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]   9.741839 0.6202458  8.554475  9.325023  9.746682 10.151450 10.931580
#> mu[2,1]   5.784420 0.7669829  4.174867  5.277436  5.826264  6.301858  7.197337
#> mu[3,1]   6.833434 0.5775605  5.661658  6.473097  6.831333  7.224195  7.955092
#> mu[4,1]  10.606610 0.6449334  9.335370 10.167511 10.606367 11.019123 11.890223
#> mu[5,1]   8.826495 0.5955508  7.646089  8.435416  8.824201  9.212493  9.991693
#> mu[6,1]   7.292662 0.5834467  6.034807  6.916271  7.311626  7.696020  8.396765
#> mu[7,1]   7.002753 0.7399025  5.560736  6.476138  7.010654  7.483124  8.472674
#> mu[8,1]   9.798457 0.6482561  8.535174  9.343831  9.802286 10.231168 11.083758
#> mu[9,1]   5.337739 0.6381254  4.146500  4.894602  5.339610  5.777923  6.606633
#> mu[10,1]  6.180391 0.6500427  4.916330  5.732644  6.189837  6.622495  7.434051
#> mu[11,1]  4.812115 0.5723821  3.704590  4.412633  4.807441  5.198342  5.979691
#> mu[12,1]  7.234092 0.5771617  6.053827  6.856033  7.231937  7.624167  8.332102
#> mu[13,1]  8.375923 0.6760842  7.037926  7.937243  8.385126  8.836838  9.671233
#> mu[14,1]  7.653414 0.5007838  6.693626  7.314376  7.642925  8.007585  8.623352
#> mu[15,1]  7.854009 0.5719025  6.770810  7.463627  7.851588  8.229646  9.010081
#> mu[16,1]  4.084637 0.5666490  2.988672  3.713045  4.098420  4.467589  5.183124
#> mu[17,1]  4.788675 0.6831552  3.410549  4.321240  4.784837  5.247887  6.116602
#> mu[18,1]  4.952307 0.6025147  3.797099  4.554260  4.941065  5.348384  6.158747
#> mu[19,1]  8.057966 0.5904431  6.863598  7.673270  8.066308  8.461709  9.218860
#> mu[20,1] 10.204644 0.6586947  8.978652  9.759132 10.181082 10.649594 11.571437
#> mu[1,2]   7.647056 0.6870529  6.268057  7.200776  7.672959  8.108289  9.039065
#> mu[2,2]   5.222089 0.6225841  3.992376  4.814016  5.250899  5.623723  6.416192
#> mu[3,2]   6.377505 0.6203773  5.167956  5.943811  6.367907  6.806000  7.659485
#> mu[4,2]   5.540160 0.5738784  4.371172  5.169935  5.544654  5.918179  6.654765
#> mu[5,2]  11.342922 0.5044430 10.390306 10.999694 11.345940 11.676307 12.343929
#> mu[6,2]   6.823425 0.6607466  5.534803  6.374414  6.815741  7.272603  8.136619
#> mu[7,2]   4.910094 0.7073583  3.573304  4.419841  4.885654  5.427628  6.236250
#> mu[8,2]   6.689205 0.7607084  5.186798  6.175815  6.695755  7.195435  8.195542
#> mu[9,2]   7.190791 0.6319521  5.959025  6.758025  7.184704  7.611038  8.450640
#> mu[10,2]  9.044671 0.7464970  7.535735  8.559145  9.056679  9.547897 10.506201
#> mu[11,2]  8.317973 0.6097930  7.156237  7.911912  8.314500  8.707120  9.499244
#> mu[12,2]  6.202465 0.6231247  4.961882  5.779055  6.194749  6.624100  7.398044
#> mu[13,2]  8.697059 0.5889092  7.520232  8.299223  8.690902  9.106084  9.870267
#> mu[14,2]  7.659511 0.6166259  6.398453  7.259875  7.651209  8.076654  8.896612
#> mu[15,2] 10.008278 0.6226446  8.806343  9.583068 10.002047 10.420862 11.216493
#> mu[16,2]  8.045865 0.5389620  6.968461  7.686137  8.033365  8.419021  9.083094
#> mu[17,2] 10.026269 0.5791227  8.898817  9.636508 10.023259 10.414615 11.152671
#> mu[18,2]  7.756478 0.5912138  6.606637  7.356090  7.756985  8.166684  8.951995
#> mu[19,2]  8.896976 0.6414044  7.663882  8.471171  8.899801  9.325152 10.138759
#> mu[20,2]  8.505275 0.5900782  7.327505  8.103123  8.511623  8.902627  9.636752
#> mu[1,3]  10.463777 0.4979735  9.516567 10.127883 10.444819 10.797164 11.465765
#> mu[2,3]   8.308894 0.5730274  7.205726  7.915044  8.306913  8.712194  9.421888
#> mu[3,3]   7.297266 0.5373918  6.251551  6.928210  7.302797  7.659203  8.369020
#> mu[4,3]   5.670619 0.6515246  4.471981  5.237810  5.660277  6.101475  6.983081
#> mu[5,3]   8.739207 0.6783365  7.380324  8.306976  8.727057  9.190912 10.097131
#> mu[6,3]   8.326946 0.6068866  7.130793  7.927302  8.330520  8.730958  9.494836
#> mu[7,3]   4.915647 0.6381523  3.671964  4.481749  4.924502  5.323452  6.190698
#> mu[8,3]  10.252285 0.5859985  9.135531  9.849669 10.247670 10.638045 11.405574
#> mu[9,3]   9.707471 0.6385461  8.425524  9.279268  9.706781 10.142662 11.008090
#> mu[10,3]  8.943322 0.6874234  7.599958  8.476048  8.950316  9.404650 10.298633
