An Application to HB Rao yu Model On sampel dataset

Load package and data

library(saeHB.panel)
data("dataPanel")

Fitting Model

area = max(dataPanel[,2])
period = max(dataPanel[,3])
vardir = dataPanel[,4]
result=Panel(ydi~xdi1+xdi2,area=area, period=period, vardir=vardir ,iter.mcmc = 10000,thin=5,burn.in = 1000,data=dataPanel)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 100
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 1045
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 100
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 1045
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 100
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 1045
#> 
#> Initializing model

Extract mean estimation

Estimation

result$Est
#>               MEAN        SD      2.5%       25%       50%       75%     97.5%
#> mu[1,1]   9.752136 0.6124659  8.609981  9.323923  9.736431 10.164796 10.963274
#> mu[2,1]   5.801203 0.7309269  4.367575  5.325107  5.795131  6.279402  7.274722
#> mu[3,1]   6.858141 0.5687987  5.797578  6.485633  6.845016  7.218864  7.985506
#> mu[4,1]  10.581704 0.6432533  9.333173 10.149241 10.585915 11.002166 11.829277
#> mu[5,1]   8.798723 0.6010973  7.584619  8.410607  8.805575  9.202984  9.989943
#> mu[6,1]   7.298191 0.5729346  6.165684  6.910407  7.319978  7.684776  8.371344
#> mu[7,1]   7.045174 0.7349421  5.604417  6.554623  7.033682  7.534953  8.533297
#> mu[8,1]   9.768334 0.6295971  8.512256  9.352599  9.774879 10.184547 11.041561
#> mu[9,1]   5.322008 0.6378247  4.062486  4.904209  5.315432  5.753291  6.559807
#> mu[10,1]  6.193670 0.6510411  4.940262  5.771715  6.201241  6.619997  7.495059
#> mu[11,1]  4.793837 0.5450891  3.735246  4.428616  4.785507  5.158345  5.907330
#> mu[12,1]  7.251186 0.5617443  6.104048  6.876969  7.264450  7.635493  8.325727
#> mu[13,1]  8.359093 0.6621224  7.042852  7.929061  8.354730  8.828422  9.641971
#> mu[14,1]  7.645729 0.5138700  6.602750  7.298795  7.642554  7.994811  8.652333
#> mu[15,1]  7.859000 0.5611347  6.773308  7.488308  7.846521  8.238432  8.934363
#> mu[16,1]  4.128804 0.5621926  3.009283  3.759037  4.132867  4.503353  5.234996
#> mu[17,1]  4.774395 0.7167687  3.404219  4.276326  4.761153  5.287048  6.118600
#> mu[18,1]  4.985327 0.6080561  3.755835  4.609342  4.977473  5.374385  6.213731
#> mu[19,1]  8.041941 0.5741725  6.894807  7.666357  8.035900  8.427448  9.178695
#> mu[20,1] 10.208848 0.6243478  9.011281  9.782419 10.208382 10.613351 11.406783
#> mu[1,2]   7.642568 0.6912977  6.303438  7.181564  7.658748  8.111204  9.020948
#> mu[2,2]   5.232766 0.6368340  3.964604  4.796478  5.232430  5.650177  6.490149
#> mu[3,2]   6.396484 0.6162629  5.196491  5.981919  6.406532  6.801545  7.610228
#> mu[4,2]   5.515802 0.5752741  4.392696  5.138365  5.531801  5.903169  6.596848
#> mu[5,2]  11.352661 0.5122295 10.359392 11.011682 11.352621 11.688131 12.344208
#> mu[6,2]   6.859733 0.6603307  5.575311  6.413047  6.882296  7.305056  8.164053
#> mu[7,2]   4.928224 0.6976758  3.479781  4.452407  4.938737  5.427567  6.221512
#> mu[8,2]   6.667404 0.7609844  5.185700  6.128314  6.689247  7.213081  8.140416
#> mu[9,2]   7.173016 0.6191522  5.967218  6.772633  7.173454  7.588003  8.404412
#> mu[10,2]  9.046880 0.7425420  7.608971  8.557280  9.037421  9.539712 10.513685
#> mu[11,2]  8.342091 0.5994254  7.207054  7.935187  8.331874  8.734188  9.543230
#> mu[12,2]  6.197042 0.6166748  4.932807  5.787667  6.206670  6.605289  7.401428
#> mu[13,2]  8.648147 0.6222672  7.401633  8.231000  8.634532  9.073373  9.840293
#> mu[14,2]  7.640987 0.6202007  6.444048  7.221241  7.646882  8.053025  8.866613
#> mu[15,2] 10.023599 0.6104519  8.806940  9.606923 10.021618 10.448493 11.189938
#> mu[16,2]  8.046220 0.5203763  7.035455  7.714451  8.040082  8.380397  9.048101
#> mu[17,2] 10.026864 0.5919834  8.918618  9.619610 10.007817 10.432482 11.212877
#> mu[18,2]  7.733113 0.5805454  6.564761  7.348397  7.730044  8.140158  8.855878
#> mu[19,2]  8.845267 0.6512973  7.609042  8.409485  8.851275  9.283214 10.112193
#> mu[20,2]  8.532086 0.5950901  7.325853  8.131277  8.540279  8.930683  9.658758
#> mu[1,3]  10.458987 0.5049596  9.467370 10.112045 10.452075 10.797381 11.495039
#> mu[2,3]   8.306386 0.5697999  7.156087  7.929692  8.300141  8.696994  9.403502
#> mu[3,3]   7.311878 0.5324306  6.272986  6.948223  7.302157  7.668975  8.339722
#> mu[4,3]   5.672559 0.6722076  4.413225  5.205020  5.659222  6.127819  7.039520
#> mu[5,3]   8.722088 0.6625361  7.429211  8.263213  8.738841  9.165897 10.032074
