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] 0.9710584 0.02057894 0.9177469 0.9632797 0.9756463 0.9843771 0.9942389
#> mu[2,1] 0.9476881 0.03566282 0.8562910 0.9331861 0.9566613 0.9715654 0.9887488
#> mu[3,1] 0.9368259 0.04668508 0.8066020 0.9212962 0.9495818 0.9666496 0.9878398
#> mu[4,1] 0.9662667 0.02601251 0.8976891 0.9578114 0.9726297 0.9827797 0.9932524
#> mu[5,1] 0.9333180 0.05618404 0.7875190 0.9145950 0.9497704 0.9700658 0.9884955
#> mu[1,2] 0.9697359 0.02231845 0.9133271 0.9615597 0.9754625 0.9845689 0.9934183
#> mu[2,2] 0.9596833 0.02967141 0.8767241 0.9498192 0.9667908 0.9791563 0.9924301
#> mu[3,2] 0.9134167 0.06140640 0.7454328 0.8914171 0.9295133 0.9536797 0.9806486
#> mu[4,2] 0.9760770 0.02027957 0.9260676 0.9692248 0.9820046 0.9890304 0.9961890
#> mu[5,2] 0.9388537 0.04141240 0.8308500 0.9217973 0.9483509 0.9667458 0.9868595
#> mu[1,3] 0.9682430 0.02370778 0.9088528 0.9595484 0.9745465 0.9843127 0.9941857
#> mu[2,3] 0.8610205 0.08105992 0.6563724 0.8221908 0.8784072 0.9180886 0.9648962
#> mu[3,3] 0.9494131 0.03540999 0.8669563 0.9354331 0.9578458 0.9730972 0.9893542
#> mu[4,3] 0.9560441 0.03070449 0.8791194 0.9439463 0.9627293 0.9762716 0.9900970
#> mu[5,3] 0.9143723 0.05661790 0.7795663 0.8891933 0.9279793 0.9527958 0.9812689
#> mu[1,4] 0.9542990 0.03173926 0.8685759 0.9412522 0.9619720 0.9762551 0.9916298
#> mu[2,4] 0.9306687 0.04577709 0.8140361 0.9091331 0.9428566 0.9634563 0.9848878
#> mu[3,4] 0.9272459 0.04748791 0.8054690 0.9105354 0.9390695 0.9591337 0.9835582
#> mu[4,4] 0.9730592 0.02136365 0.9141024 0.9668098 0.9786095 0.9872150 0.9951920
#> mu[5,4] 0.8505676 0.10246820 0.5684405 0.8117544 0.8795844 0.9201375 0.9657176
#> mu[1,5] 0.9659128 0.02552295 0.8971741 0.9566952 0.9719825 0.9823286 0.9934743
#> mu[2,5] 0.8836532 0.07525011 0.6996923 0.8513415 0.9009438 0.9346673 0.9734696
#> mu[3,5] 0.9555719 0.03202953 0.8709708 0.9436078 0.9640848 0.9765593 0.9913267
#> mu[4,5] 0.9307952 0.04531389 0.8230618 0.9128414 0.9402726 0.9618390 0.9855510
#> mu[5,5] 0.8574624 0.09037705 0.6204258 0.8223576 0.8802195 0.9175263 0.9637740

Coefficient Estimation

result$coefficient
#>          Mean        SD        2.5%       25%      50%      75%    97.5%
#> b[0] 1.932906 0.3893955 1.197039876 1.6713883 1.923383 2.182387 2.723243
#> b[1] 1.070334 0.5375531 0.009439937 0.7243931 1.055136 1.416719 2.151125
#> b[2] 1.132315 0.4807609 0.210924826 0.8118513 1.131265 1.456961 2.058949

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. 
#> 0.0004113 0.0006767 0.0012718 0.0024558 0.0031566 0.0104997

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   2.078   2.692   3.763   4.828   6.020  12.047

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.   :0.8506  
#>  1st Qu.:0.9702   1st Qu.:0.9272  
#>  Median :1.0000   Median :0.9477  
#>  Mean   :0.9423   Mean   :0.9357  
#>  3rd Qu.:1.0000   3rd Qu.:0.9659  
#>  Max.   :1.0000   Max.   :0.9761
MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir              MSE_HB         
#>  Min.   :0.0004401   Min.   :0.0004113  
#>  1st Qu.:0.0036464   1st Qu.:0.0006767  
#>  Median :0.0228563   Median :0.0012718  
#>  Mean   :0.0256965   Mean   :0.0024558  
#>  3rd Qu.:0.0428368   3rd Qu.:0.0031566  
#>  Max.   :0.0887137   Max.   :0.0104997
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.   : 2.078  
#>  1st Qu.: 6.039   1st Qu.: 2.692  
#>  Median :15.118   Median : 3.763  
#>  Mean   :16.266   Mean   : 4.828  
#>  3rd Qu.:21.629   3rd Qu.: 6.020  
#>  Max.   :59.741   Max.   :12.047