#> mu[11,3]  8.010829 0.6355028  6.756148  7.587969  8.029508  8.440465  9.267415
#> mu[12,3]  8.186298 0.6932502  6.836035  7.731587  8.186918  8.655538  9.487327
#> mu[13,3]  8.811474 0.7207384  7.402890  8.331512  8.800468  9.306086 10.216466
#> mu[14,3]  8.789901 0.6644813  7.510244  8.337490  8.804346  9.235012 10.081122
#> mu[15,3]  8.418618 0.6375802  7.171603  7.978759  8.416512  8.855417  9.637558
#> mu[16,3]  3.840521 0.6119024  2.606023  3.438393  3.865851  4.247149  5.000575
#> mu[17,3]  9.595180 0.5710353  8.396258  9.217468  9.622462  9.965425 10.662230
#> mu[18,3]  5.871301 0.6561212  4.600318  5.443418  5.886784  6.318467  7.175506
#> mu[19,3]  8.131881 0.4771496  7.216237  7.800638  8.129903  8.461915  9.046658
#> mu[20,3]  5.528586 0.6989829  4.181057  5.055743  5.536906  5.982018  6.931620
#> mu[1,4]   6.315642 0.5494646  5.260518  5.939853  6.300373  6.691158  7.362296
#> mu[2,4]   5.059348 0.6334947  3.777366  4.635772  5.063329  5.482616  6.301496
#> mu[3,4]   7.889229 0.6612283  6.604872  7.444825  7.875631  8.344590  9.160105
#> mu[4,4]   7.557047 0.5727449  6.429986  7.178957  7.564791  7.947285  8.637189
#> mu[5,4]   8.352081 0.6902227  7.011870  7.883717  8.367073  8.833879  9.649200
#> mu[6,4]   7.325979 0.6930734  5.923900  6.852733  7.354538  7.789444  8.677824
#> mu[7,4]   8.665464 0.5811230  7.538089  8.279183  8.667624  9.051079  9.798051
#> mu[8,4]   6.658494 0.6367422  5.402157  6.236250  6.665918  7.081684  7.915252
#> mu[9,4]   4.462531 0.6527338  3.228670  4.034171  4.441300  4.913374  5.751043
#> mu[10,4]  7.611514 0.6169655  6.341137  7.211442  7.617683  8.002330  8.834176
#> mu[11,4]  6.140704 0.5553467  5.024631  5.769161  6.148629  6.522605  7.201242
#> mu[12,4]  7.457102 0.6244227  6.242284  7.028501  7.464589  7.885470  8.682966
#> mu[13,4]  9.541980 0.5593490  8.484762  9.165138  9.530785  9.902450 10.648247
#> mu[14,4]  8.304119 0.4990056  7.320759  7.967113  8.302541  8.647704  9.273260
#> mu[15,4]  9.972787 0.7451469  8.521064  9.466458  9.962541 10.462270 11.449964
#> mu[16,4]  2.984284 0.5588522  1.873632  2.608820  3.005638  3.349396  4.107695
#> mu[17,4]  6.278812 0.6459580  4.980837  5.852285  6.300338  6.699948  7.563774
#> mu[18,4]  3.665760 0.5649335  2.587828  3.283378  3.667452  4.048360  4.798466
#> mu[19,4]  7.996029 0.6008137  6.861532  7.574407  7.987558  8.398943  9.189161
#> mu[20,4]  6.768376 0.6123010  5.592608  6.334278  6.768711  7.190481  7.937137
#> mu[1,5]   8.024193 0.6668391  6.785990  7.584910  8.035926  8.473224  9.312520
#> mu[2,5]   8.019152 0.6184314  6.840517  7.600548  8.009808  8.430838  9.301994
#> mu[3,5]   3.899570 0.6017088  2.681116  3.511906  3.904505  4.294766  5.041059
#> mu[4,5]   7.501428 0.5989298  6.333601  7.102500  7.509760  7.907246  8.720009
#> mu[5,5]   8.341686 0.5675706  7.238005  7.965179  8.341497  8.709594  9.495836
#> mu[6,5]  10.955171 0.5889729  9.825883 10.558122 10.939309 11.342989 12.137315
#> mu[7,5]   8.155806 0.7728081  6.678244  7.646446  8.171872  8.654540  9.663698
#> mu[8,5]   8.216300 0.6943835  6.941004  7.749169  8.195693  8.671179  9.627771
#> mu[9,5]   4.881358 0.5014078  3.934482  4.539594  4.879266  5.208732  5.863881
#> mu[10,5]  7.354155 0.5896299  6.184005  6.946273  7.338401  7.774014  8.495989
#> mu[11,5]  5.408518 0.5691351  4.273276  5.032654  5.429462  5.789250  6.550464
#> mu[12,5]  9.474026 0.6548884  8.215947  9.030170  9.442902  9.910495 10.800454
#> mu[13,5] 11.192047 0.7884469  9.716437 10.638868 11.167308 11.707144 12.803152
#> mu[14,5] 10.090446 0.5563525  9.001099  9.703694 10.100468 10.456299 11.174711
#> mu[15,5]  7.563713 0.5435459  6.486133  7.195713  7.561552  7.918155  8.650917
#> mu[16,5]  6.356204 0.6743140  5.042991  5.908633  6.341328  6.812832  7.675486
#> mu[17,5]  7.718129 0.7161006  6.266500  7.263775  7.733802  8.168672  9.172368
#> mu[18,5]  7.438865 0.6662133  6.114538  6.977819  7.452675  7.877363  8.761825
#> mu[19,5]  9.628319 0.5868765  8.501983  9.214922  9.624864 10.047279 10.743036
#> mu[20,5]  8.969609 0.6486362  7.715099  8.535345  8.960963  9.414809 10.246984

