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]  13.780298 3.1242503  7.50273147 11.690764 13.792776 15.828061
#> theta[2]  10.989797 1.8981155  7.12041917  9.715565 11.039185 12.303694
#> theta[3]  14.302299 2.6039495  9.00294372 12.585254 14.337183 16.047153
#> theta[4]  11.588444 1.3286712  8.95652182 10.685969 11.598707 12.482586
#> theta[5]  14.744293 0.7859334 13.22601757 14.214410 14.736454 15.253636
#> theta[6]  10.651047 1.2614145  8.13979551  9.808854 10.658346 11.488420
#> theta[7]  14.242012 0.8735333 12.57613650 13.616607 14.230843 14.825683
#> theta[8]  13.446216 1.8537028  9.73057624 12.231050 13.482724 14.653488
#> theta[9]  16.167305 0.9064670 14.40086202 15.572165 16.188558 16.777500
#> theta[10] 14.854531 0.8877080 13.12199080 14.261126 14.856188 15.410373
#> theta[11] 14.262827 0.6956257 12.90689928 13.819804 14.265476 14.724628
#> theta[12] 15.737660 1.9905903 11.89700176 14.375516 15.713994 17.024923
#> theta[13]  9.277209 0.5715203  8.17098063  8.877468  9.281310  9.662741
#> theta[14]  9.928485 0.9684581  8.00047521  9.306171  9.950999 10.588758
#> theta[15] 15.551448 0.7185856 14.16904772 15.081206 15.543023 16.032062
#> theta[16] 12.629901 1.5661850  9.56128376 11.577160 12.616781 13.727163
#> theta[17]  2.212020 0.6967543  0.87617932  1.740014  2.186296  2.675703
#> theta[18]  7.192566 1.1115290  5.01237126  6.448762  7.213917  7.946201
#> theta[19]  2.105457 0.7603976  0.61355601  1.570720  2.112733  2.595447
#> theta[20]  6.068644 1.9011341  2.35352151  4.789609  6.037870  7.285847
#> theta[21]  4.417669 0.7637626  2.95272523  3.919619  4.422241  4.915489
#> theta[22] 14.725331 1.1975655 12.36512669 13.932228 14.708471 15.543364
#> theta[23] 13.994013 0.4738736 13.06143203 13.672144 13.997742 14.313077
#> theta[24] 17.584413 1.1406406 15.25270339 16.835999 17.599543 18.301520
#> theta[25] 14.454554 1.3498378 11.84829017 13.521700 14.459040 15.306862
#> theta[26] 10.296657 2.0016819  6.40899890  8.986287 10.258250 11.626253
#> theta[27]  9.427399 2.7902017  4.01832370  7.559480  9.445007 11.345112
#> theta[28] 15.007497 0.9252306 13.22469797 14.377737 15.010341 15.599422
#> theta[29] 13.191170 1.6446327  9.84914005 12.100848 13.250591 14.269838
#> theta[30] 10.128905 1.6930025  6.92584620  8.952537 10.081985 11.255618
#> theta[31] 13.995094 2.2298685  9.42260032 12.501023 14.055313 15.481307
#> theta[32] 14.593401 0.9560774 12.67849110 13.965419 14.603681 15.242259
#> theta[33]  9.853677 3.2619884  3.74099479  7.627444  9.823720 12.061697
#> theta[34] 13.781547 1.4065935 11.06641486 12.843207 13.764285 14.697525
#> theta[35] 14.621477 2.0383041 10.61505929 13.297478 14.567846 15.964285
#> theta[36] 13.476941 1.9884456  9.77565143 12.131593 13.493906 14.818431
#> theta[37] 13.978453 0.8349509 12.33098030 13.404954 14.000262 14.573366
#> theta[38] 14.239997 0.9337390 12.45593619 13.615982 14.222594 14.852591
#> theta[39] 12.506030 1.4206141  9.75540196 11.531036 12.547838 13.470163
#> theta[40]  9.195767 2.3351767  4.81122935  7.614040  9.182069 10.784840
#> theta[41] 18.446621 0.8272620 16.85598440 17.885462 18.433786 18.994211
#> theta[42] 12.487609 1.0178688 10.51787388 11.787133 12.466348 13.180391
