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 = 100000,thin=50,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
#> Warning in par(opar): argument 1 does not name a graphical parameter

STEP 3 Extract mean estimation

Subarea Estimation

model$Est_sub
#>                Mean        SD       2.5%       25%       50%       75%
#> theta[1]  13.656585 2.9580855  8.0601928 11.583714 13.582628 15.733572
#> theta[2]  11.010943 1.8997054  7.3391790  9.811139 11.007839 12.274414
#> theta[3]  14.136903 2.5505598  9.0939889 12.468421 14.105094 15.790863
#> theta[4]  11.627181 1.3360887  9.0080557 10.680446 11.661273 12.556871
#> theta[5]  14.723387 0.7638602 13.2585324 14.209251 14.714347 15.233962
#> theta[6]  10.663619 1.2221444  8.2663797  9.830389 10.676006 11.456475
#> theta[7]  14.264904 0.8740068 12.5489640 13.676293 14.267300 14.849981
#> theta[8]  13.420448 1.8524351  9.8578901 12.184495 13.396780 14.691191
#> theta[9]  16.219356 0.9068785 14.4167937 15.616023 16.243732 16.823430
#> theta[10] 14.844457 0.9178027 13.0240150 14.241689 14.822046 15.507231
#> theta[11] 14.271445 0.6935847 12.9111368 13.802214 14.255214 14.743814
#> theta[12] 15.845014 1.9667137 12.0571161 14.547877 15.862430 17.172910
#> theta[13]  9.283656 0.5972613  8.1833677  8.862502  9.281342  9.679493
#> theta[14]  9.881093 0.9691465  7.9725675  9.222120  9.883319 10.555564
#> theta[15] 15.553985 0.7022727 14.1738327 15.100149 15.550704 16.033472
#> theta[16] 12.641026 1.5425032  9.6132091 11.638564 12.627214 13.662226
#> theta[17]  2.213511 0.7049527  0.8700343  1.722723  2.233929  2.686308
#> theta[18]  7.181415 1.1212247  5.0324121  6.403925  7.191231  7.965801
#> theta[19]  2.159699 0.7432461  0.6619205  1.688409  2.165297  2.649938
#> theta[20]  6.094652 1.8964479  2.2794241  4.847636  6.096380  7.396682
#> theta[21]  4.392211 0.7914774  2.7783532  3.855013  4.395192  4.942735
#> theta[22] 14.791004 1.1767017 12.5374467 13.984944 14.781488 15.585006
#> theta[23] 13.981256 0.4834064 13.0442882 13.654300 13.983301 14.311166
#> theta[24] 17.619198 1.0969206 15.4793813 16.898801 17.576993 18.361296
#> theta[25] 14.454390 1.3529032 11.7900601 13.550989 14.456959 15.349460
#> theta[26] 10.363669 1.9433414  6.4193341  9.138492 10.358130 11.656235
#> theta[27]  9.629347 2.6955764  4.3454076  7.881800  9.607782 11.366817
#> theta[28] 14.973998 0.9062653 13.2039982 14.376367 14.976222 15.605905
#> theta[29] 13.164185 1.6317912 10.0378338 12.080746 13.118395 14.262821
#> theta[30] 10.110877 1.7053928  6.9102655  8.965771 10.049431 11.290907
#> theta[31] 14.154748 2.2099007  9.9871491 12.613554 14.135025 15.573553
#> theta[32] 14.610557 0.9200989 12.7837994 13.995908 14.597585 15.193696
#> theta[33]  9.957603 3.1529236  3.8246771  7.799632  9.900137 12.076418
#> theta[34] 13.737536 1.4145142 11.0657306 12.757703 13.749717 14.709430
#> theta[35] 14.593375 2.0199477 10.7029609 13.175519 14.584171 15.986758
#> theta[36] 13.443373 1.9710764  9.5380060 12.112573 13.452587 14.843817
