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

STEP 3 Extract mean estimation

Subarea Estimation

model$Est_sub
#>                Mean        SD       2.5%       25%       50%       75%
#> theta[1]  13.693083 3.1440877  7.6832926 11.452546 13.658045 15.847425
#> theta[2]  11.028092 1.9476199  7.2031187  9.702023 11.040583 12.366932
#> theta[3]  14.230878 2.6124705  9.2873893 12.410842 14.235370 16.018759
#> theta[4]  11.577260 1.3905414  8.7743643 10.631342 11.550436 12.526189
#> theta[5]  14.735163 0.7741062 13.1954115 14.223904 14.722909 15.272836
#> theta[6]  10.641018 1.2109329  8.2982773  9.785565 10.650227 11.441117
#> theta[7]  14.275010 0.8857167 12.5192338 13.664551 14.259416 14.862331
#> theta[8]  13.476120 1.8895907  9.5744488 12.197310 13.487324 14.765132
#> theta[9]  16.232074 0.9254906 14.4405762 15.632787 16.255426 16.864185
#> theta[10] 14.868367 0.8985164 13.1358977 14.249684 14.876336 15.484935
#> theta[11] 14.294192 0.7045536 12.9411873 13.797291 14.299715 14.776237
#> theta[12] 15.773707 1.9868464 12.0818426 14.411446 15.739904 17.181337
#> theta[13]  9.294758 0.5857204  8.1406314  8.907932  9.293555  9.696288
#> theta[14]  9.944960 0.9574875  8.1522911  9.288496  9.943981 10.586095
#> theta[15] 15.538239 0.6862474 14.2001090 15.065190 15.554895 16.003303
#> theta[16] 12.614884 1.6061677  9.4728918 11.524949 12.593249 13.731509
#> theta[17]  2.221883 0.7016079  0.7907812  1.772288  2.237079  2.694662
#> theta[18]  7.211860 1.1394558  5.0166906  6.431565  7.199878  8.019271
#> theta[19]  2.159517 0.7524996  0.6794804  1.661969  2.165973  2.672639
#> theta[20]  6.151451 1.8713014  2.5624420  4.927957  6.109277  7.343471
#> theta[21]  4.399953 0.7706870  2.8797601  3.883330  4.392508  4.929039
#> theta[22] 14.699025 1.1840966 12.3193659 13.900294 14.714661 15.505189
#> theta[23] 13.994480 0.4804456 13.0233971 13.674675 14.011437 14.319228
#> theta[24] 17.569426 1.1210654 15.3417614 16.845339 17.550858 18.289364
#> theta[25] 14.467208 1.3651250 11.9028782 13.542303 14.463241 15.405291
#> theta[26] 10.386252 1.9479378  6.5479940  9.070976 10.390593 11.692419
#> theta[27]  9.564839 2.7540803  4.2003969  7.753060  9.495424 11.390808
#> theta[28] 14.997177 0.9055971 13.2155629 14.402814 15.017186 15.591486
#> theta[29] 13.168407 1.6704232  9.8415944 12.074664 13.163306 14.321000
#> theta[30] 10.066898 1.6694198  6.8351666  8.966443 10.094843 11.181342
#> theta[31] 13.995446 2.2247726  9.5919360 12.558646 13.989420 15.445391
#> theta[32] 14.611941 0.9259295 12.8695354 14.002221 14.587259 15.201997
#> theta[33]  9.933734 3.1427197  3.7709129  7.802090  9.903038 12.148100
#> theta[34] 13.786827 1.3691273 11.1864560 12.849485 13.771693 14.732491
#> theta[35] 14.608376 2.0204835 10.6619412 13.177090 14.642519 16.039637
#> theta[36] 13.498561 2.0289658  9.5073451 12.130812 13.511275 14.853664
#> theta[37] 13.985715 0.8068030 12.4290307 13.422881 13.988506 14.538562
#> theta[38] 14.236547 0.9153553 12.3965573 13.618666 14.251199 14.883424
#> theta[39] 12.491367 1.4431576  9.6897742 11.510528 12.498683 13.515129
#> theta[40]  9.182744 2.3580874  4.5142494  7.617768  9.225080 10.793401
#> theta[41] 18.435056 0.8439042 16.7381271 17.853716 18.430786 19.009655