#> theta[43] 16.318743 3.3940545  9.43114020 14.040964 16.371559 18.639568
#> theta[44] 17.002904 1.5146661 14.03903962 15.979602 17.015843 18.009529
#> theta[45] 18.567948 1.4238096 15.76836756 17.606204 18.566025 19.550843
#> theta[46] 13.661889 1.9671030  9.88056780 12.257638 13.665720 14.972522
#> theta[47] 12.517711 2.6560618  7.24477032 10.659875 12.579555 14.374877
#> theta[48] 11.380916 0.6548801 10.05521705 10.967220 11.391213 11.817640
#> theta[49]  6.672183 1.3658900  3.97906356  5.759477  6.678551  7.605580
#> theta[50] 15.996889 1.5578191 13.05273820 14.893135 16.022389 17.063798
#> theta[51]  7.882397 1.3744073  5.26669274  6.957594  7.868502  8.809277
#> theta[52] 26.572648 0.8301478 24.98048612 26.023508 26.563494 27.149969
#> theta[53] 18.487463 1.6070242 15.29333794 17.418419 18.485024 19.561466
#> theta[54] 17.936920 1.2415471 15.54802913 17.062561 17.979671 18.787380
#> theta[55] 11.994361 0.7037263 10.63854657 11.521198 12.002251 12.481799
#> theta[56] 11.474792 0.5245083 10.45195069 11.123292 11.471811 11.840864
#> theta[57]  8.991126 0.6544203  7.65986800  8.547704  9.005040  9.431313
#> theta[58] 13.774279 1.4260052 11.04268826 12.782300 13.772780 14.708877
#> theta[59] 16.522484 0.9200353 14.66280631 15.904449 16.523112 17.129335
#> theta[60] 15.159308 0.8337887 13.54732709 14.587418 15.182572 15.712298
#> theta[61]  5.491942 1.9999821  1.48416128  4.105306  5.543011  6.856681
#> theta[62]  5.906371 0.8244725  4.26721163  5.332648  5.915484  6.460061
#> theta[63]  5.314971 0.8974201  3.52598735  4.710940  5.316833  5.903053
#> theta[64] 12.266334 1.5620995  9.27270043 11.193041 12.237317 13.298500
#> theta[65] 12.477806 2.4553193  7.53509863 10.836028 12.520269 14.114132
#> theta[66]  9.894469 1.2647218  7.45463250  9.019608  9.909055 10.758937
#> theta[67] 16.756831 1.0689289 14.67182315 16.045123 16.743914 17.481421
#> theta[68] 11.117471 1.2842271  8.56722072 10.270727 11.148906 11.995390
#> theta[69]  8.146350 0.8537684  6.42767511  7.580527  8.156900  8.703165
#> theta[70] 11.768361 0.8579245 10.10257532 11.183818 11.763236 12.351572
#> theta[71] 13.746542 0.7599761 12.25533845 13.240706 13.744106 14.260461
#> theta[72] 10.771531 0.7191706  9.35556064 10.289392 10.785825 11.249000
#> theta[73]  3.819286 1.4822380  0.96351705  2.784060  3.791011  4.803617
#> theta[74] 10.459246 1.4688567  7.48858025  9.464247 10.449492 11.441275
#> theta[75]  5.978901 1.3193890  3.46322666  5.062878  5.976377  6.853721
#> theta[76]  9.430605 0.7741122  7.92223569  8.917419  9.434866  9.958717
#> theta[77] 13.924839 0.7724853 12.41847692 13.406771 13.922485 14.460898
#> theta[78]  9.632494 1.9662929  5.90760703  8.264226  9.659134 10.994182
#> theta[79] 10.407839 1.1746981  8.11157047  9.603303 10.428853 11.172783
#> theta[80]  5.865590 0.7324261  4.42568186  5.363312  5.860410  6.357288
#> theta[81]  6.497564 0.7303601  5.10889594  5.988884  6.503639  6.999388
#> theta[82] 14.417067 2.2110465 10.20345957 12.941152 14.311959 15.949257
#> theta[83] 10.613193 1.8195836  7.06406375  9.391602 10.616721 11.849376
#> theta[84]  9.911591 2.8915792  4.32868727  7.900814  9.864745 11.838474