#> theta[37] 14.000726 0.8202411 12.3247499 13.472986 14.010655 14.541340
#> theta[38] 14.254464 0.9051423 12.5742378 13.632261 14.225446 14.892548
#> theta[39] 12.530695 1.4270131  9.7125610 11.600208 12.559748 13.528935
#> theta[40]  9.139265 2.3884232  4.5451770  7.557969  9.194711 10.736043
#> theta[41] 18.435849 0.8464657 16.7563424 17.855571 18.433813 19.003912
#> theta[42] 12.503729 0.9841150 10.4947234 11.856052 12.500018 13.201332
#> theta[43] 16.487494 3.3127609  9.9138087 14.296203 16.527124 18.655136
#> theta[44] 17.020459 1.5002096 14.0493772 15.983029 17.034778 18.034820
#> theta[45] 18.527392 1.4274095 15.7148213 17.544332 18.568611 19.482013
#> theta[46] 13.747650 2.0078290  9.8253114 12.357231 13.725681 15.097484
#> theta[47] 12.440440 2.6255701  7.3106544 10.721064 12.502191 14.140595
#> theta[48] 11.374906 0.6415743 10.1270572 10.946319 11.371874 11.804118
#> theta[49]  6.649062 1.4038299  3.9428795  5.704359  6.656848  7.618892
#> theta[50] 15.951065 1.5746233 12.9448016 14.847254 15.918729 17.033547
#> theta[51]  7.848257 1.3964807  5.0625853  6.904500  7.846086  8.786260
#> theta[52] 26.605760 0.8512759 24.9204740 26.036059 26.614647 27.192282
#> theta[53] 18.506119 1.6821142 15.3074051 17.333473 18.499143 19.632142
#> theta[54] 17.924267 1.2651189 15.4841589 17.028989 17.932236 18.778759
#> theta[55] 11.995617 0.7278636 10.5318375 11.524851 12.014544 12.478911
#> theta[56] 11.468417 0.5379209 10.4191958 11.107077 11.449085 11.821500
#> theta[57]  8.990402 0.6843726  7.6046642  8.525414  8.997788  9.462868
#> theta[58] 13.788191 1.5193910 10.8194784 12.741248 13.783973 14.802429
#> theta[59] 16.493914 0.9212657 14.7248238 15.857293 16.483093 17.132969
#> theta[60] 15.185936 0.8136214 13.5799745 14.648710 15.187160 15.727600
#> theta[61]  5.509686 1.9932950  1.6946123  4.150742  5.497495  6.826930
#> theta[62]  5.940865 0.8164432  4.3557205  5.375455  5.934572  6.507615
#> theta[63]  5.304178 0.9172484  3.5034750  4.678228  5.319864  5.921129
#> theta[64] 12.262891 1.5609209  9.2344846 11.210507 12.281838 13.313685
#> theta[65] 12.323383 2.4119334  7.5679170 10.722637 12.271998 14.006264
#> theta[66]  9.854969 1.2880916  7.4109726  8.945790  9.847608 10.756192
#> theta[67] 16.814481 1.0535153 14.7908042 16.108678 16.814270 17.535196
#> theta[68] 11.134649 1.2648308  8.7431577 10.296935 11.112542 11.971859
#> theta[69]  8.147483 0.8191918  6.5538735  7.620439  8.142148  8.679587
#> theta[70] 11.758012 0.8501846 10.0688147 11.208966 11.735190 12.296623
#> theta[71] 13.719524 0.7567327 12.3327227 13.199824 13.708316 14.214442
#> theta[72] 10.762617 0.7185623  9.3792451 10.275282 10.749862 11.242563
#> theta[73]  3.809997 1.5041934  0.8385846  2.807424  3.787178  4.770524
#> theta[74] 10.422654 1.4955538  7.4599230  9.416967 10.417665 11.431905
#> theta[75]  5.917783 1.3292202  3.1966095  5.010714  5.950349  6.850404
#> theta[76]  9.441327 0.7910580  7.9528616  8.904639  9.430767  9.982940
#> theta[77] 13.932729 0.7443582 12.5401935 13.419064 13.922585 14.444297
