An Application to HB Twofold Normal Model On sampel dataset

FIRST STEPS: Load package and load the data

library(saeHB.twofold)
data("dataTwofold")

STEPS 2: Fitting HB Model

model=NormalTF(y~x1+x2,vardir="vardir",area = "codearea",weight = "w",iter.mcmc = 50000,thin=20,burn.in = 1000,data=dataTwofold)
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 90
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 953
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 90
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 953
#> 
#> Initializing model
#> 
#> Compiling model graph
#>    Resolving undeclared variables
#>    Allocating nodes
#> Graph information:
#>    Observed stochastic nodes: 90
#>    Unobserved stochastic nodes: 125
#>    Total graph size: 953
#> 
#> Initializing model

STEP 3 Extract mean estimation

model$Est_sub
#>                Mean        SD        2.5%       25%       50%       75%
#> theta[1]  13.725168 3.1379853  7.62663989 11.583826 13.685444 15.829902
#> theta[2]  10.935899 1.8533622  7.36018712  9.752051 10.921555 12.166174
#> theta[3]  14.226787 2.5829306  9.04871940 12.562955 14.259543 15.928971
#> theta[4]  11.574323 1.3371794  9.00013208 10.677613 11.579403 12.450177
#> theta[5]  14.780411 0.7872340 13.16988265 14.263228 14.766383 15.341684
#> theta[6]  10.668894 1.2747770  8.07372994  9.857929 10.656260 11.498398
#> theta[7]  14.300576 0.9012782 12.46308650 13.696045 14.316966 14.910081
#> theta[8]  13.436003 1.8500674  9.78548730 12.227606 13.435233 14.648841
#> theta[9]  16.230466 0.9346209 14.37118764 15.605398 16.204836 16.880522
#> theta[10] 14.840176 0.8976981 13.06136809 14.230436 14.857166 15.445702
#> theta[11] 14.269403 0.6997982 12.88189736 13.800207 14.273496 14.751847
#> theta[12] 15.785458 1.9001749 12.07927310 14.530933 15.766527 17.089008
#> theta[13]  9.301634 0.5700974  8.12913784  8.912135  9.301705  9.702340
#> theta[14]  9.911900 0.9703148  8.00673734  9.251323  9.908362 10.580055
#> theta[15] 15.539721 0.6863734 14.16603709 15.092091 15.550888 15.993637
#> theta[16] 12.583437 1.5634371  9.54610275 11.547640 12.579180 13.623015
#> theta[17]  2.222162 0.6899959  0.92127714  1.768255  2.220066  2.680375
#> theta[18]  7.176740 1.1204827  5.05348624  6.418527  7.156766  7.939193
#> theta[19]  2.122447 0.7378603  0.71806359  1.610707  2.125196  2.636430
#> theta[20]  6.137452 1.8618924  2.49570664  4.884950  6.098550  7.385725
#> theta[21]  4.411511 0.7768093  2.89354297  3.870171  4.404917  4.939384
#> theta[22] 14.714180 1.2064978 12.40417509 13.869488 14.726790 15.547078
#> theta[23] 13.982680 0.4858322 13.01506019 13.658348 13.976415 14.303555
#> theta[24] 17.584944 1.1301640 15.40007116 16.807732 17.585056 18.354161
#> theta[25] 14.456366 1.3751360 11.73822599 13.523916 14.478036 15.389408
#> theta[26] 10.344507 1.9665894  6.58925658  8.990690 10.317793 11.656818
#> theta[27]  9.636441 2.7734942  4.08460256  7.778849  9.699384 11.507672
#> theta[28] 14.951810 0.9070340 13.22639600 14.326983 14.929099 15.557934
#> theta[29] 13.206170 1.7057431  9.81620559 12.058798 13.209577 14.329002
#> theta[30] 10.092390 1.7021837  6.93851818  8.949548 10.004525 11.236508
#> theta[31] 14.127678 2.2415296  9.55070264 12.659976 14.110648 15.628944
#> theta[32] 14.595380 0.9320687 12.76321738 13.974709 14.592362 15.231024
#> theta[33] 10.056352 3.1994433  3.73843150  7.987092  9.986894 12.146300
#> theta[34] 13.749597 1.3891284 10.98395769 12.814387 13.751154 14.678671
#> theta[35] 14.584657 2.0547146 10.47377018 13.216751 14.606767 16.004981
#> theta[36] 13.472506 1.9410349  9.61711560 12.178649 13.439675 14.796645
#> theta[37] 13.959960 0.8253868 12.31657456 13.407482 13.971975 14.512624
#> theta[38] 14.281220 0.9232013 12.53268121 13.669959 14.258656 14.925212
#> theta[39] 12.533974 1.4331481  9.77956898 11.531822 12.542057 13.505911
#> theta[40]  9.227196 2.2765109  4.79267792  7.659038  9.268473 10.811795
#> theta[41] 18.420350 0.8609274 16.77431545 17.826046 18.420725 18.996785
#> theta[42] 12.469720 1.0369666 10.39258873 11.736051 12.480392 13.172512
#> theta[43] 16.429065 3.2397107  9.94704119 14.327000 16.471386 18.559989
#> theta[44] 16.927576 1.5014782 14.06301097 15.923770 16.940769 17.927751
#> theta[45] 18.540252 1.3916079 15.88860262 17.635866 18.537840 19.497175
#> theta[46] 13.702100 1.9527468  9.82057055 12.410323 13.714519 15.010273
#> theta[47] 12.468641 2.6291190  7.36086642 10.676236 12.428709 14.227477
#> theta[48] 11.391948 0.6393583 10.16192340 10.975817 11.382472 11.804204
#> theta[49]  6.654902 1.3567873  3.98544946  5.741696  6.667277  7.558688
#> theta[50] 15.945516 1.5405982 12.89033944 14.959202 15.937100 16.922211
#> theta[51]  7.832679 1.4150803  4.91122508  6.903057  7.831024  8.836636
#> theta[52] 26.623027 0.8247411 25.03155484 26.051126 26.627672 27.184333
#> theta[53] 18.473295 1.6233905 15.16111719 17.412880 18.501168 19.563503