#> theta[85] 13.413900 1.6175309 10.20224798 12.304231 13.410742 14.520527
#> theta[86] 18.548327 1.4583818 15.62296268 17.598672 18.557821 19.538362
#> theta[87] 11.466484 0.7774595  9.99015003 10.949277 11.426799 11.976225
#> theta[88]  7.957290 1.9477432  4.21817064  6.659337  7.951922  9.245385
#> theta[89]  7.709310 1.3976003  4.89360237  6.735464  7.735047  8.643738
#> theta[90]  4.542775 2.2879888 -0.01891893  2.976651  4.616457  6.139879
#>               97.5%
#> theta[1]  19.899519
#> theta[2]  14.532984
#> theta[3]  19.401557
#> theta[4]  14.172216
#> theta[5]  16.307308
#> theta[6]  13.076825
#> theta[7]  15.965373
#> theta[8]  17.149293
#> theta[9]  17.910225
#> theta[10] 16.670144
#> theta[11] 15.651003
#> theta[12] 19.698542
#> theta[13] 10.402226
#> theta[14] 11.781687
#> theta[15] 16.910439
#> theta[16] 15.567023
#> theta[17]  3.574591
#> theta[18]  9.348795
#> theta[19]  3.582551
#> theta[20]  9.916299
#> theta[21]  5.955085
#> theta[22] 17.089969
#> theta[23] 14.925314
#> theta[24] 19.808926
#> theta[25] 17.122917
#> theta[26] 14.342850
#> theta[27] 14.776552
#> theta[28] 16.840783
#> theta[29] 16.380888
#> theta[30] 13.575275
#> theta[31] 18.356736
#> theta[32] 16.477235
#> theta[33] 16.371028
#> theta[34] 16.578133
#> theta[35] 18.662100
#> theta[36] 17.396603
#> theta[37] 15.558724
#> theta[38] 16.150883
#> theta[39] 15.218792
#> theta[40] 13.813879
#> theta[41] 20.113549
#> theta[42] 14.505628
#> theta[43] 23.015847
#> theta[44] 20.087386
#> theta[45] 21.421827
#> theta[46] 17.459185
#> theta[47] 17.587811
#> theta[48] 12.633548
#> theta[49]  9.315379
#> theta[50] 19.025454
#> theta[51] 10.633564
#> theta[52] 28.221004
#> theta[53] 21.666140
#> theta[54] 20.374352
#> theta[55] 13.365830
#> theta[56] 12.533182
#> theta[57] 10.250962
#> theta[58] 16.607013
#> theta[59] 18.363974
#> theta[60] 16.732722
#> theta[61]  9.160355
#> theta[62]  7.490205
#> theta[63]  7.133660
#> theta[64] 15.368025
#> theta[65] 17.217332
#> theta[66] 12.373385
#> theta[67] 18.831362
#> theta[68] 13.560890
#> theta[69]  9.775442
#> theta[70] 13.486144
#> theta[71] 15.190769
#> theta[72] 12.149589
#> theta[73]  6.913184
#> theta[74] 13.408404
#> theta[75]  8.596500
#> theta[76] 10.910431
#> theta[77] 15.423584
#> theta[78] 13.488810
#> theta[79] 12.705488
#> theta[80]  7.306717
#> theta[81]  7.953674
#> theta[82] 18.890580
#> theta[83] 14.145646
#> theta[84] 15.410361
#> theta[85] 16.539336
#> theta[86] 21.298038
#> theta[87] 13.068772
#> theta[88] 11.792573
#> theta[89] 10.365822
#> theta[90]  9.118942

Area Estimatio

model$Est_area
#>         Mean        SD      2.5%       25%       50%       75%     97.5%
#> 1  13.210979 1.9380949  9.505877 11.906510 13.213485 14.450016 17.040837
#> 2  12.436534 0.6699768 11.126497 11.986014 12.452073 12.882142 13.755698
#> 3  14.441778 0.7776659 12.905122 13.910207 14.443650 14.959831 15.974126
#> 4  14.846531 0.6824594 13.533365 14.403184 14.824115 15.297871 16.241433
#> 5  11.298036 0.4461963 10.427999 10.991139 11.301914 11.590375 12.160421
#> 6   7.812635 0.7606686  6.285047  7.349826  7.813565  8.332198  9.330336
#> 7   4.496987 0.8543292  2.846008  3.917947  4.525853  5.059576  6.216664
