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

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] 0.9713731 0.02328292 0.9079123 0.9625973 0.9777934 0.9868270 0.9960250
#> mu[2,1] 0.9569757 0.03324846 0.8755690 0.9460993 0.9657183 0.9787156 0.9926591
#> mu[3,1] 0.9393633 0.04957912 0.7970808 0.9236493 0.9520683 0.9707649 0.9901039
#> mu[4,1] 0.9658961 0.02798058 0.8913413 0.9560956 0.9737534 0.9846068 0.9950255
#> mu[5,1] 0.9385088 0.05338035 0.7846902 0.9230321 0.9543239 0.9729578 0.9901186
#> mu[1,2] 0.9701842 0.02503484 0.9044870 0.9614728 0.9766194 0.9862512 0.9955072
#> mu[2,2] 0.9652112 0.02802308 0.8904712 0.9554232 0.9725827 0.9833270 0.9942910
#> mu[3,2] 0.9181959 0.06386394 0.7433878 0.8940435 0.9361087 0.9601812 0.9858488
#> mu[4,2] 0.9763548 0.02105958 0.9189624 0.9700028 0.9827027 0.9903026 0.9969880
#> mu[5,2] 0.9424182 0.04372767 0.8352181 0.9278862 0.9531731 0.9697931 0.9897842
#> mu[1,3] 0.9687955 0.02724247 0.8923014 0.9611683 0.9762906 0.9867519 0.9958210
#> mu[2,3] 0.8727048 0.08015318 0.6633978 0.8365484 0.8907476 0.9288464 0.9713757
#> mu[3,3] 0.9589801 0.03034478 0.8803231 0.9463271 0.9666111 0.9799933 0.9936224
#> mu[4,3] 0.9557647 0.03383615 0.8688497 0.9429073 0.9652019 0.9791047 0.9935937
#> mu[5,3] 0.9257019 0.04910279 0.7971302 0.9066043 0.9372174 0.9590961 0.9849859
#> mu[1,4] 0.9538652 0.03615603 0.8566988 0.9403275 0.9632428 0.9784399 0.9931700
#> mu[2,4] 0.9392213 0.04329936 0.8217429 0.9241023 0.9499753 0.9683103 0.9885660
#> mu[3,4] 0.9344597 0.04617361 0.8124747 0.9169184 0.9454070 0.9661673 0.9876194
#> mu[4,4] 0.9724688 0.02626781 0.8988352 0.9651721 0.9801582 0.9885622 0.9965840
#> mu[5,4] 0.8539960 0.10516566 0.5752763 0.8125300 0.8838448 0.9258455 0.9687237
#> mu[1,5] 0.9656977 0.02847380 0.8953434 0.9565754 0.9734931 0.9845512 0.9953143
#> mu[2,5] 0.8897345 0.07813767 0.6765461 0.8600749 0.9112217 0.9437139 0.9776705
#> mu[3,5] 0.9598528 0.03131756 0.8717586 0.9484348 0.9682738 0.9808066 0.9937804
#> mu[4,5] 0.9330710 0.04980811 0.7949374 0.9141878 0.9453854 0.9670004 0.9890399
#> mu[5,5] 0.8682562 0.08506625 0.6421667 0.8302648 0.8900370 0.9289515 0.9685002

Coefficient Estimation

result$coefficient
#>          Mean        SD      2.5%       25%      50%      75%    97.5%
#> b[0] 2.005972 0.4063064 1.2091470 1.7307123 1.998160 2.277578 2.814624
#> b[1] 1.112682 0.5038805 0.1361614 0.7630400 1.110898 1.461489 2.102108
#> b[2] 1.120562 0.4591467 0.2195766 0.8216082 1.109322 1.440124 2.019678

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. 
#> 0.0004435 0.0007853 0.0013073 0.0024762 0.0024808 0.0110598

Extract RSE

RSE_HB<-sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   2.157   2.903   3.790   4.858   5.338  12.315

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.   :0.8540  
#>  1st Qu.:0.9702   1st Qu.:0.9331  
#>  Median :1.0000   Median :0.9539  
#>  Mean   :0.9423   Mean   :0.9399  
#>  3rd Qu.:1.0000   3rd Qu.:0.9657  
#>  Max.   :1.0000   Max.   :0.9764
MSE_dir<-dataPanelbeta[,4]
MSE<-as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir              MSE_HB         
#>  Min.   :0.0004401   Min.   :0.0004435  
#>  1st Qu.:0.0036464   1st Qu.:0.0007853  
#>  Median :0.0228563   Median :0.0013073  
#>  Mean   :0.0256965   Mean   :0.0024762  
#>  3rd Qu.:0.0428368   3rd Qu.:0.0024808  
#>  Max.   :0.0887137   Max.   :0.0110598
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.   : 2.157  
#>  1st Qu.: 6.039   1st Qu.: 2.903  
#>  Median :15.118   Median : 3.790  
#>  Mean   :16.266   Mean   : 4.858  
#>  3rd Qu.:21.629   3rd Qu.: 5.338  
#>  Max.   :59.741   Max.   :12.315

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