#> theta[54] 17.926356 1.2560155 15.57005935 17.055932 17.946087 18.784977
#> theta[55] 11.980331 0.7328091 10.57025584 11.481914 11.964777 12.470124
#> theta[56] 11.480044 0.5351074 10.40066348 11.124666 11.478618 11.830887
#> theta[57]  8.972373 0.6356738  7.68490164  8.552501  8.966974  9.408883
#> theta[58] 13.745200 1.4219480 10.93337114 12.767308 13.723241 14.729572
#> theta[59] 16.506086 0.9377239 14.64385164 15.867703 16.504014 17.163184
#> theta[60] 15.187971 0.8202313 13.57178969 14.626309 15.183064 15.722513
#> theta[61]  5.524040 1.9760900  1.70623140  4.251715  5.505133  6.830825
#> theta[62]  5.911897 0.8259979  4.23070348  5.357259  5.936550  6.471473
#> theta[63]  5.312795 0.9215117  3.47553647  4.702910  5.310399  5.938751
#> theta[64] 12.306631 1.6005208  9.20404329 11.207943 12.308978 13.404381
#> theta[65] 12.356765 2.4692469  7.58300063 10.663645 12.380252 13.991170
#> theta[66]  9.882624 1.2665449  7.39475649  9.005249  9.897013 10.760215
#> theta[67] 16.800324 1.0033494 14.84822506 16.109994 16.781358 17.488368
#> theta[68] 11.136850 1.2579698  8.71383725 10.294431 11.137076 11.996090
#> theta[69]  8.141735 0.8429920  6.52435841  7.565294  8.131594  8.723975
#> theta[70] 11.773923 0.8359913 10.11532162 11.215118 11.754812 12.340037
#> theta[71] 13.704210 0.7143069 12.31309552 13.218276 13.718494 14.217118
#> theta[72] 10.750623 0.7298402  9.34750187 10.234482 10.746992 11.255651
#> theta[73]  3.819779 1.4703407  0.93876035  2.803103  3.834338  4.789283
#> theta[74] 10.451384 1.4923015  7.49403938  9.449776 10.464324 11.494459
#> theta[75]  5.923229 1.3408746  3.23080685  5.039858  5.903575  6.859075
#> theta[76]  9.423038 0.7764190  7.96037320  8.874884  9.409800  9.962714
#> theta[77] 13.919653 0.7561695 12.41864456 13.412152 13.923913 14.433488
#> theta[78]  9.622741 1.9722353  5.84737795  8.293898  9.594311 10.925932
#> theta[79] 10.418374 1.1583574  8.25562402  9.621097 10.394330 11.192785
#> theta[80]  5.879632 0.7530648  4.38701031  5.374812  5.887167  6.393929
#> theta[81]  6.485223 0.7472478  5.08379049  5.967792  6.470765  6.969461
#> theta[82] 14.441943 2.2368920  9.94429130 12.901870 14.450003 15.913614
#> theta[83] 10.693752 1.8176690  7.16864257  9.468445 10.695598 11.868218
#> theta[84]  9.951169 2.9546052  4.11261535  7.998551 10.003323 11.885052
#> theta[85] 13.414307 1.6278172 10.20429837 12.317090 13.382584 14.505087
#> theta[86] 18.591283 1.4647792 15.66480363 17.608633 18.646097 19.582916
#> theta[87] 11.456350 0.7899293  9.92599437 10.917661 11.439960 11.964642
#> theta[88]  7.961298 1.8668257  4.31061794  6.670839  7.937392  9.268355
#> theta[89]  7.715535 1.4568699  4.90889521  6.728872  7.722854  8.679941
#> theta[90]  4.559638 2.3171343 -0.07601127  3.028895  4.629509  6.103409
#>               97.5%
#> theta[1]  20.070933
#> theta[2]  14.604325
#> theta[3]  19.340022
#> theta[4]  14.221220
#> theta[5]  16.312612
#> theta[6]  13.185188
#> theta[7]  16.063935
#> theta[8]  17.037032
#> theta[9]  18.021505
#> theta[10] 16.600548
#> theta[11] 15.644527
#> theta[12] 19.450623
#> theta[13] 10.380588
#> theta[14] 11.768346
#> theta[15] 16.903506
#> theta[16] 15.762007
#> theta[17]  3.560417
#> theta[18]  9.307450
#> theta[19]  3.563777
#> theta[20]  9.807185
#> theta[21]  5.935262
#> theta[22] 17.071385
#> theta[23] 14.969337
#> theta[24] 19.822071
#> theta[25] 17.164410
#> theta[26] 14.190382
#> theta[27] 15.003334
#> theta[28] 16.775629
#> theta[29] 16.454138
#> theta[30] 13.560827
#> theta[31] 18.385516
#> theta[32] 16.429371
#> theta[33] 16.427202
#> theta[34] 16.494671
#> theta[35] 18.592556
#> theta[36] 17.274854
#> theta[37] 15.567466
#> theta[38] 16.089799
#> theta[39] 15.336738
#> theta[40] 13.690150
#> theta[41] 20.116981
#> theta[42] 14.381715
#> theta[43] 22.913535
#> theta[44] 19.900971
#> theta[45] 21.252899
#> theta[46] 17.545733
#> theta[47] 17.626218
#> theta[48] 12.655137
#> theta[49]  9.331618
#> theta[50] 19.003533
#> theta[51] 10.602324
#> theta[52] 28.271194
#> theta[53] 21.572419
#> theta[54] 20.402651
#> theta[55] 13.424698
#> theta[56] 12.533022
#> theta[57] 10.182155
#> theta[58] 16.408325
#> theta[59] 18.324467
#> theta[60] 16.874226
#> theta[61]  9.428285
#> theta[62]  7.509941
#> theta[63]  7.132504
#> theta[64] 15.431084
#> theta[65] 17.279708
#> theta[66] 12.319293
#> theta[67] 18.801927
#> theta[68] 13.490076
#> theta[69]  9.757069
#> theta[70] 13.416265
#> theta[71] 15.078507
#> theta[72] 12.163848
#> theta[73]  6.711399
#> theta[74] 13.340247
#> theta[75]  8.435306
#> theta[76] 10.937433
#> theta[77] 15.375920
#> theta[78] 13.477486
#> theta[79] 12.697109
#> theta[80]  7.348107
#> theta[81]  7.999626
#> theta[82] 18.831723
#> theta[83] 14.236328
#> theta[84] 15.661551
#> theta[85] 16.735347
#> theta[86] 21.383982
#> theta[87] 13.002931
#> theta[88] 11.625760
#> theta[89] 10.623876
#> theta[90]  9.080262