#> 8  15.858407 0.6485665 14.595497 15.427397 15.857631 16.275079 17.137505
#> 9  11.299898 1.3793362  8.578959 10.385017 11.294657 12.247095 13.999471
#> 10 12.315492 0.9491214 10.480428 11.677050 12.319935 12.957447 14.174295
#> 11 12.516021 1.7221005  9.273842 11.319931 12.598127 13.653543 15.904313
#> 12 13.971221 1.1475310 11.746713 13.174721 13.985229 14.718047 16.254527
#> 13 13.460128 0.6879917 12.100292 13.000850 13.467664 13.925689 14.824770
#> 14 13.262517 0.9482905 11.424205 12.610922 13.273238 13.899337 15.186283
#> 15 17.232847 1.6441343 14.042808 16.135582 17.253587 18.328547 20.464123
#> 16 12.652173 1.3365664  9.988232 11.740161 12.647279 13.535908 15.245354
#> 17 10.533934 0.8843751  8.760395  9.942628 10.545136 11.129266 12.257456
#> 18 20.787820 0.7568388 19.304665 20.277401 20.778386 21.309698 22.217832
#> 19 10.413053 0.3952150  9.635534 10.142938 10.416143 10.691528 11.174730
#> 20 15.250516 0.5935284 14.101183 14.843713 15.240964 15.649119 16.447418
#> 21  5.540535 0.8293924  3.892919  4.974649  5.536557  6.090460  7.155547
#> 22 11.563401 1.0915893  9.402816 10.847541 11.576049 12.301669 13.675216
#> 23 12.058277 0.6438665 10.787743 11.620275 12.047544 12.501643 13.298537
#> 24 12.141311 0.4864941 11.185986 11.797143 12.149427 12.473229 13.123429
#> 25  6.496448 0.8574342  4.811472  5.899650  6.508405  7.076957  8.196597
#> 26 11.369481 0.7213271  9.994064 10.889985 11.363380 11.855389 12.813311
#> 27  7.445352 0.5372727  6.399843  7.084737  7.447279  7.815466  8.493360
#> 28 12.048524 1.5133422  9.001044 11.042677 12.042714 13.050435 14.953986
#> 29 14.730450 0.8259421 13.059377 14.179878 14.761802 15.276725 16.308044
#> 30  6.516625 1.2911534  4.029320  5.620797  6.534162  7.388815  9.133667

Coefficient Estimation

model$coefficient
#>               Mean         SD       2.5%        25%        50%        75%
#> beta[0] -0.3715745 0.64509490 -1.5979456 -0.8161531 -0.3686178 0.07934783
#> beta[1]  0.2095470 0.61179664 -0.9802871 -0.2018037  0.2016350 0.61913497
#> beta[2]  1.2289213 0.06471573  1.1035608  1.1846458  1.2309631 1.27125770
#>             97.5%
#> beta[0] 0.8478696
#> beta[1] 1.4523138
#> beta[2] 1.3578533

Random effect variance estimation

model$refVar
#>   var_area  var_sub
#> 1 8.085016 8.828761

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.   : 3.124   Min.   : 0.2246  
#>  1st Qu.: 6.587   1st Qu.: 0.6957  
#>  Median :11.508   Median : 1.6950  
#>  Mean   :13.763   Mean   : 2.3983  
#>  3rd Qu.:17.285   3rd Qu.: 3.4049  
#>  Max.   :50.365   Max.   :11.5196

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.   : 3.641   Min.   :0.1562  
#>  1st Qu.: 5.168   1st Qu.:0.4531  
#>  Median : 7.461   Median :0.6850  
#>  Mean   : 8.643   Mean   :1.0243  
#>  3rd Qu.:11.796   3rd Qu.:1.2855  
#>  Max.   :19.813   Max.   :3.7562

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.   : 3.124  
#>  1st Qu.:  6.642   1st Qu.: 6.587  
#>  Median : 12.763   Median :11.508  
#>  Mean   : 25.141   Mean   :13.763  
#>  3rd Qu.: 21.041   3rd Qu.:17.285  
#>  Max.   :680.378   Max.   :50.365
  • Look that! ,CV on our model is less than CV on direct estimator.