#> theta[78]  9.637592 1.9369700  5.8142497  8.367058  9.655673 10.902682
#> theta[79] 10.433941 1.1545925  8.2930967  9.639781 10.420129 11.224800
#> theta[80]  5.861936 0.7004749  4.4366540  5.420497  5.863112  6.339664
#> theta[81]  6.476561 0.7145320  5.1205356  5.970659  6.484750  6.947216
#> theta[82] 14.519677 2.2474842 10.1556995 12.982027 14.538294 16.031649
#> theta[83] 10.685734 1.9145536  6.9133076  9.317520 10.712837 11.959062
#> theta[84]  9.963029 3.0020591  3.8679028  8.080709 10.098427 11.943289
#> theta[85] 13.351115 1.6339219 10.0497532 12.262038 13.347301 14.523977
#> theta[86] 18.618413 1.4752929 15.7927116 17.602232 18.636844 19.624712
#> theta[87] 11.512284 0.8112569  9.9395109 10.935372 11.515782 12.071857
#> theta[88]  8.020277 1.8749519  4.4683039  6.714588  7.996468  9.306053
#> theta[89]  7.665618 1.4146811  4.9591322  6.716934  7.676991  8.634893
#> theta[90]  4.574091 2.3074873  0.1568413  3.041737  4.568173  6.085182
#>               97.5%
#> theta[1]  19.339325
#> theta[2]  14.641914
#> theta[3]  19.222155
#> theta[4]  14.245300
#> theta[5]  16.226026
#> theta[6]  13.089797
#> theta[7]  15.951292
#> theta[8]  17.180869
#> theta[9]  17.977569
#> theta[10] 16.626957
#> theta[11] 15.649129
#> theta[12] 19.656163
#> theta[13] 10.512211
#> theta[14] 11.773128
#> theta[15] 16.876500
#> theta[16] 15.590357
#> theta[17]  3.576621
#> theta[18]  9.332526
#> theta[19]  3.635592
#> theta[20]  9.955135
#> theta[21]  5.912783
#> theta[22] 17.056177
#> theta[23] 14.930743
#> theta[24] 19.811418
#> theta[25] 17.131784
#> theta[26] 14.167602
#> theta[27] 14.994144
#> theta[28] 16.705779
#> theta[29] 16.384422
#> theta[30] 13.492674
#> theta[31] 18.559517
#> theta[32] 16.484347
#> theta[33] 15.939543
#> theta[34] 16.508280
#> theta[35] 18.511779
#> theta[36] 17.272039
#> theta[37] 15.590762
#> theta[38] 16.069383
#> theta[39] 15.273948
#> theta[40] 13.792879
#> theta[41] 20.061696
#> theta[42] 14.399516
#> theta[43] 22.960662
#> theta[44] 19.899203
#> theta[45] 21.295662
#> theta[46] 17.727951
#> theta[47] 17.535071
#> theta[48] 12.656099
#> theta[49]  9.502173
#> theta[50] 18.975109
#> theta[51] 10.495032
#> theta[52] 28.239472
#> theta[53] 21.822110
#> theta[54] 20.339925
#> theta[55] 13.432069
#> theta[56] 12.522274
#> theta[57] 10.332397
#> theta[58] 16.849104
#> theta[59] 18.274672
#> theta[60] 16.746275
#> theta[61]  9.564677
#> theta[62]  7.542974
#> theta[63]  7.067427
#> theta[64] 15.332594
#> theta[65] 17.057683
#> theta[66] 12.353142
#> theta[67] 18.854133
#> theta[68] 13.731691
#> theta[69]  9.818482
#> theta[70] 13.484869
#> theta[71] 15.225901
#> theta[72] 12.221182
#> theta[73]  6.687987
#> theta[74] 13.383391
#> theta[75]  8.421638
#> theta[76] 11.002320
#> theta[77] 15.360848
#> theta[78] 13.555200
#> theta[79] 12.714959
#> theta[80]  7.208104
#> theta[81]  7.870397
#> theta[82] 18.948013
#> theta[83] 14.324692
#> theta[84] 15.857182
#> theta[85] 16.443277
#> theta[86] 21.473231
#> theta[87] 13.047953
#> theta[88] 11.649362
#> theta[89] 10.401497
#> theta[90]  9.133512