#> theta[42] 12.468216 1.0189513 10.5166812 11.742584 12.501564 13.164567
#> theta[43] 16.587733 3.2902597 10.1489821 14.389634 16.571027 18.830568
#> theta[44] 16.942030 1.5163762 13.9474269 15.931024 16.962564 17.985927
#> theta[45] 18.565029 1.4246628 15.7316881 17.611005 18.536197 19.530658
#> theta[46] 13.558985 1.9159420  9.7497179 12.233877 13.529070 14.866261
#> theta[47] 12.380883 2.6921164  6.9305270 10.494454 12.513709 14.246675
#> theta[48] 11.378970 0.6581733 10.0871739 10.937791 11.389309 11.824283
#> theta[49]  6.625032 1.4031738  3.8138213  5.665701  6.664181  7.613624
#> theta[50] 15.943631 1.5971104 12.8232057 14.849792 15.929222 17.018080
#> theta[51]  7.795446 1.4032797  4.9835896  6.887490  7.804643  8.754055
#> theta[52] 26.587616 0.8397789 24.9578346 26.050062 26.626583 27.120344
#> theta[53] 18.572019 1.6872590 15.0938206 17.499583 18.599007 19.720802
#> theta[54] 17.937396 1.2941764 15.4409154 17.037701 17.945989 18.838885
#> theta[55] 11.982599 0.7382594 10.5566326 11.506152 11.982299 12.472112
#> theta[56] 11.462592 0.5394953 10.4346778 11.090512 11.457644 11.813362
#> theta[57]  8.953105 0.6519583  7.6656329  8.517062  8.934962  9.391141
#> theta[58] 13.829112 1.4014025 11.0147771 12.908479 13.896182 14.807294
#> theta[59] 16.501365 0.9395752 14.6410364 15.858763 16.488845 17.132360
#> theta[60] 15.184499 0.8322890 13.5583307 14.626956 15.188710 15.742744
#> theta[61]  5.607510 1.9610594  1.7013786  4.300218  5.564937  6.935284
#> theta[62]  5.906083 0.8030804  4.3571843  5.387584  5.899245  6.476853
#> theta[63]  5.315941 0.9107320  3.4773846  4.690521  5.320311  5.946399
#> theta[64] 12.245855 1.5821479  9.1878934 11.178769 12.190655 13.299034
#> theta[65] 12.376994 2.4233458  7.6387125 10.733958 12.364552 14.053226
#> theta[66]  9.883870 1.2711434  7.3491687  9.055714  9.885523 10.729562
#> theta[67] 16.759269 0.9995374 14.8334802 16.104133 16.775115 17.459750
#> theta[68] 11.170258 1.2916323  8.7465822 10.271161 11.192107 12.025393
#> theta[69]  8.160848 0.8348065  6.4812734  7.586328  8.162028  8.734331
#> theta[70] 11.767139 0.8354719 10.1664851 11.180040 11.768260 12.346204
#> theta[71] 13.699673 0.7586153 12.1912459 13.185651 13.692133 14.204726
#> theta[72] 10.757707 0.7155263  9.3980962 10.273134 10.757595 11.235465
#> theta[73]  3.804579 1.4959573  0.8892903  2.856966  3.795619  4.821655
#> theta[74] 10.474337 1.5020797  7.5365570  9.454884 10.474929 11.507532
#> theta[75]  5.950642 1.3723098  3.2896206  5.021904  5.936676  6.868045
#> theta[76]  9.442338 0.7830600  7.9365019  8.910990  9.460827  9.983924
#> theta[77] 13.933855 0.7646112 12.4454286 13.426355 13.917348 14.447013
#> theta[78]  9.614104 1.9551872  5.7041481  8.302080  9.630629 10.969309
#> theta[79] 10.453441 1.1816588  8.1541486  9.662413 10.467478 11.275382
#> theta[80]  5.871553 0.7374465  4.4157499  5.391050  5.876002  6.375063
#> theta[81]  6.491376 0.7243533  5.0722614  6.015931  6.496226  6.974689
#> theta[82] 14.392942 2.2746116  9.9091305 12.887726 14.379639 15.902145
#> theta[83] 10.695579 1.8178572  7.0522314  9.462519 10.684482 11.934158
#> theta[84] 10.149466 3.0110538  4.1772799  8.130430 10.240022 12.228205