boxplot(cbind(dirCV,CV),ylim=c(0,50))

model$refVar
#>   var_area  var_sub
#> 1 8.085016 8.828761
model$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,]  0.241624462  0.4476526287 1.245501
#>    [2,] -0.128314720  0.1193991458 1.188790
#>    [3,]  0.485335153 -0.6795958908 1.196801
#>    [4,]  0.138013320  0.4904752957 1.093812
#>    [5,] -0.479717971 -0.0956399574 1.225508
#>    [6,]  0.361640603  0.0518144981 1.153586
#>    [7,] -0.878749522  0.6519765774 1.265095
#>    [8,] -0.222329174 -0.0176393960 1.276749
#>    [9,]  0.143053164  0.2847920908 1.162858
#>   [10,] -1.788429061 -0.3930318479 1.317838
#>   [11,] -1.274343427 -0.2728579088 1.306119
#>   [12,] -0.515083651  1.0791580368 1.280770
#>   [13,]  0.818654701 -0.4777767060 1.141289
#>   [14,] -0.103411605  0.4231381229 1.112074
#>   [15,] -0.859878260  0.4467432660 1.255256
#>   [16,] -0.318764780  0.7320868769 1.265033
#>   [17,]  0.292926397  0.0844303063 1.131794
#>   [18,]  0.317818607  0.5105131133 1.213762
#>   [19,]  0.508631043  0.5935940566 1.080929
#>   [20,] -0.012720913 -0.4024671385 1.222869
#>   [21,] -1.460529330 -0.1863605480 1.269223
#>   [22,] -1.170666002  0.2989098092 1.367505
#>   [23,]  0.038941093  0.7195166700 1.076106
#>   [24,] -0.540593800  0.1878627426 1.322064
#>   [25,] -1.425422631  0.2668612964 1.328410
#>   [26,]  0.477582882  0.6274042575 1.188882
#>   [27,] -0.812790548  0.7273256273 1.249465
#>   [28,]  0.785627876 -0.0908253123 1.133339
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#>  [879,] -0.653564122  1.1395250064 1.260046
#>  [880,] -0.650289979 -1.0775119697 1.256851
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#>  [884,]  0.030845769 -0.1569199484 1.198592
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#>  [886,] -0.586504541 -0.7714574335 1.314558
#>  [887,] -0.973841733  0.0251852200 1.288289
#>  [888,]  0.049168820  0.1260132099 1.284953
#>  [889,]  0.604085459 -0.1944381441 1.212621
#>  [890,]  0.195812847  0.5498998493 1.136123
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#>  [897,] -0.496294881 -0.7801589520 1.225511
#>  [898,]  0.135721459  0.6336414902 1.184784
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#>  [902,]  0.672130397  0.4730266869 1.189997
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#>  [904,] -0.662024367  0.0172850356 1.185670
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#> [1785,] -0.209024937  0.5330532079 1.337928
#> [1786,]  0.340539324  0.6899988821 1.169348
#> [1787,] -1.245598743 -0.1278893135 1.232065
#> [1788,] -1.349087126  0.3690395363 1.391953
#> [1789,] -0.084773352  0.8337264748 1.166582
#> [1790,]  0.328902956 -0.9593865779 1.241035
#> [1791,]  0.001202624 -0.0969463144 1.187120
#> [1792,]  0.337791392  0.5721372287 1.193774
#> [1793,] -0.145480529  0.3177093556 1.196863
#> [1794,] -1.136763627  0.2523499408 1.239173
#> [1795,] -1.108756944  0.0288120097 1.200330