Area Estimatio

model$Est_area
#>         Mean        SD      2.5%       25%       50%       75%     97.5%
#> 1  13.112861 1.8669477  9.472995 11.828803 13.141696 14.387150 16.809550
#> 2  12.442938 0.6547000 11.204208 11.993255 12.452008 12.862146 13.775726
#> 3  14.455800 0.7651794 12.957570 13.935538 14.470175 14.945290 15.982015
#> 4  14.873073 0.6739849 13.597659 14.408155 14.878974 15.325577 16.159360
#> 5  11.285434 0.4457506 10.415264 10.976053 11.282870 11.590284 12.153922
#> 6   7.813570 0.7457612  6.339388  7.302444  7.812351  8.330816  9.264062
#> 7   4.513793 0.8655781  2.840851  3.942822  4.521845  5.075294  6.229954
#> 8  15.889007 0.6146330 14.715044 15.454043 15.911133 16.292118 17.108146
#> 9  11.393853 1.3677526  8.744798 10.483858 11.342762 12.337566 14.065120
#> 10 12.290737 0.9704777 10.358643 11.634964 12.267667 12.938277 14.155229
#> 11 12.622541 1.6718557  9.462308 11.493340 12.562632 13.759246 16.037736
#> 12 13.935762 1.1326277 11.679802 13.188834 13.941073 14.725676 16.140100
#> 13 13.481186 0.6932531 12.159388 13.002915 13.496821 13.943560 14.857748
#> 14 13.245106 0.9524923 11.415875 12.615644 13.267992 13.869133 15.127857
#> 15 17.294131 1.6184974 14.089352 16.209557 17.270779 18.370499 20.582206
#> 16 12.653265 1.3312434 10.152123 11.759611 12.663990 13.558166 15.314025
#> 17 10.498456 0.9138101  8.715475  9.867302 10.500910 11.117351 12.248628
#> 18 20.798129 0.7759491 19.267308 20.295944 20.783675 21.304575 22.312736
#> 19 10.411445 0.4072246  9.614250 10.133052 10.422577 10.684546 11.200711
#> 20 15.256848 0.6169629 14.036744 14.862327 15.248486 15.687966 16.463126
#> 21  5.552236 0.8274041  3.991227  4.976185  5.558113  6.104660  7.176307
#> 22 11.505605 1.1051442  9.305047 10.787607 11.496975 12.211097 13.698685
#> 23 12.083948 0.6243320 10.862995 11.667072 12.073059 12.502527 13.313226
#> 24 12.126091 0.4765603 11.216002 11.809915 12.122450 12.447214 13.058079
#> 25  6.461086 0.8855227  4.708991  5.840811  6.448510  7.045427  8.232623
#> 26 11.377372 0.7211434  9.972268 10.892885 11.390433 11.872036 12.795170
#> 27  7.445924 0.5046306  6.459264  7.099104  7.443888  7.795008  8.448205
#> 28 12.128517 1.5841732  9.071070 11.049119 12.087673 13.257357 15.198030
#> 29 14.752014 0.8155932 13.188449 14.179039 14.764792 15.301388 16.345289
#> 30  6.536073 1.2588735  3.993554  5.687683  6.531630  7.424947  8.966441

Coefficient Estimation

model$coefficient
#>               Mean         SD       2.5%        25%        50%       75%
#> beta[0] -0.3165487 0.64681111 -1.5667176 -0.7592380 -0.3013639 0.1316713
#> beta[1]  0.2091258 0.62104149 -0.9952668 -0.1972264  0.1983896 0.6302324
#> beta[2]  1.2230880 0.06595171  1.0980937  1.1781846  1.2207522 1.2677698
#>             97.5%
#> beta[0] 0.9074489
#> beta[1] 1.4474891
#> beta[2] 1.3523344

Random effect variance estimation

model$refVar
#>   var_area  var_sub
#> 1  7.97186 8.814458

STEP 3 : Extract CV and MSE Subarea

  • CV \(CV(\theta \hat)=\frac{SD(\theta \hat)}{(\theta \hat)} \times 100\)
  • 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.   : 3.200   Min.   : 0.2337  
#>  1st Qu.: 6.494   1st Qu.: 0.6837  
#>  Median :11.425   Median : 1.7130  
#>  Mean   :13.722   Mean   : 2.3748  
#>  3rd Qu.:17.886   3rd Qu.: 3.4945  
#>  Max.   :50.447   Max.   :10.9744

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.   : 3.731   Min.   :0.1658  
#>  1st Qu.: 5.148   1st Qu.:0.4350  
#>  Median : 7.544   Median :0.6749  
#>  Mean   : 8.600   Mean   :1.0110  
#>  3rd Qu.:11.633   3rd Qu.:1.2675  
#>  Max.   :19.260   Max.   :3.4855