#> theta[85] 13.424261 1.6268704 10.4410820 12.284611 13.353378 14.483667
#> theta[86] 18.581322 1.4411382 15.6562851 17.637658 18.562201 19.545442
#> theta[87] 11.461157 0.8153415  9.8838962 10.894198 11.475687 12.022233
#> theta[88]  7.937114 1.8534939  4.1763113  6.690297  7.936301  9.194541
#> theta[89]  7.681839 1.3870161  4.9015391  6.736417  7.700307  8.627863
#> theta[90]  4.496498 2.2976317  0.1412894  2.989440  4.418699  6.033469
#>               97.5%
#> theta[1]  20.024416
#> theta[2]  14.783491
#> theta[3]  19.409936
#> theta[4]  14.347383
#> theta[5]  16.230054
#> theta[6]  12.953242
#> theta[7]  16.019005
#> theta[8]  17.135818
#> theta[9]  18.027018
#> theta[10] 16.630439
#> theta[11] 15.674026
#> theta[12] 19.644615
#> theta[13] 10.459364
#> theta[14] 11.876632
#> theta[15] 16.889552
#> theta[16] 15.726620
#> theta[17]  3.537638
#> theta[18]  9.398716
#> theta[19]  3.545101
#> theta[20] 10.017021
#> theta[21]  5.872819
#> theta[22] 16.960955
#> theta[23] 14.908415
#> theta[24] 19.816687
#> theta[25] 17.143287
#> theta[26] 14.129561
#> theta[27] 15.340597
#> theta[28] 16.773500
#> theta[29] 16.324237
#> theta[30] 13.291106
#> theta[31] 18.410778
#> theta[32] 16.468881
#> theta[33] 15.961584
#> theta[34] 16.467527
#> theta[35] 18.602474
#> theta[36] 17.481540
#> theta[37] 15.558744
#> theta[38] 16.008392
#> theta[39] 15.295539
#> theta[40] 13.662692
#> theta[41] 20.072320
#> theta[42] 14.401603
#> theta[43] 22.955701
#> theta[44] 19.925851
#> theta[45] 21.363896
#> theta[46] 17.195101
#> theta[47] 17.600038
#> theta[48] 12.669554
#> theta[49]  9.298010
#> theta[50] 19.058629
#> theta[51] 10.579699
#> theta[52] 28.236667
#> theta[53] 21.753361
#> theta[54] 20.499342
#> theta[55] 13.410588
#> theta[56] 12.530700
#> theta[57] 10.233307
#> theta[58] 16.503562
#> theta[59] 18.390968
#> theta[60] 16.800835
#> theta[61]  9.439057
#> theta[62]  7.409539
#> theta[63]  7.075681
#> theta[64] 15.389867
#> theta[65] 17.027609
#> theta[66] 12.478461
#> theta[67] 18.659603
#> theta[68] 13.750180
#> theta[69]  9.749195
#> theta[70] 13.422721
#> theta[71] 15.212797
#> theta[72] 12.195832
#> theta[73]  6.742366
#> theta[74] 13.335573
#> theta[75]  8.616952
#> theta[76] 10.980308
#> theta[77] 15.407137
#> theta[78] 13.324944
#> theta[79] 12.693853
#> theta[80]  7.307281
#> theta[81]  7.926550
#> theta[82] 18.783402
#> theta[83] 14.195369
#> theta[84] 15.918991
#> theta[85] 16.587520
#> theta[86] 21.501483
#> theta[87] 13.058441
#> theta[88] 11.658328
#> theta[89] 10.375250
#> theta[90]  9.083414

Area Estimatio

model$Est_area
#>         Mean        SD      2.5%       25%       50%       75%     97.5%
#> 1  13.160031 1.9948229  9.459440 11.735945 13.121369 14.513535 17.198566
#> 2  12.426558 0.6615648 11.122448 11.961968 12.430937 12.885701 13.716912
#> 3  14.481335 0.7743711 12.949539 13.948040 14.473699 15.029910 15.930923
#> 4  14.872708 0.6827833 13.593633 14.400190 14.876632 15.346764 16.184443
#> 5  11.306383 0.4470488 10.461412 10.997881 11.296571 11.604144 12.200389
#> 6   7.816214 0.7521311  6.390458  7.285782  7.813765  8.350420  9.254231
#> 7   4.539827 0.8630685  2.844766  3.937791  4.536925  5.109756  6.311777
#> 8  15.844433 0.6440762 14.585973 15.418236 15.844423 16.281268 17.086809