#> [1796,] -0.289685423  0.1382316673 1.227431
#> [1797,] -0.449446986  0.1900828719 1.194906
#> [1798,] -0.171461633  0.3136893643 1.284489
#> [1799,] -0.654656953 -1.0604939331 1.207897
#> [1800,] -0.639905591  0.0435541296 1.277506
#> [1801,] -1.053480795  0.9720056559 1.201294
#> [1802,] -1.626608597  1.7467806037 1.234471
#> [1803,] -0.046414404  0.3863826906 1.197276
#> [1804,] -0.902542530  0.9713417661 1.146277
#> [1805,]  0.400782581 -0.0653745254 1.200456
#> [1806,] -0.217606352  0.3050765478 1.211956
#> [1807,] -1.226464922 -0.1483991096 1.263066
#> [1808,] -1.351386720 -1.1046791329 1.437235
#> [1809,] -1.532173043 -0.2015021157 1.264773
#> [1810,]  0.069676984 -0.3601950566 1.175796
#> [1811,]  0.220770127 -0.0492575459 1.162467
#> [1812,] -0.851129718 -0.2633750240 1.173552
#> [1813,] -0.597843400 -0.3278820158 1.263294
#> [1814,]  0.159964305 -0.2817113963 1.140081
#> [1815,]  0.320070158  0.2346836602 1.234292
#> [1816,]  0.125547167 -0.4814854573 1.185596
#> [1817,] -0.332056437 -0.9111142780 1.319139
#> [1818,] -1.703484298  0.3901566125 1.337118
#> [1819,] -0.904809742  0.6722159686 1.250180
#> [1820,] -1.200451939  0.8340915087 1.283278
#> [1821,] -0.347576734  0.0882302817 1.315352
#> [1822,] -0.242051598  0.5013416117 1.139608
#> [1823,]  0.671122678 -0.3560981684 1.182901
#> [1824,] -0.368950487  0.1253707957 1.259368
#> [1825,]  0.553530647  0.1213334244 1.156329
#> [1826,] -0.876877781  0.5805610188 1.277586
#> [1827,] -0.339399572 -1.4736720903 1.267167
#> [1828,] -0.226746409  0.0778804606 1.316597
#> [1829,] -0.164379546 -0.7413226838 1.212257
#> [1830,] -0.417658660 -0.5388157069 1.204612
#> [1831,] -0.210022656  1.3015892999 1.237703
#> [1832,]  0.473718735 -1.4931854838 1.306950
#> [1833,] -0.130695070  0.6509486493 1.136727
#> [1834,] -0.267376850 -0.0276782985 1.206867
#> [1835,] -0.379103114 -0.3710042225 1.265071
#> [1836,]  0.007316998 -0.2051339335 1.281314
#> [1837,] -0.431744371 -0.4781109112 1.281945
#> [1838,] -0.650356852  0.4895432058 1.265880
#> [1839,]  0.309333188 -0.7050129113 1.247567
#> [1840,] -0.385346811 -0.2996745367 1.297633
#> [1841,]  0.114391051 -0.3350881948 1.272304
#> [1842,] -0.040978735  0.7728814367 1.191795
#> [1843,] -0.012285321  0.4529283873 1.239326
#> [1844,]  0.346900669 -0.7753191119 1.200224
#> [1845,] -0.743095782 -0.4212269839 1.329296
#> [1846,]  0.248140246 -0.3825887521 1.194022
#> [1847,] -0.106388123  0.0972026498 1.128453
#> [1848,] -0.436425938 -0.1984569255 1.231230
#> [1849,] -1.287468481  0.2926607697 1.266969
#> [1850,] -0.769259102 -0.5501891978 1.338610
#> [1851,] -0.351048875  1.6235003557 1.261063
#> [1852,] -0.281537295  0.5601032181 1.216452
#> [1853,] -1.090256192  0.6626978913 1.351712
#> [1854,]  0.115857896  0.7170858097 1.163736
#> [1855,] -0.270182499  0.2491725604 1.152529
#> [1856,]  0.103374439  0.7578583442 1.154620
#> [1857,]  0.886549202 -0.9376873028 1.167013