#> mu[6,3]   8.340975 0.5854464  7.183491  7.944676  8.330770  8.731775  9.487852
#> mu[7,3]   4.897288 0.6522877  3.658184  4.456548  4.895338  5.353783  6.161907
#> mu[8,3]  10.264373 0.5753236  9.118180  9.888915 10.265643 10.655508 11.368562
#> mu[9,3]   9.683942 0.6370450  8.447277  9.244335  9.690344 10.104347 10.925345
#> mu[10,3]  8.959605 0.6941541  7.541456  8.502210  8.956843  9.410482 10.304983
#> mu[11,3]  8.045272 0.6230408  6.706032  7.647451  8.064941  8.468146  9.203010
#> mu[12,3]  8.141284 0.6797666  6.814727  7.672620  8.143289  8.613034  9.441586
#> mu[13,3]  8.767303 0.7212964  7.350859  8.276934  8.755779  9.261225 10.199863
#> mu[14,3]  8.765207 0.6563833  7.459108  8.325459  8.784806  9.190914 10.006986
#> mu[15,3]  8.410449 0.6376941  7.195252  7.975103  8.400425  8.834605  9.645621
#> mu[16,3]  3.853502 0.6257575  2.630678  3.448299  3.861271  4.272773  5.055215
#> mu[17,3]  9.599412 0.5733406  8.420623  9.225125  9.617020  9.984542 10.698477
#> mu[18,3]  5.874432 0.6802476  4.532222  5.429343  5.854807  6.317597  7.240923
#> mu[19,3]  8.103983 0.4839114  7.173966  7.776756  8.098452  8.417259  9.066292
#> mu[20,3]  5.541383 0.6975923  4.159091  5.074002  5.559757  6.032522  6.852095
#> mu[1,4]   6.325169 0.5450947  5.258529  5.951589  6.318683  6.688744  7.348998
#> mu[2,4]   5.047717 0.6524987  3.781742  4.604759  5.051208  5.482710  6.297373
#> mu[3,4]   7.901430 0.6462716  6.624330  7.466352  7.914908  8.336323  9.142926
#> mu[4,4]   7.506377 0.5898328  6.399958  7.109784  7.495731  7.926312  8.626216
#> mu[5,4]   8.337158 0.6852664  6.989692  7.879843  8.331808  8.814511  9.682981
#> mu[6,4]   7.339889 0.6739121  5.999174  6.898068  7.350481  7.811748  8.587974
#> mu[7,4]   8.673375 0.5785137  7.522647  8.288404  8.684442  9.064596  9.805344
#> mu[8,4]   6.668995 0.6269314  5.456354  6.257542  6.661650  7.074012  7.900555
#> mu[9,4]   4.488113 0.6686146  3.143271  4.048468  4.502463  4.948500  5.781034
#> mu[10,4]  7.619808 0.6013100  6.451413  7.204990  7.619711  8.029753  8.808889
#> mu[11,4]  6.135479 0.5692275  5.032192  5.746322  6.139935  6.497904  7.288834
#> mu[12,4]  7.478214 0.5835217  6.415812  7.076661  7.465343  7.873691  8.645476
#> mu[13,4]  9.560203 0.5575599  8.422277  9.194787  9.557173  9.945789 10.662804
#> mu[14,4]  8.301249 0.4844674  7.356745  7.968952  8.293394  8.607174  9.251752
#> mu[15,4]  9.977907 0.7405957  8.576440  9.490480  9.949042 10.453777 11.437915
#> mu[16,4]  2.988291 0.5645520  1.862218  2.602842  3.003986  3.375541  4.043800
#> mu[17,4]  6.278503 0.6532120  4.988435  5.828989  6.296636  6.726917  7.551022
#> mu[18,4]  3.697684 0.5439708  2.598984  3.338845  3.701209  4.069050  4.760269
#> mu[19,4]  7.986930 0.5746981  6.815116  7.604943  7.974848  8.368753  9.120709
#> mu[20,4]  6.782302 0.6003881  5.632427  6.378508  6.780111  7.180121  7.954862
#> mu[1,5]   8.073887 0.6637309  6.703122  7.659978  8.097506  8.514359  9.345665
#> mu[2,5]   8.011364 0.6422046  6.780716  7.576589  7.991577  8.454892  9.251322
#> mu[3,5]   3.926218 0.5983334  2.762718  3.527956  3.932377  4.335054  5.063799
#> mu[4,5]   7.472436 0.5919003  6.299083  7.084743  7.465183  7.852019  8.676658
#> mu[5,5]   8.345445 0.5530180  7.254370  7.978404  8.362646  8.718580  9.426851
#> mu[6,5]  10.961103 0.6028754  9.810578 10.556025 10.948844 11.359035 12.170743
#> mu[7,5]   8.146307 0.8039913  6.597035  7.626960  8.136255  8.651029  9.729764
#> mu[8,5]   8.177322 0.6861243  6.837553  7.713267  8.178094  8.641857  9.549685
#> mu[9,5]   4.899703 0.4980033  3.940790  4.557847  4.896511  5.243789  5.895168
#> mu[10,5]  7.353186 0.5816796  6.207749  6.963996  7.363834  7.748520  8.456249
#> mu[11,5]  5.440817 0.5470165  4.350330  5.075553  5.455526  5.808367  6.506125
#> mu[12,5]  9.479360 0.6420196  8.279229  9.013894  9.473832  9.926340 10.734548
#> mu[13,5] 11.166559 0.7608682  9.671523 10.627655 11.168319 11.669159 12.676869
#> mu[14,5] 10.096374 0.5638302  9.019645  9.717334 10.095405 10.481477 11.215986
#> mu[15,5]  7.601468 0.5407422  6.527761  7.226207  7.603056  7.958274  8.636101
#> mu[16,5]  6.389745 0.6884731  5.119944  5.894932  6.403136  6.880268  7.735017
#> mu[17,5]  7.715552 0.7230206  6.309554  7.258293  7.742355  8.191344  9.151261
#> mu[18,5]  7.472576 0.6605719  6.201693  7.005696  7.477455  7.926210  8.751628
#> mu[19,5]  9.619481 0.6043400  8.419692  9.219359  9.616381 10.026470 10.812570
#> mu[20,5]  8.977355 0.6379558  7.738110  8.533683  8.974069  9.411419 10.176824