#> 9  11.382264 1.3783137  8.613691 10.427922 11.386918 12.291970 14.113021
#> 10 12.278519 0.9396207 10.408935 11.680755 12.291980 12.904691 14.055451
#> 11 12.551395 1.6522608  9.319044 11.442609 12.521933 13.704303 15.749068
#> 12 13.975309 1.1481513 11.800898 13.207123 13.961027 14.751204 16.241012
#> 13 13.455601 0.7085069 11.993626 12.977414 13.472711 13.920558 14.821073
#> 14 13.247813 0.9483213 11.352111 12.599345 13.272407 13.899315 15.122412
#> 15 17.328075 1.6114079 14.158295 16.290939 17.340782 18.353933 20.496237
#> 16 12.562124 1.3321473  9.886418 11.680208 12.613239 13.485614 15.160992
#> 17 10.469977 0.9184278  8.719874  9.837378 10.448031 11.089201 12.281369
#> 18 20.816082 0.7813159 19.318823 20.287632 20.809118 21.343452 22.337011
#> 19 10.388490 0.3920947  9.638808 10.125908 10.368243 10.649618 11.155229
#> 20 15.268407 0.5952838 14.092599 14.861201 15.280339 15.666452 16.431537
#> 21  5.581087 0.8267128  3.951674  5.013597  5.578924  6.144622  7.166213
#> 22 11.523350 1.0957552  9.396975 10.766746 11.514461 12.215882 13.660216
#> 23 12.081280 0.6352067 10.832980 11.668868 12.060541 12.506389 13.361016
#> 24 12.122649 0.4822149 11.179669 11.808896 12.118894 12.446792 13.060382
#> 25  6.485602 0.9029781  4.763085  5.881210  6.498559  7.114451  8.195030
#> 26 11.371258 0.7105175  9.957484 10.887851 11.387724 11.861037 12.741615
#> 27  7.460068 0.5188561  6.467991  7.123007  7.463002  7.816064  8.458960
#> 28 12.124730 1.5488464  9.066439 11.110487 12.146864 13.159068 15.069800
#> 29 14.744368 0.8234171 13.163593 14.170597 14.757245 15.307429 16.337171
#> 30  6.483875 1.2737518  3.982710  5.648936  6.480304  7.327727  8.919021

Coefficient Estimation

Random effect variance estimation

STEP 3 : Extract CV and MSE Subarea

CV=(model$Est_sub$SD)/(model$Est_sub$Mean)*100
MSE=model$Est_sub$SD^2
summary(cbind(CV,MSE))
#>        CV              MSE         
#>  Min.   : 3.159   Min.   : 0.2308  
#>  1st Qu.: 6.485   1st Qu.: 0.6972  
#>  Median :11.558   Median : 1.7692  
#>  Mean   :13.750   Mean   : 2.3980  
#>  3rd Qu.:17.624   3rd Qu.: 3.4027  
#>  Max.   :51.098   Max.   :10.8258

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.   : 3.753   Min.   :0.1537  
#>  1st Qu.: 5.260   1st Qu.:0.4448  
#>  Median : 7.405   Median :0.6807  
#>  Mean   : 8.648   Mean   :1.0261  
#>  3rd Qu.:11.733   3rd Qu.:1.2889  
#>  Max.   :19.645   Max.   :3.9793

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.   : 3.159  
#>  1st Qu.:  6.642   1st Qu.: 6.485  
#>  Median : 12.764   Median :11.558  
#>  Mean   : 25.141   Mean   :13.750  
#>  3rd Qu.: 21.041   3rd Qu.:17.624  
#>  Max.   :680.378   Max.   :51.098
boxplot(cbind(dirCV,CV),ylim=c(0,50))

model$refVar
#>   var_area  var_sub
#> 1 8.196509 8.749809
model$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,]  0.1558351621  1.022709018 1.1627795
#>    [2,]  0.0436677898  0.704355286 1.1827617
#>    [3,] -0.2604370700 -0.457955265 1.2797772
#>    [4,] -0.3243633380 -0.550295485 1.1902768
#>    [5,] -0.4218323582  0.328992642 1.2007462
#>    [6,] -0.2379853565  0.031688451 1.2333364
#>    [7,]  0.1015615934  0.422568842 1.2325608
#>    [8,]  0.7700810798 -0.102004847 1.0786786