#> [1858,]  0.341021730 -0.4520189487 1.249511
#> [1859,] -1.629269238  0.6983972839 1.265573
#> [1860,] -1.830629816 -0.2233563041 1.330684
#> [1861,]  0.070925362 -0.8669358604 1.277465
#> [1862,] -1.214606215  1.4806344677 1.230721
#> [1863,] -0.991309488  0.8996884039 1.259794
#> [1864,]  0.111179283  0.3775436367 1.193899
#> [1865,] -0.494938006  0.5846406300 1.233612
#> [1866,] -1.226917020  0.6719241010 1.322328
#> [1867,]  0.054280777 -0.2781378983 1.311921
#> [1868,] -0.368285052 -0.6774978537 1.260657
#> [1869,] -0.440062798 -0.2701040938 1.234595
#> [1870,] -0.478771418  1.2215765111 1.246309
#> [1871,]  1.049129834 -0.1014804323 1.225660
#> [1872,]  0.099989433  0.5406628096 1.113376
#> [1873,]  0.688355038  0.5156258079 1.150477
#> [1874,]  1.182813190 -0.7357183289 1.123032
#> [1875,] -0.274362722 -0.8568461004 1.217754
#> [1876,] -0.871917449 -0.1193251516 1.229286
#> [1877,]  0.144546336  1.4905932982 1.133811
#> [1878,] -0.861172910 -0.3333367180 1.299395
#> [1879,]  1.252671066 -0.6530986948 1.197731
#> [1880,]  0.141998047  0.1450247226 1.167340
#> [1881,]  0.058131956  0.4764628467 1.196967
#> [1882,] -0.626929534 -0.2850548626 1.236854
#> [1883,] -0.317094564 -0.3383247538 1.181146
#> [1884,] -0.176783879 -0.4233558469 1.318690
#> [1885,]  0.617853260 -0.8800686744 1.177390
#> [1886,] -1.009674529  0.2586944658 1.287725
#> [1887,] -0.804804415 -0.2027086443 1.397802
#> [1888,]  0.088848033 -1.4317665944 1.260114
#> [1889,] -0.655638960 -0.0931224296 1.294600
#> [1890,] -1.117331214  0.9582538882 1.218683
#> [1891,] -1.106013075 -0.5233949335 1.328302
#> [1892,] -0.653337118  0.3257912467 1.244354
#> [1893,]  0.434457191 -0.0851884177 1.158785
#> [1894,] -1.027421893 -0.0403389666 1.208648
#> [1895,] -1.226163454  1.3492600164 1.218106
#> [1896,] -0.175590908  0.0530166572 1.218491
#> [1897,] -1.211194499  1.0613550870 1.234129
#> [1898,]  0.798815555  0.7596602367 1.128104
#> [1899,] -0.005280227 -0.6666653339 1.243538
#> [1900,] -0.279687986  0.1285281625 1.147984
#> [1901,] -0.846338763 -0.4512672850 1.292847
#> [1902,] -0.185670116  0.4314044681 1.117884
#> [1903,]  0.549438566  0.3930381759 1.149250
#> [1904,]  0.423162549 -0.0286202460 1.082243
#> [1905,] -1.164393836 -0.3335810752 1.302235
#> [1906,] -1.526512484 -0.5828485523 1.302773
#> [1907,] -0.452297039 -0.1013732682 1.268739
#> [1908,] -0.565416882  1.3261541037 1.265630
#> [1909,]  0.906613140 -0.2762251756 1.108005
#> [1910,] -0.189607705  0.2094408854 1.310653
#> [1911,]  1.161586725 -0.1640683807 1.110691
#> [1912,] -0.950429503  0.1652136123 1.240496
#> [1913,] -1.063526198  0.6478517712 1.291682
#> [1914,] -0.905240495  1.0057012769 1.253860
#> [1915,] -0.795043750  0.4902773106 1.189918
#> [1916,] -1.236555215  0.0571018263 1.314405
#> [1917,] -1.014930485  0.4740259948 1.258815
#> [1918,]  0.311749101  0.6497128323 1.204879
#> [1919,] -1.487626549  0.0421672358 1.217034