Coefficient Estimation

result$coefficient
#>            Mean        SD      2.5%        25%        50%        75%     97.5%
#> b[0] -0.1270417 0.2984369 -0.721951 -0.3245736 -0.1324369 0.07419669 0.4568618
#> b[1]  2.1831679 0.1799421  1.830949  2.0629472  2.1820772 2.30181042 2.5397202
#> b[2]  2.2730059 0.1032029  2.070343  2.2045506  2.2710199 2.34258539 2.4762505

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. 
#>  0.2342  0.3294  0.3818  0.3890  0.4369  0.6464

Extract RSE

RSE_HB=sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   4.512   6.946   7.921   8.799  10.081  18.892

You can compare with direct estimator

y_dir=dataPanel[,1]
y_HB=result$Est$MEAN
y=as.data.frame(cbind(y_dir,y_HB))
summary(y)
#>      y_dir             y_HB       
#>  Min.   : 2.555   Min.   : 2.988  
#>  1st Qu.: 6.144   1st Qu.: 6.314  
#>  Median : 7.684   Median : 7.724  
#>  Mean   : 7.562   Mean   : 7.565  
#>  3rd Qu.: 8.822   3rd Qu.: 8.733  
#>  Max.   :12.835   Max.   :11.353
MSE_dir=dataPanel[,4]
MSE=as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir           MSE_HB      
#>  Min.   :0.3133   Min.   :0.2342  
#>  1st Qu.:0.4971   1st Qu.:0.3294  
#>  Median :0.6294   Median :0.3818  
#>  Mean   :0.6800   Mean   :0.3890  
#>  3rd Qu.:0.7749   3rd Qu.:0.4369  
#>  Max.   :1.6929   Max.   :0.6464
RSE_dir=sqrt(MSE_dir)/y_dir*100
RSE=as.data.frame(cbind(MSE_dir, MSE_HB))
summary(RSE)
#>     MSE_dir           MSE_HB      
#>  Min.   :0.3133   Min.   :0.2342  
#>  1st Qu.:0.4971   1st Qu.:0.3294  
#>  Median :0.6294   Median :0.3818  
#>  Mean   :0.6800   Mean   :0.3890  
#>  3rd Qu.:0.7749   3rd Qu.:0.4369  
#>  Max.   :1.6929   Max.   :0.6464