model$Est_area
#>         Mean        SD      2.5%       25%       50%       75%     97.5%
#> 1  13.150630 1.7101651  9.430447 11.824837 13.111320 14.489858 16.941367
#> 2  12.453338 0.6516009 11.157063 12.010785 12.458471 12.901433 13.730604
#> 3  14.479087 0.7523651 12.970998 13.939008 14.489095 14.992852 16.029649
#> 4  14.855827 0.6367631 13.573142 14.409113 14.857264 15.311981 16.111059
#> 5  11.298413 0.4360290 10.452631 10.992241 11.297587 11.597428 12.159308
#> 6   7.792709 0.7272945  6.325627  7.287582  7.789445  8.295382  9.236507
#> 7   4.528025 0.8354027  2.834986  3.958449  4.526131  5.108834  6.232121
#> 8  15.852628 0.6315112 14.590272 15.421418 15.866748 16.280664 17.086824
#> 9  11.390741 1.2580605  8.593078 10.424096 11.411970 12.372441 14.144932
#> 10 12.287839 0.9314540 10.413851 11.604111 12.284464 12.949481 14.196113
#> 11 12.647044 1.5351566  9.407115 11.466765 12.596070 13.801488 16.043666
#> 12 13.946049 1.0381763 11.729929 13.159776 13.975981 14.717877 16.161869
#> 13 13.476926 0.6833799 12.149443 12.999618 13.470468 13.928453 14.890830
#> 14 13.258880 0.8993004 11.475153 12.612973 13.258819 13.879832 15.147344
#> 15 17.250307 1.4726703 14.162263 16.237455 17.233044 18.273275 20.348663
#> 16 12.651366 1.2357838 10.167859 11.776158 12.622016 13.564722 15.132109
#> 17 10.492282 0.8478719  8.788214  9.879402 10.493849 11.095850 12.222248
#> 18 20.795303 0.7310363 19.340344 20.311755 20.792667 21.301950 22.263036
#> 19 10.401558 0.3879382  9.647379 10.141187 10.398981 10.661682 11.167774
#> 20 15.251181 0.5810132 14.079364 14.829079 15.235392 15.663392 16.449856
#> 21  5.552436 0.8034655  3.907004  5.012492  5.556895  6.124497  7.173478
#> 22 11.541239 1.0271249  9.433235 10.737525 11.540071 12.324416 13.847564
#> 23 12.077954 0.6049040 10.851965 11.648385 12.066070 12.497558 13.264864
#> 24 12.125288 0.4660931 11.204042 11.799708 12.126659 12.442531 13.061845
#> 25  6.474824 0.8292940  4.794467  5.895682  6.467974  7.065788  8.102032
#> 26 11.362270 0.6955486  9.930066 10.878472 11.362887 11.834542 12.804487
#> 27  7.450796 0.5163825  6.403602  7.100610  7.440647  7.796827  8.454892
#> 28 12.095242 1.3401683  9.091003 11.076452 12.076152 13.135546 15.074207
#> 29 14.743537 0.7852948 13.133092 14.187492 14.739670 15.300099 16.359573
#> 30  6.526427 1.1727306  3.934748  5.693180  6.536006  7.385403  9.005833

