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] 0.9723646 0.01988546 0.9201079 0.9646390 0.9774696 0.9857622 0.9945419
#> mu[2,1] 0.9504942 0.03502089 0.8630018 0.9374191 0.9594256 0.9741599 0.9897589
#> mu[3,1] 0.9404827 0.04303135 0.8381143 0.9232752 0.9506896 0.9693902 0.9868566
#> mu[4,1] 0.9677085 0.02480553 0.9019329 0.9593819 0.9746669 0.9838332 0.9937106
#> mu[5,1] 0.9384048 0.05155455 0.8004536 0.9211984 0.9519668 0.9726031 0.9891087
#> mu[1,2] 0.9711678 0.02332950 0.9099700 0.9643911 0.9772097 0.9854531 0.9946645
#> mu[2,2] 0.9620485 0.02922454 0.8832680 0.9528096 0.9699462 0.9816409 0.9931068
#> mu[3,2] 0.9194822 0.05957849 0.7495519 0.8995691 0.9362532 0.9589887 0.9842574
#> mu[4,2] 0.9784132 0.01757202 0.9343099 0.9723248 0.9835214 0.9897303 0.9962552
#> mu[5,2] 0.9393995 0.04227668 0.8276464 0.9231419 0.9503435 0.9680730 0.9872528
#> mu[1,3] 0.9697070 0.02613028 0.9053255 0.9618591 0.9769549 0.9862914 0.9947748
#> mu[2,3] 0.8631422 0.08080947 0.6527226 0.8248033 0.8804411 0.9213678 0.9650013
#> mu[3,3] 0.9527766 0.03312935 0.8691812 0.9392385 0.9610126 0.9754243 0.9906854
#> mu[4,3] 0.9588217 0.02935259 0.8826801 0.9478538 0.9658777 0.9785639 0.9917609
#> mu[5,3] 0.9180031 0.05377716 0.7854486 0.8933838 0.9308135 0.9563594 0.9844536
#> mu[1,4] 0.9565112 0.03063022 0.8770255 0.9443020 0.9641875 0.9776012 0.9908984
#> mu[2,4] 0.9343353 0.04453758 0.8239361 0.9144727 0.9452385 0.9648954 0.9859498
#> mu[3,4] 0.9324975 0.04650926 0.8107264 0.9154400 0.9432929 0.9637524 0.9865727
#> mu[4,4] 0.9749582 0.02061524 0.9197123 0.9687723 0.9810302 0.9882767 0.9958226
#> mu[5,4] 0.8532826 0.10352755 0.5807657 0.8146789 0.8794483 0.9249112 0.9697079
#> mu[1,5] 0.9685318 0.02296780 0.9132705 0.9593471 0.9738331 0.9843447 0.9941896
#> mu[2,5] 0.8845380 0.07616064 0.6805150 0.8564243 0.9037395 0.9363240 0.9746034
#> mu[3,5] 0.9584088 0.02957844 0.8815666 0.9483947 0.9656051 0.9783522 0.9920855
#> mu[4,5] 0.9322914 0.04443227 0.8145631 0.9129610 0.9425996 0.9635384 0.9858808
#> mu[5,5] 0.8656492 0.08341843 0.6587511 0.8264686 0.8841106 0.9270130 0.9668841

Coefficient Estimation

result$coefficient
#>          Mean        SD      2.5%       25%      50%      75%    97.5%
#> b[0] 1.957370 0.3994095 1.1508246 1.7048597 1.949409 2.223458 2.748593
#> b[1] 1.117109 0.4837017 0.1651149 0.7962683 1.102792 1.441359 2.068929
#> b[2] 1.147147 0.4666575 0.2191646 0.8366313 1.128705 1.437442 2.093535

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. 
#> 0.0003088 0.0006828 0.0012265 0.0023287 0.0026579 0.0107180

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.796   2.695   3.684   4.668   5.494  12.133

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.   :0.8533  
#>  1st Qu.:0.9702   1st Qu.:0.9323  
#>  Median :1.0000   Median :0.9505  
#>  Mean   :0.9423   Mean   :0.9385  
#>  3rd Qu.:1.0000   3rd Qu.:0.9677  
#>  Max.   :1.0000   Max.   :0.9784
MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir              MSE_HB         
#>  Min.   :0.0004401   Min.   :0.0003088  
#>  1st Qu.:0.0036464   1st Qu.:0.0006828  
#>  Median :0.0228563   Median :0.0012265  
#>  Mean   :0.0256965   Mean   :0.0023287  
#>  3rd Qu.:0.0428368   3rd Qu.:0.0026579  
#>  Max.   :0.0887137   Max.   :0.0107180
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.   : 1.796  
#>  1st Qu.: 6.039   1st Qu.: 2.695  
#>  Median :15.118   Median : 3.684  
#>  Mean   :16.266   Mean   : 4.668  
#>  3rd Qu.:21.629   3rd Qu.: 5.494  
#>  Max.   :59.741   Max.   :12.133