#> [1920,]  0.002211793  1.0855294778 1.266816
#> [1921,]  0.581449587 -0.0773631033 1.183290
#> [1922,] -1.539320577  0.4437939645 1.226656
#> [1923,] -0.476058080  0.9843682123 1.176719
#> [1924,] -1.330361688  1.0804314819 1.312819
#> [1925,] -0.539205176 -0.3299354747 1.253914
#> [1926,] -1.076437692  0.6755113299 1.260128
#> [1927,] -0.573417879  1.0658383541 1.248252
#> [1928,]  0.302786078 -0.6734516229 1.238573
#> [1929,]  0.142244567  0.3544276109 1.196238
#> [1930,] -0.577711700 -0.9776208538 1.335830
#> [1931,]  0.520929077  0.1089413015 1.143424
#> [1932,]  1.101857163  0.5517745105 1.134464
#> [1933,] -0.444733149 -0.2983245921 1.164609
#> [1934,] -0.179213747 -0.1360913928 1.255179
#> [1935,] -0.639760175  0.4445310029 1.220200
#> [1936,] -0.781240572  0.6439369422 1.268260
#> [1937,] -0.761179164  1.2579494563 1.193746
#> [1938,]  0.632275804  1.2760722030 1.100951
#> [1939,]  0.095911025  0.0946747132 1.161074
#> [1940,] -0.827104019  1.0379555712 1.280372
#> [1941,]  0.065725306  1.0823562841 1.085266
#> [1942,] -0.714870200  0.5087587748 1.155961
#> [1943,] -0.163775606  0.9304403777 1.284346
#> [1944,]  0.319233789  0.9964698703 1.082057
#> [1945,] -0.148489084 -0.2276626817 1.210291
#> [1946,] -0.839697567  0.9543235364 1.269875
#> [1947,] -0.599460807 -0.1240313381 1.304764
#> [1948,] -0.106361368 -0.3427565083 1.207435
#> [1949,] -0.089441289 -1.6221007407 1.268120
#> [1950,] -0.669283692  0.3991254056 1.356604
#> [1951,] -0.147258483  0.1451616134 1.231238
#> [1952,]  0.881760871 -0.2520864534 1.228431
#> [1953,] -0.775232407  0.3410157268 1.226946
#> [1954,] -1.093729797  0.6412482828 1.339187
#> [1955,] -0.495388951 -0.7579623822 1.360708
#> [1956,]  0.316246169 -0.0999225144 1.159388
#> [1957,] -1.022739095  1.0552113749 1.179245
#> [1958,] -0.741114027  0.3384964668 1.141942
#> [1959,]  0.149209879 -0.2676532954 1.181896
#> [1960,]  0.991151338  0.1252573622 1.119790
#> [1961,]  0.462334806 -0.1695818683 1.074099
#> [1962,] -0.966202137  0.7208790336 1.306727
#> [1963,] -1.386343511  1.2217933813 1.302450
#> [1964,] -1.038535446  0.9952072491 1.232174
#> [1965,] -0.514888570 -0.2254197000 1.249179
#> [1966,] -0.400596793 -0.0414112866 1.170659
#> [1967,]  0.026489495  0.1026858834 1.132198
#> [1968,]  0.561993430  0.1617227818 1.173025
#> [1969,] -0.550694337  0.4537593596 1.206836
#> [1970,] -0.207986225  0.2005757710 1.213271
#> [1971,] -0.986185792  1.0195656442 1.197716
#> [1972,] -0.471913756 -0.0355703287 1.285234
#> [1973,] -0.705372604  0.3809798790 1.241107
#> [1974,] -0.659110913  0.0508985085 1.220782
#> [1975,] -0.608377821 -0.2067524012 1.226081
#> [1976,]  0.125024104 -0.3302995765 1.224594
#> [1977,] -0.093024126 -0.7939716790 1.213668
#> [1978,] -1.170163433  0.6339202340 1.295023
#> [1979,] -0.618509350  0.3911386917 1.187980
#> [1980,]  0.749955628 -0.0860244039 1.178732
#> 
#> attr(,"class")
#> [1] "mcmc.list"
#> 
#> [[4]]
#> NULL