model$coefficient
#>               Mean         SD       2.5%        25%        50%       75%
#> beta[0] -0.2969634 0.62684171 -1.5260395 -0.7150085 -0.2986366 0.1299395
#> beta[1]  0.2110469 0.60531399 -0.9918017 -0.1836667  0.2173075 0.6120990
#> beta[2]  1.2197197 0.06417584  1.0963231  1.1763376  1.2193106 1.2653226
#>             97.5%
#> beta[0] 0.9398143
#> beta[1] 1.3728984
#> beta[2] 1.3427139

model$refvar
#>   var_area  var_sub
#> 1  8.07377 8.747938

STEP 3 : Extract CV and MSE Subarea

• CV \(CV(\theta\hat)=\sqrt(V(\theta\hat ))/\theta\hat\)
• MSE \(MSE= V(\theta\hat)\)

CV=(model$Est_sub$SD)/(model$Est_sub$Mean)*100
MSE=model$Est_sub$SD^2
summary(cbind(CV,MSE))
#>        CV              MSE         
#>  Min.   : 3.098   Min.   : 0.2360  
#>  1st Qu.: 6.546   1st Qu.: 0.6864  
#>  Median :11.538   Median : 1.7066  
#>  Mean   :13.704   Mean   : 2.3760  
#>  3rd Qu.:17.543   3rd Qu.: 3.3930  
#>  Max.   :50.818   Max.   :10.4957

STEP 4 Extract CV and MSE of Area

CV2=(model$Est_area$SD)/(model$Est_area$Mean)*100
MSE2=model$Est_area$SD^2
summary(cbind(CV2,MSE2))
#>       CV2              MSE2       
#>  Min.   : 3.515   Min.   :0.1505  
#>  1st Qu.: 5.024   1st Qu.:0.4102  
#>  Median : 7.187   Median :0.6311  
#>  Mean   : 8.110   Mean   :0.8748  
#>  3rd Qu.:10.725   3rd Qu.:1.0721  
#>  Max.   :18.450   Max.   :2.9247

STEP 5 : You can also compare the CV between subarea direct estimator and HB Twofold estimator

dirCV=sqrt(dataTwofold$vardir)/(dataTwofold$y)*100
summary(cbind(dirCV,CV))
#>      dirCV               CV        
#>  Min.   :  3.187   Min.   : 3.098  
#>  1st Qu.:  6.642   1st Qu.: 6.546  
#>  Median : 12.764   Median :11.538  
#>  Mean   : 25.141   Mean   :13.704  
#>  3rd Qu.: 21.041   3rd Qu.:17.543  
#>  Max.   :680.378   Max.   :50.818

• Look that! ,CV on our model is less than CV on direct estimator.

boxplot(cbind(dirCV,CV),ylim=c(0,50))

model$refvar
#>   var_area  var_sub
#> 1  8.07377 8.747938