An Application to HB Rao yu Model Under Beta Distribution On sampel dataset

Load package and data

library(saeHB.panel.beta)
data("dataPanelbeta")

Fitting Model

dataPanelbeta <- dataPanelbeta[1:25,] #for the example only use part of the dataset
area <- max(dataPanelbeta[,2])
period <- max(dataPanelbeta[,3])
result<-Panel.beta(ydi~xdi1+xdi2,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 mean estimation

Estimation

result$Est
#>              MEAN         SD      2.5%       25%       50%       75%     97.5%
#> mu[1,1] 0.9715606 0.02041852 0.9203568 0.9633999 0.9765683 0.9854062 0.9942387
#> mu[2,1] 0.9477231 0.03722948 0.8546639 0.9335519 0.9571519 0.9721773 0.9885852
#> mu[3,1] 0.9420694 0.04109096 0.8366193 0.9254650 0.9520202 0.9699483 0.9882071
#> mu[4,1] 0.9679009 0.02354598 0.9070196 0.9588508 0.9741587 0.9834968 0.9937798
#> mu[5,1] 0.9398689 0.05074443 0.8071438 0.9234227 0.9539235 0.9725740 0.9901445
#> mu[1,2] 0.9718030 0.02033796 0.9178540 0.9646181 0.9766786 0.9860063 0.9945791
#> mu[2,2] 0.9613276 0.02867886 0.8824150 0.9500238 0.9689116 0.9808281 0.9930026
#> mu[3,2] 0.9218819 0.05496428 0.7731063 0.9010465 0.9363732 0.9590512 0.9837168
#> mu[4,2] 0.9773340 0.01859778 0.9257727 0.9709759 0.9823204 0.9895456 0.9963013
#> mu[5,2] 0.9392130 0.04522412 0.8281190 0.9235998 0.9502550 0.9690026 0.9874561
#> mu[1,3] 0.9699925 0.02413013 0.9095392 0.9621010 0.9760820 0.9851613 0.9948403
#> mu[2,3] 0.8646523 0.07772166 0.6681956 0.8295668 0.8807569 0.9199075 0.9635835
#> mu[3,3] 0.9521936 0.03085478 0.8705490 0.9379794 0.9594410 0.9736315 0.9901888
#> mu[4,3] 0.9579856 0.02793382 0.8870496 0.9467738 0.9645635 0.9768359 0.9916759
#> mu[5,3] 0.9143644 0.05777379 0.7746396 0.8921799 0.9268380 0.9523405 0.9824364
#> mu[1,4] 0.9560309 0.03279288 0.8707281 0.9443073 0.9637896 0.9776447 0.9913856
#> mu[2,4] 0.9318552 0.04686944 0.8108655 0.9151794 0.9439828 0.9634688 0.9846294
#> mu[3,4] 0.9314057 0.04308526 0.8250752 0.9121812 0.9418000 0.9616466 0.9858158
#> mu[4,4] 0.9750315 0.01959234 0.9230244 0.9682083 0.9805433 0.9880159 0.9953955
#> mu[5,4] 0.8574879 0.09453895 0.5972792 0.8187320 0.8814479 0.9253846 0.9662069
#> mu[1,5] 0.9681461 0.02381155 0.9078094 0.9605515 0.9743709 0.9838181 0.9939303
#> mu[2,5] 0.8889299 0.07040826 0.7109140 0.8612449 0.9058258 0.9374863 0.9709366
#> mu[3,5] 0.9569093 0.03210086 0.8726688 0.9462314 0.9649670 0.9778204 0.9917101
#> mu[4,5] 0.9321876 0.04254882 0.8240138 0.9146160 0.9417190 0.9617918 0.9864306
#> mu[5,5] 0.8661576 0.08281186 0.6511093 0.8271177 0.8850069 0.9259076 0.9679304

Coefficient Estimation

result$coefficient
#>          Mean        SD       2.5%       25%      50%      75%    97.5%
#> b[0] 1.990836 0.3974607 1.21969892 1.7210717 1.982474 2.246929 2.754171
#> b[1] 1.072706 0.4971808 0.09933002 0.7384358 1.071070 1.403068 2.060664
#> b[2] 1.160849 0.4937285 0.21198137 0.8083115 1.156328 1.503292 2.115507

Random effect variance estimation

result$refvar
#> NULL

Extract MSE

MSE_HB<-result$Est$SD^2
summary(MSE_HB)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> 0.0003459 0.0005823 0.0013860 0.0021854 0.0025750 0.0089376

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.903   2.488   3.928   4.556   5.399  11.025

You can compare with direct estimator

y_dir<-dataPanelbeta[,1]
y_HB<-result$Est$MEAN
y<-as.data.frame(cbind(y_dir,y_HB))
summary(y)
#>      y_dir             y_HB       
#>  Min.   :0.3836   Min.   :0.8575  
#>  1st Qu.:0.9702   1st Qu.:0.9314  
#>  Median :1.0000   Median :0.9477  
#>  Mean   :0.9423   Mean   :0.9386  
#>  3rd Qu.:1.0000   3rd Qu.:0.9679  
#>  Max.   :1.0000   Max.   :0.9773
MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir              MSE_HB         
#>  Min.   :0.0004401   Min.   :0.0003459  
#>  1st Qu.:0.0036464   1st Qu.:0.0005823  
#>  Median :0.0228563   Median :0.0013860  
#>  Mean   :0.0256965   Mean   :0.0021854  
#>  3rd Qu.:0.0428368   3rd Qu.:0.0025750  
#>  Max.   :0.0887137   Max.   :0.0089376
RSE_dir<-sqrt(MSE_dir)/y_dir*100
RSE<-as.data.frame(cbind(RSE_dir, RSE_HB))
summary(RSE)
#>     RSE_dir           RSE_HB      
#>  Min.   : 2.098   Min.   : 1.903  
#>  1st Qu.: 6.039   1st Qu.: 2.488  
#>  Median :15.118   Median : 3.928  
#>  Mean   :16.266   Mean   : 4.556  
#>  3rd Qu.:21.629   3rd Qu.: 5.399  
#>  Max.   :59.741   Max.   :11.025