta distribution when rho = 0

Installation

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

# install.packages("devtools")
devtools::install_github("DianRahmawatiSalis/saeHB.panel.beta")
#> Skipping install of 'saeHB.panel.beta' from a github remote, the SHA1 (fe67bb61) has not changed since last install.
#>   Use `force = TRUE` to force installation

Example

This is a basic example which shows you how to solve a common problem:

library(saeHB.panel.beta)
data("dataPanelbeta")
dataPanelbeta <- dataPanelbeta[1:25,] #for the example only use part of the dataset
formula <- ydi~xdi1+xdi2 
area <- max(dataPanelbeta[,2])
period <- max(dataPanelbeta[,3])
result<-Panel.beta(formula,area=area, period=period ,iter.mcmc = 10000,thin=5,burn.in = 1000,data=dataPanelbeta)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 25
#>    Unobserved stochastic nodes: 62
#>    Total graph size: 359
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 25
#>    Unobserved stochastic nodes: 62
#>    Total graph size: 359
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 25
#>    Unobserved stochastic nodes: 62
#>    Total graph size: 359
#> 
#> Initializing model

Extract area mean estimation

result$Est
#>              MEAN         SD      2.5%       25%       50%       75%     97.5%
#> mu[1,1] 0.9745402 0.02043167 0.9242318 0.9671592 0.9798158 0.9874685 0.9962959
#> mu[2,1] 0.9529850 0.03378111 0.8687035 0.9391639 0.9606148 0.9762169 0.9920275
#> mu[3,1] 0.9416476 0.04334522 0.8257088 0.9271068 0.9515223 0.9695644 0.9886169
#> mu[4,1] 0.9707650 0.02343253 0.9100078 0.9631909 0.9768535 0.9858918 0.9956301
#> mu[5,1] 0.9392371 0.05230504 0.7937674 0.9226590 0.9552521 0.9731984 0.9904665
#> mu[1,2] 0.9730519 0.02075604 0.9151144 0.9651103 0.9784012 0.9872296 0.9955669
#> mu[2,2] 0.9644632 0.02716892 0.8916524 0.9553131 0.9715651 0.9825200 0.9941719
#> mu[3,2] 0.9190929 0.05909138 0.7582093 0.8974757 0.9337880 0.9586956 0.9846804
#> mu[4,2] 0.9806928 0.01626167 0.9376644 0.9753268 0.9851461 0.9914809 0.9977165
#> mu[5,2] 0.9414686 0.04347486 0.8300576 0.9253633 0.9528456 0.9703039 0.9899214
#> mu[1,3] 0.9727516 0.02296491 0.9084448 0.9653176 0.9785098 0.9877710 0.9961441
#> mu[2,3] 0.8650717 0.08258513 0.6512432 0.8283691 0.8813968 0.9243896 0.9664624
#> mu[3,3] 0.9547238 0.03083291 0.8773217 0.9424085 0.9616815 0.9760577 0.9921776
#> mu[4,3] 0.9604722 0.02744216 0.8909641 0.9491892 0.9671605 0.9790931 0.9939556
#> mu[5,3] 0.9185326 0.05607900 0.7741958 0.8964084 0.9307007 0.9567351 0.9842448
#> mu[1,4] 0.9584364 0.03167149 0.8737031 0.9456576 0.9671949 0.9791662 0.9929711
#> mu[2,4] 0.9360060 0.04438870 0.8225671 0.9184701 0.9461601 0.9665405 0.9865605
#> mu[3,4] 0.9350573 0.04267082 0.8231444 0.9169837 0.9452816 0.9656088 0.9877537
#> mu[4,4] 0.9774635 0.01875693 0.9297391 0.9713515 0.9826057 0.9896004 0.9971276
#> mu[5,4] 0.8457488 0.10996071 0.5617364 0.8037121 0.8748879 0.9238268 0.9705472
#> mu[1,5] 0.9700137 0.02447969 0.9072987 0.9622983 0.9762001 0.9854658 0.9954380
#> mu[2,5] 0.8870202 0.07028000 0.7023668 0.8552202 0.9036043 0.9369899 0.9772847
#> mu[3,5] 0.9605815 0.03019414 0.8833168 0.9502352 0.9675795 0.9797505 0.9936401
#> mu[4,5] 0.9366477 0.04333110 0.8299269 0.9170241 0.9469230 0.9665555 0.9886723
#> mu[5,5] 0.8613721 0.08544666 0.6459957 0.8197358 0.8803638 0.9229781 0.9675223

Extract coefficient estimation

result$coefficient
#>          Mean        SD      2.5%       25%      50%      75%    97.5%
#> b[0] 1.932909 0.3961688 1.1738158 1.6717925 1.933390 2.195974 2.704684
#> b[1] 1.188665 0.5270641 0.1656371 0.8391137 1.179424 1.531993 2.244406
#> b[2] 1.206062 0.4730080 0.3134756 0.8882160 1.197545 1.528039 2.165126

Extract area random effect variance

result$refVar
#> [1] 0.5076331

Extract MSE

MSE_HB<-result$Est$SD^2
summary(MSE_HB)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> 0.0002644 0.0005993 0.0011412 0.0023440 0.0027358 0.0120914

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.658   2.524   3.545   4.626   5.569  13.002

Extract convergence diagnostic using geweke test

result$convergence.test
#>              b[0]      b[1]     b[2]
#> Z-score 0.7387093 0.1672595 1.760278

References

• Rao, J.N.K & Molina. (2015). Small Area Estimation 2nd Edition. New York: John Wiley and Sons, Inc.
• Torabi, M., & Shokoohi, F. (2012). Likelihood inference in small area estimation by combining time-series and cross-sectional data. Journal of Multivariate Analysis, 111, 213–221. https://doi.org/10.1016/j.jmva.2012.05.016