#>    [9,] -0.0731453322  0.111730970 1.1959962
#>   [10,] -0.6149920841 -0.093399795 1.3491447
#>   [11,] -0.3312022715  0.808283706 1.1832055
#>   [12,] -0.6142717010  1.221787187 1.2551724
#>   [13,] -0.3408359319 -0.802410322 1.2001040
#>   [14,] -0.3154049492 -0.228728744 1.3096973
#>   [15,] -0.9137568242 -0.308868873 1.2634340
#>   [16,]  0.2224293228 -0.272178330 1.1505687
#>   [17,]  0.8585461940 -0.720581643 1.1568536
#>   [18,] -0.9295907779  0.532616179 1.1634887
#>   [19,] -0.7218882595  1.132199437 1.2499080
#>   [20,] -0.3309726374 -0.874833814 1.3173392
#>   [21,]  0.0890124740  0.638703261 1.2915332
#>   [22,]  0.4603868334  0.435799741 1.1220850
#>   [23,] -0.5359499261 -0.453610287 1.2718069
#>   [24,] -0.0985040596  1.440562011 1.1398560
#>   [25,]  0.4040686426  0.425581842 1.0820378
#>   [26,] -0.2581545989  0.734931865 1.1271706
#>   [27,]  0.6960980300  0.566691070 1.1475422
#>   [28,]  0.1622577603  0.196296102 1.2492979
#>   [29,]  0.0860036031  0.373844799 1.2719555
#>   [30,] -0.4829137413  0.946485303 1.1483744
#>   [31,] -0.2239328008 -0.898797797 1.2844998
#>   [32,] -1.1291366149  0.815825394 1.2837194
#>   [33,] -0.1978185405  0.256384701 1.2419610
#>   [34,] -0.5379379978 -0.073190807 1.2931606
#>   [35,]  0.0607862162 -0.523406250 1.2420952
#>   [36,] -0.3260040601  0.679218542 1.1642560
#>   [37,] -0.4000332475  1.063917596 1.2446446
#>   [38,] -0.6241145894  1.187616521 1.2454371
#>   [39,]  0.5743335935  0.468793693 1.1671366
#>   [40,] -0.2936867462  0.665999508 1.1696712
#>   [41,] -1.7858782272  1.464905139 1.2253127
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#>  [808,]  0.2703090066  1.515648195 0.9995014
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#>  [879,]  0.0024988207  0.296574594 1.1275570
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#>  [881,]  0.7200507308  0.632443364 1.1881146
#>  [882,] -0.0331451099 -0.250321667 1.1834267
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#>  [884,]  0.0838918064 -0.301709474 1.2164871
#>  [885,] -0.9125612345  0.177937291 1.2660922
#>  [886,] -0.5703133107  0.906684309 1.1757769
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#>  [888,]  0.3707523360  0.346267581 1.0987920
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#>  [891,] -0.8975211036  0.107800886 1.2317253
#>  [892,]  0.0289601619  1.273605874 1.2113767
#>  [893,] -0.2305349391 -0.173599192 1.1671367
#>  [894,]  0.2440581876  0.810422679 1.2140206
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#>  [897,] -1.1232795855  1.501433024 1.2176336
#>  [898,] -0.6335904437  0.919458910 1.2205140
#>  [899,]  0.5146847347 -0.311364603 1.1690414
#>  [900,]  0.0829774747  1.083336128 1.1936649
#>  [901,] -0.1599733948 -0.893139012 1.1882913
#>  [902,] -1.3558721773  0.610525534 1.3218797
#>  [903,] -0.3370694347  0.672727482 1.2226456
#>  [904,]  0.7243771643  0.043323403 1.1653789
#>  [905,] -0.4025120502  0.354051808 1.2208645
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#> [1777,]  0.4358392296  0.748927193 1.1271932
#> [1778,] -1.3386505908  0.371564653 1.2987731
#> [1779,] -0.5567231848  1.602422570 1.1834765
#> [1780,] -0.6521615678  1.421879995 1.0660676