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.   : 3.200  
#>  1st Qu.:  6.642   1st Qu.: 6.494  
#>  Median : 12.763   Median :11.425  
#>  Mean   : 25.141   Mean   :13.722  
#>  3rd Qu.: 21.041   3rd Qu.:17.886  
#>  Max.   :680.378   Max.   :50.447
  • Look that! ,CV on our model is less than CV on direct estimator.
boxplot(cbind(dirCV,CV),ylim=c(0,50))

model$refVar
#>   var_area  var_sub
#> 1  7.97186 8.814458
model$plot
#> [[1]]
#> NULL
#> 
#> [[2]]
#> [[2]]$mar
#> [1] 5.1 4.1 4.1 2.1
#> 
#> 
#> [[3]]
#> [[1]]
#> Markov Chain Monte Carlo (MCMC) output:
#> Start = 1050 
#> End = 1e+05 
#> Thinning interval = 50 
#>               beta[0]       beta[1]  beta[2]
#>    [1,] -0.4811336282  3.384543e-01 1.203792
#>    [2,] -0.7625586435  1.065051e+00 1.112953
#>    [3,]  0.8875320015  1.142190e-01 1.210463
#>    [4,] -0.0998069321 -7.797942e-02 1.241209
#>    [5,] -1.1327999207  5.344089e-01 1.208405
#>    [6,] -0.2965096736 -3.056069e-01 1.254397
#>    [7,] -2.0075042348  1.441512e+00 1.292266
#>    [8,]  0.0582052671 -3.971134e-01 1.307783
#>    [9,] -0.9515453489  6.600406e-02 1.326739
#>   [10,]  0.0557752857  1.088377e-01 1.233243
#>   [11,] -1.1619351011 -6.439785e-01 1.341746
#>   [12,] -0.1601914597 -1.089526e+00 1.236731
#>   [13,] -1.2248305610  3.982850e-02 1.348882
#>   [14,]  0.0049145896  1.119505e+00 1.261051
#>   [15,] -0.1195849916  9.701584e-01 1.122025
#>   [16,]  0.3369793585 -4.437545e-01 1.175021
#>   [17,] -0.2265924254  9.669591e-02 1.281884
#>   [18,] -0.1980301646  1.008015e+00 1.215512
#>   [19,] -1.5039136245  3.803098e-01 1.265606
#>   [20,] -0.1793501939  2.814723e-01 1.181846
#>   [21,] -0.2318176382  2.567575e-02 1.216814
#>   [22,]  0.2116357568 -1.033963e-01 1.255774
#>   [23,] -0.0936095383 -2.459509e-01 1.253291
#>   [24,]  0.2722676110 -7.710943e-01 1.163849
#>   [25,] -0.5518214133  8.472348e-01 1.246385
#>   [26,] -0.6236172543  6.814184e-01 1.295076
#>   [27,] -0.6387198283 -3.221364e-01 1.317832
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#> [1953,] -0.9202260652  1.508186e+00 1.192984
#> [1954,]  1.0389884429 -5.804718e-01 1.171823
#> [1955,] -0.1459513768 -9.020885e-01 1.250401
#> [1956,] -1.2452067269 -1.497620e-01 1.253958
#> [1957,] -0.3386049198  2.729143e-01 1.261714
#> [1958,] -0.6705231049  2.150219e-01 1.190197
#> [1959,] -0.2753696388 -8.958330e-02 1.126692
#> [1960,]  0.2225320537 -3.709587e-01 1.207486
#> [1961,]  0.5644376594 -9.301476e-02 1.272533
#> [1962,] -0.8137027184  7.337114e-01 1.231508
#> [1963,] -0.9879954539  4.059098e-01 1.277392
#> [1964,] -1.0642837239  3.560611e-01 1.317561
#> [1965,]  0.3675385757 -3.302004e-01 1.198238
#> [1966,] -0.5508130479  1.235579e+00 1.173876
#> [1967,] -0.8067161253  1.861951e+00 1.188647
#> [1968,] -0.5198737916 -2.009243e-02 1.227338
#> [1969,]  0.9135507427 -4.299443e-01 1.274957
#> [1970,] -0.3046758668  5.512260e-01 1.102580
#> [1971,] -1.5114093166 -2.736396e-01 1.269267
#> [1972,] -1.4211389305  4.923604e-01 1.280095
#> [1973,] -1.0844358847  6.529899e-01 1.284919
#> [1974,] -0.6442564992 -2.891343e-01 1.285483
#> [1975,] -0.5667962196  3.120966e-01 1.281982
#> [1976,] -0.5072946935  2.440155e-01 1.299859
#> [1977,]  0.6972302695 -8.690309e-01 1.241739
#> [1978,]  0.1485536092  1.567109e-01 1.023722
#> [1979,] -0.1411380575  3.053208e-01 1.162399
#> [1980,]  0.0136653698  4.721650e-01 1.246755
#> 
#> attr(,"class")
#> [1] "mcmc.list"
#> 
#> [[4]]
#> NULL