Coefficient Estimation

result$coefficient
#>            Mean        SD       2.5%        25%        50%        75%    97.5%
#> b[0] -0.1470914 0.2810070 -0.6941989 -0.3439236 -0.1426284 0.03744075 0.412166
#> b[1]  2.1909277 0.1724024  1.8577987  2.0699878  2.1900806 2.31049421 2.520493
#> b[2]  2.2772364 0.1004356  2.0748067  2.2095749  2.2810411 2.34362373 2.471967

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. 
#>  0.2277  0.3335  0.3848  0.3923  0.4367  0.6216

Extract RSE

RSE_HB=sqrt(MSE_HB)/result$Est$MEAN*100
summary(RSE_HB)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   4.447   6.931   8.061   8.837  10.276  18.727

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.   : 2.984  
#>  1st Qu.: 6.144   1st Qu.: 6.306  
#>  Median : 7.684   Median : 7.737  
#>  Mean   : 7.562   Mean   : 7.563  
#>  3rd Qu.: 8.822   3rd Qu.: 8.752  
#>  Max.   :12.835   Max.   :11.343
MSE_dir=dataPanel[,4]
MSE=as.data.frame(cbind(MSE_dir, MSE_HB))
summary(MSE)
#>     MSE_dir           MSE_HB      
#>  Min.   :0.3133   Min.   :0.2277  
#>  1st Qu.:0.4971   1st Qu.:0.3335  
#>  Median :0.6294   Median :0.3848  
#>  Mean   :0.6800   Mean   :0.3923  
#>  3rd Qu.:0.7749   3rd Qu.:0.4367  
#>  Max.   :1.6929   Max.   :0.6216
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.   :0.2277  
#>  1st Qu.:0.4971   1st Qu.:0.3335  
#>  Median :0.6294   Median :0.3848  
#>  Mean   :0.6800   Mean   :0.3923  
#>  3rd Qu.:0.7749   3rd Qu.:0.4367  
#>  Max.   :1.6929   Max.   :0.6216