#> [1781,] -0.5813018783  1.201038956 1.1672105
#> [1782,]  0.6282541406  0.124293454 1.2188406
#> [1783,] -0.6247627578 -0.072916311 1.2030504
#> [1784,] -1.2986566845 -0.875241703 1.3010532
#> [1785,] -0.6718674373 -0.298371760 1.3128738
#> [1786,]  0.3361576209  0.832336545 1.2295280
#> [1787,] -0.8219856163 -0.327456352 1.2400289
#> [1788,]  0.3077232622  1.121821816 1.1178405
#> [1789,] -1.1731000391 -0.140196701 1.1862085
#> [1790,] -0.4409348275  0.056164680 1.3516315
#> [1791,] -0.7126930598  1.279667130 1.2120083
#> [1792,] -0.2772232030  0.080160768 1.1445689
#> [1793,] -0.4597329887  1.128936623 1.1505009
#> [1794,] -0.8569557905 -0.405501506 1.2668474
#> [1795,]  1.0132754714 -0.285362329 1.0389993
#> [1796,] -0.9460878700  1.128777171 1.1726630
#> [1797,]  0.1595581993  0.766723655 1.1829679
#> [1798,]  0.0274275616  1.259899446 1.1482668
#> [1799,] -1.3337353186  0.516234031 1.2096907
#> [1800,] -0.1143507485 -0.120750011 1.2339413
#> [1801,]  0.4774961648 -0.654779282 1.2190385
#> [1802,] -0.2189467766  0.162561470 1.2345137
#> [1803,] -0.8511445235  1.093968181 1.1953994
#> [1804,]  1.1288963853 -0.604228615 1.1723154
#> [1805,] -0.1621492334  0.970911460 1.1501094
#> [1806,]  0.4917988775 -1.354932066 1.1585552
#> [1807,] -0.1382643030  0.291627537 1.1636516
#> [1808,]  0.7282375772 -1.097903805 1.2324142
#> [1809,]  0.7753518321 -0.461669334 1.1941902
#> [1810,]  0.2567138304 -0.220572115 1.1977079
#> [1811,]  0.3935310021  0.634226928 1.1964162
#> [1812,] -0.2426458791  0.846200214 1.1892208
#> [1813,] -0.6812855852  0.404636991 1.2060567
#> [1814,]  0.2348435534  0.483377827 1.0587708
#> [1815,] -1.5169656605 -0.334940198 1.2934299
#> [1816,]  0.2383140728  1.800776302 1.1429304
#> [1817,]  0.2296973117  1.547362398 1.1195678
#> [1818,]  0.0977417046  0.947006924 1.1518616
#> [1819,] -0.6487660264 -0.061318840 1.1687484
#> [1820,] -0.6322809278 -0.190769805 1.2074722
#> [1821,] -0.8527109570  1.135450440 1.1770412
#> [1822,] -0.3817086400 -0.620251173 1.2203678
#> [1823,]  0.2587365105 -0.328856515 1.2163994
#> [1824,] -0.1547454147  0.852602509 1.1767783
#> [1825,] -0.0445008976 -0.356714415 1.1916037
#> [1826,] -0.5873363233  0.918829589 1.2214612
#> [1827,] -0.7725196616  0.460332383 1.1463772
#> [1828,] -0.8303192153  0.604795978 1.1719794
#> [1829,] -1.5402576865  0.545322447 1.3528215
#> [1830,] -0.0020167572  1.163002830 1.2590739
#> [1831,] -0.1477537155  1.098364729 1.0692828
#> [1832,] -0.2758225735  0.454714350 1.2492721
#> [1833,] -1.6171941980  0.325126115 1.3460839
#> [1834,]  0.7196126980  0.443411433 1.1338001
#> [1835,] -1.3803030294 -0.596840972 1.1831601
#> [1836,] -0.7927332574  0.620380817 1.2515131
#> [1837,] -0.5538199229  0.030771892 1.2600261
#> [1838,] -0.8103078555  0.135083651 1.1837460
#> [1839,]  0.1272880034  0.984047845 1.1410239
#> [1840,] -0.3245654734  0.096415370 1.2185640
#> [1841,] -0.1892531371 -0.057193338 1.2451942
#> [1842,] -0.2672407535  0.623410292 1.3065682
#> [1843,]  0.8097876658  0.928321570 1.2511798
#> [1844,]  1.6732744734  0.679078293 1.0538237
#> [1845,]  1.0323202420 -0.629780626 1.1424366
#> [1846,] -0.5601416981  0.444221069 1.2101742
#> [1847,] -0.4189443653  0.703964909 1.3532934
