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: 42
#>    Total graph size: 339
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 25
#>    Unobserved stochastic nodes: 42
#>    Total graph size: 339
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 25
#>    Unobserved stochastic nodes: 42
#>    Total graph size: 339
#> 
#> Initializing model

Extract mean estimation

Estimation

result$Est
#>              MEAN         SD      2.5%       25%       50%       75%     97.5%
#> mu[1,1] 0.9713957 0.02433871 0.9143929 0.9633304 0.9777242 0.9866414 0.9962473
#> mu[2,1] 0.9580010 0.03212776 0.8712837 0.9470552 0.9664510 0.9785057 0.9921969
#> mu[3,1] 0.9383701 0.05280326 0.7956264 0.9240364 0.9525547 0.9706921 0.9895314
#> mu[4,1] 0.9648086 0.03007377 0.8823714 0.9552219 0.9730418 0.9840946 0.9945929
#> mu[5,1] 0.9360625 0.05572265 0.7838854 0.9202336 0.9523564 0.9709396 0.9888169
#> mu[1,2] 0.9696177 0.02468299 0.9061383 0.9612052 0.9766512 0.9859674 0.9955490
#> mu[2,2] 0.9659763 0.02775714 0.8928422 0.9565177 0.9727674 0.9837246 0.9941634
#> mu[3,2] 0.9198703 0.06268703 0.7492873 0.9012890 0.9381876 0.9600665 0.9856970
#> mu[4,2] 0.9754150 0.02431120 0.9120835 0.9693692 0.9822373 0.9899630 0.9970006
#> mu[5,2] 0.9440012 0.04066542 0.8473476 0.9297397 0.9537064 0.9699746 0.9893101
#> mu[1,3] 0.9687984 0.02788204 0.8948663 0.9614923 0.9762707 0.9863422 0.9958964
#> mu[2,3] 0.8738200 0.08064478 0.6624012 0.8414712 0.8919430 0.9297159 0.9701729
#> mu[3,3] 0.9605108 0.02895871 0.8790897 0.9497376 0.9679034 0.9802633 0.9934799
#> mu[4,3] 0.9560835 0.03470147 0.8598127 0.9447551 0.9650232 0.9784957 0.9935205
#> mu[5,3] 0.9300201 0.04782236 0.8184490 0.9113753 0.9409107 0.9612108 0.9862697
#> mu[1,4] 0.9516297 0.04131640 0.8332512 0.9394271 0.9634047 0.9779832 0.9926483
#> mu[2,4] 0.9391893 0.04508967 0.8192724 0.9229162 0.9515609 0.9687701 0.9883871
#> mu[3,4] 0.9365444 0.04613908 0.8122724 0.9182601 0.9487098 0.9676487 0.9883243
#> mu[4,4] 0.9726462 0.02487536 0.9059785 0.9653861 0.9797950 0.9882836 0.9963833
#> mu[5,4] 0.8556849 0.10405428 0.5899622 0.8142326 0.8889341 0.9274962 0.9695810
#> mu[1,5] 0.9655930 0.02797952 0.8894854 0.9570538 0.9732329 0.9841548 0.9949500
#> mu[2,5] 0.8900625 0.07624848 0.6977548 0.8618737 0.9082344 0.9403927 0.9756348
#> mu[3,5] 0.9590975 0.03319855 0.8694306 0.9489825 0.9673564 0.9802910 0.9937005
#> mu[4,5] 0.9330082 0.05068706 0.8029932 0.9143721 0.9468291 0.9660900 0.9885444
#> mu[5,5] 0.8695013 0.09196205 0.6162615 0.8395680 0.8932854 0.9286103 0.9711836

Coefficient Estimation

result$coefficient
#>          Mean        SD      2.5%       25%      50%      75%    97.5%
#> b[0] 2.047287 0.3885552 1.2735230 1.7880747 2.055952 2.314104 2.768787
#> b[1] 1.144158 0.5166463 0.1554118 0.7854928 1.126240 1.498182 2.146272
#> b[2] 1.069515 0.4586804 0.1873014 0.7515532 1.066693 1.377383 1.985275

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. 
#> 0.0005910 0.0007829 0.0016537 0.0025451 0.0027882 0.0108273

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   2.492   2.898   4.308   4.928   5.627  12.160

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.   :0.8557  
#>  1st Qu.:0.9702   1st Qu.:0.9330  
#>  Median :1.0000   Median :0.9516  
#>  Mean   :0.9423   Mean   :0.9402  
#>  3rd Qu.:1.0000   3rd Qu.:0.9656  
#>  Max.   :1.0000   Max.   :0.9754
MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir              MSE_HB         
#>  Min.   :0.0004401   Min.   :0.0005910  
#>  1st Qu.:0.0036464   1st Qu.:0.0007829  
#>  Median :0.0228563   Median :0.0016537  
#>  Mean   :0.0256965   Mean   :0.0025451  
#>  3rd Qu.:0.0428368   3rd Qu.:0.0027882  
#>  Max.   :0.0887137   Max.   :0.0108273
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.   : 2.492  
#>  1st Qu.: 6.039   1st Qu.: 2.898  
#>  Median :15.118   Median : 4.308  
#>  Mean   :16.266   Mean   : 4.928  
#>  3rd Qu.:21.629   3rd Qu.: 5.627  
#>  Max.   :59.741   Max.   :12.160