#> [1848,] -0.6186553905  0.835061101 1.1959826
#> [1849,] -0.2292809521 -1.047025002 1.2545115
#> [1850,] -1.0724186876  1.771025720 1.2218477
#> [1851,] -0.5334171196  0.876539176 1.2573719
#> [1852,] -0.1402681547  0.396700343 1.1115253
#> [1853,] -0.8794031802  0.120382630 1.2983088
#> [1854,] -0.9484212362  0.265879174 1.3063024
#> [1855,] -0.5779513010  0.740798990 1.2653550
#> [1856,]  0.2135252729 -0.023394000 1.1596497
#> [1857,]  0.4893158206 -0.144482838 1.2131245
#> [1858,] -0.1928353595  1.940373700 1.1728800
#> [1859,]  0.5207702839  0.090930575 1.1509538
#> [1860,]  0.1769265439  0.128635358 1.2059188
#> [1861,] -0.5586591644  0.740148507 1.2787794
#> [1862,] -0.4224824643 -0.125971859 1.2442911
#> [1863,] -0.5222110808  0.718316896 1.3288370
#> [1864,] -0.2723057659  0.242895986 1.2718383
#> [1865,]  0.3489241146 -0.608453513 1.1070805
#> [1866,] -1.5106464166  0.303244508 1.2555716
#> [1867,] -0.2283685520  0.330930304 1.2967197
#> [1868,]  0.0942010761 -0.306933023 1.1493617
#> [1869,]  0.1502925623  0.499991921 1.2212715
#> [1870,] -0.0372396454  0.807996717 1.1429625
#> [1871,] -0.9302927384  0.336168318 1.2653314
#> [1872,]  0.1652908677  0.376237018 1.2411644
#> [1873,]  0.2580270717  0.556639968 1.2096699
#> [1874,]  0.7295874994 -0.532073998 1.2473957
#> [1875,] -0.4528204558  0.632716926 1.2267858
#> [1876,] -0.5960161679 -0.169530018 1.2793262
#> [1877,] -0.1831640904  0.452641877 1.2526773
#> [1878,] -0.1219689302  0.976433023 1.2442667
#> [1879,] -0.2856978884  1.264165290 1.1609638
#> [1880,] -0.8323676872 -0.176121287 1.2647605
#> [1881,]  0.3023074030  0.278140242 1.1335995
#> [1882,] -1.2024508131  0.465319892 1.2790999
#> [1883,] -0.7587637727  0.928055737 1.2768055
#> [1884,]  0.1591742764 -0.213863843 1.2829296
#> [1885,]  1.7968274355  0.151894636 1.1521367
#> [1886,] -0.6991419978  0.093703800 1.1953778
#> [1887,] -0.2097073431  0.116641443 1.2081684
#> [1888,] -0.8778303977  0.010548827 1.2555950
#> [1889,] -0.3171147442  0.597032383 1.2375776
#> [1890,] -1.5285581072 -0.419782853 1.2558220
#> [1891,] -0.7661495135  0.393823168 1.1919489
#> [1892,] -0.1483994349  0.454334853 1.2600737
#> [1893,] -0.9823128870 -0.044454666 1.1676480
#> [1894,] -0.8514065549  0.276897169 1.3946463
#> [1895,] -0.1948494746  0.508672967 1.2319084
#> [1896,] -0.5016761606  0.133505451 1.2317299
#> [1897,] -0.1297145706  1.345710472 1.1598809
#> [1898,]  0.0614529761  0.949533400 1.1083394
#> [1899,]  0.7756008633 -0.277861366 1.1312190
#> [1900,] -1.1875591865  0.217056457 1.2643556
#> [1901,] -0.3541744982  0.375262486 1.2524320
#> [1902,]  0.4389050338 -0.029543353 1.1044312
#> [1903,] -0.5527668151  0.168791830 1.2079531
#> [1904,] -0.3538269184  0.518154186 1.2407146
#> [1905,] -0.0879130434 -0.414802456 1.2423740
#> [1906,] -0.6995232463  0.475710537 1.1820551
#> [1907,] -0.2955490300 -0.282813950 1.2083515
#> [1908,] -0.1127821168 -0.516193808 1.2080765
#> [1909,] -0.4388231072  0.204689917 1.2218144
#> [1910,] -1.0148643451  0.531080944 1.2587190
#> [1911,] -0.0165825467 -1.027863080 1.3473391
#> [1912,] -0.8205439049  0.038324051 1.3201317
#> [1913,] -0.6513282673  0.258220123 1.2082567
#> [1914,] -0.1679714675  0.565629763 1.1316400
#> [1915,] -0.4283666230  0.447298382 1.2239742
#> [1916,] -0.8788443976  0.901242181 1.2919886
#> [1917,]  1.1624131927 -0.245699240 1.1066205
#> [1918,]  0.7380221957 -0.511576143 1.1808257
#> [1919,]  0.2966864294  0.200146067 1.1256220
#> [1920,] -0.9961994413  0.618408105 1.2287106
#> [1921,] -0.5451017076  0.793865755 1.1970398
#> [1922,]  0.6899680932  0.592661986 1.0507718
#> [1923,]  0.9068306420  0.363923007 1.1729620
#> [1924,]  0.9320921468 -0.490519416 1.1385207
#> [1925,] -1.4913011448  1.345998415 1.2250161
#> [1926,] -0.8505771484  0.626781954 1.1776978
#> [1927,] -1.5019322209 -0.247052436 1.2464037
#> [1928,] -0.6890352168  0.453820113 1.2802847
#> [1929,] -0.9752131260  0.175814898 1.2188964
#> [1930,] -1.2744912771 -0.105625792 1.3532056
#> [1931,] -0.7936753364  1.778444664 1.1668999
#> [1932,] -0.6334872790  0.556615313 1.2883606
#> [1933,]  0.2708967283 -0.070406791 1.2175893
#> [1934,] -0.1418693835  0.696190645 1.2393754
#> [1935,]  0.7557020185 -0.106535356 1.0542840
#> [1936,] -1.3796371292 -0.185568011 1.3039139
#> [1937,] -0.8247047916  0.307103923 1.2232307
#> [1938,]  0.2660219569  0.576383832 1.2171448
#> [1939,] -0.8868157811  0.903153912 1.2054866
#> [1940,] -0.7114371896 -0.328063880 1.2213146
#> [1941,] -0.1860087061  0.214646453 1.1723892
#> [1942,]  0.6197062850 -0.442043029 1.1563907
#> [1943,] -0.6295947516  0.055047624 1.2911079
#> [1944,] -1.0368309547  1.067354714 1.2572655
#> [1945,] -0.1287976132 -0.191021714 1.2058877
#> [1946,] -1.0646550127  1.307780987 1.2446006
#> [1947,] -0.7980555206  1.290836164 1.3006421
#> [1948,] -0.4058123922  0.351337104 1.2632734
#> [1949,]  0.2739389353  0.514739054 1.2104460
#> [1950,] -0.3433484480  0.024500993 1.2109507
#> [1951,] -1.0170959351  0.458186875 1.3106002
#> [1952,] -1.1866431851  2.314068025 1.2056339
#> [1953,] -1.2426289643  0.778550856 1.2239517
#> [1954,] -0.7447920052 -0.164411764 1.2765712
#> [1955,] -0.6414627703  0.560008996 1.2057200
#> [1956,] -0.9046140849  0.626963661 1.2029707
#> [1957,] -0.3629558229 -0.711961872 1.2507066
#> [1958,]  0.1052483840 -0.274657905 1.1879631
#> [1959,]  0.5055306602  1.821636524 1.1112450
#> [1960,] -0.7792186041 -0.917965897 1.3335370
#> [1961,]  0.2281701061 -0.264373283 1.2242599
#> [1962,] -0.1252312628  0.652628119 1.1510235
#> [1963,] -0.8751467477 -0.947971037 1.2026683
#> [1964,] -1.0545853987  0.821844025 1.2787494
#> [1965,] -1.3315204218 -0.068419116 1.3894152
#> [1966,] -0.5119967009 -0.538072592 1.2914857
#> [1967,] -0.0335814489 -0.105476259 1.2951194
#> [1968,] -0.5388336303  0.266645317 1.1877851
#> [1969,]  0.4357375981  0.198425067 1.2012741
#> [1970,] -0.4383895616 -1.653342543 1.2189053
#> [1971,]  0.1758581845  0.744021961 1.2517162
#> [1972,] -0.5587594778  0.307803949 1.2101255
#> [1973,]  0.0499628196 -0.814987337 1.2357979
#> [1974,] -0.0700571625 -0.485088916 1.2563415
#> [1975,] -0.8272072913  0.987906549 1.1464852
#> [1976,] -1.6383810410  0.103123380 1.2660788
#> [1977,]  0.0578646639 -0.282510857 1.2469062
#> [1978,] -1.2161976054  0.281954172 1.2251941
#> [1979,] -0.9537303067  0.722956903 1.3500850
#> [1980,] -0.4933947910  0.752114758 1.2676265
#> 
#> attr(,"class")
#> [1] "mcmc.list"
#> 
#> [[4]]
#> NULL