BNPMediation

The goal of BNPMediation is to provide two functions bnpmediation and bnpconmediation. The function bnpmediation provides the posterior means and credible intervals of the effects of mediation, whereas bnpconmediation provides the posterior means and credible intervals of the conditional effects. Another function plot_effects is provide that obtains the posterior plots of the effects. Bayesian Nonparametric (BNP) models are used for the observed data to identify and estimate the causal effects. The published journal can be found at http://dx.doi.org/10.1111/biom.12575.

Installation

You can install BNPMediation from github with:

# install.packages("devtools")
devtools::install_github("mjdaniels/BNPMediationProject") 

Example


dataTreatment = c(11.163989,  13.357644,  12.264292,  16.848934,  20.902562,  13.037647,  10.523266, 13.869733,  16.399047,  13.249197,  11.284890,  11.450062,  10.817139,  15.245700, 9.920019,  11.573960,  10.911009,  10.489587,  10.814474,  10.479123,  11.576099, 9.527664,  19.139293,  10.419879,  11.477210, 9.974351,  11.661321,  11.107294, 10.703919,  10.229351,  14.304395,  11.966633,  12.320991,  17.905459,  9.661749, 10.385607,  20.406423,  10.777457,  9.825228,  13.691681, 9.871743,  10.500229, 10.285037,  14.930915,  13.608770,  16.167101,  13.602650,  14.786788,  10.867811, 10.512889,  11.412777,  11.982880,  8.774465,  10.481118,  9.444334,  15.367506,  9.772886,  10.974271,  9.893823,  20.102887,  11.444247,  10.500275,  9.847932,  11.732694,  11.462192,  13.380679,  12.794651,  9.678496,  17.062716,  14.091250,  9.289893,  10.719766,  10.636155,  9.798370,  10.298192,  10.618451,  10.365415,  18.189078,  15.972311,  11.072824,  12.343840,  11.811951,  10.639700,  15.114964,  11.880889,  11.335969,  11.388849,  10.878676,  10.722346,  11.307921,  9.956277,  9.213929,  10.085210,  11.800195,  10.658099,  10.718170,  11.422773,  10.623135,  11.142688,  10.719141,  12.885994,  9.060620,  13.221060,  9.687241,  12.399068,  12.719150,  10.968212,  12.011608,  11.513917,  9.541409,  11.621904,  13.197714,  11.697384,  14.032590,  12.267005,  15.554890,  11.958848 )
dataControl = c(9.060491, 7.566083, 8.081978, 6.450560, 7.252086, 7.545289, 9.019265 ,7.678507, 7.353213, 10.708195, 8.253596, 8.413139, 9.588276, 10.589635 ,8.619169, 9.088016, 7.063381, 6.403902, 8.413106, 7.254758, 7.946906,7.013008, 6.828835, 7.198124, 8.133756, 14.843925, 8.043300, 9.978774,11.630415, 6.912515, 7.354103, 6.634561, 9.672022, 9.785791, 7.490891,12.384268, 9.223109, 6.719683, 8.311750, 9.388895, 7.773400, 14.815319,20.050661, 6.417857, 10.674383, 9.293519, 14.880615, 8.090496, 7.880399, 7.181893, 7.913207, 7.086220, 10.728450, 8.687074, 6.958637, 14.135874, 7.273476, 10.325233, 7.736805, 14.173735, 7.773935, 9.227020, 8.257979 ,11.986135, 7.875595, 7.341740, 6.036009, 8.976403, 7.396193, 7.217195, 6.849920, 10.399304, 12.968451, 7.879505, 7.816833, 7.270345, 7.299595,10.799175, 6.471268, 6.234942, 8.203609, 6.411400, 10.768465, 8.162683, 7.262786, 8.473937, 9.886522, 7.018580, 6.836707, 7.283106, 7.344599, 8.686345, 9.547393, 10.468727, 14.321967, 7.183868, 10.743336, 6.865275, 7.725663, 7.168826, 9.654838, 14.515487, 9.493838, 12.502887, 9.970782, 7.366840, 8.856238, 7.529891, 15.989223, 7.827295, 7.505671, 7.966335, 8.062032, 6.708697, 10.414558, 10.033180, 7.512152, 10.476679, 9.338416, 6.898800, 7.380856, 10.896545, 9.672738 )

  
 nburn <- 500
 nsave <- 1000
 nskip <- 10
 ndisplay <- 100
 mcmc <- list(nburn=nburn,nsave=nsave,nskip=nskip,ndisplay=ndisplay)

 s2 <- matrix(c(1000,0,0,1),ncol=2)
 m2 <- c(20,3)
 psiinv2 <- solve(matrix(c(1000,0,0,1),ncol=2))
 prior <- list(a0=1,b0=1/5,nu1=4,nu2=4,s2=s2,m2=m2,psiinv2=psiinv2,tau1=0.01,tau2=0.01)

library(BNPMediation)
bnpmediation(dataTreatment, dataControl, prior, mcmc, state, status = TRUE, na.action, q = 2, NN = 10, n1 = 10, n0 = 10, extra.thin = 0, seed= 12345)
#> ***** Fitting observed data models via DPpackage::DPdensity()
#> 
#> MCMC scan 100 of 1000 (CPU time: 0.368 s)
#> MCMC scan 200 of 1000 (CPU time: 0.697 s)
#> MCMC scan 300 of 1000 (CPU time: 1.012 s)
#> MCMC scan 400 of 1000 (CPU time: 1.350 s)
#> MCMC scan 500 of 1000 (CPU time: 1.660 s)
#> MCMC scan 600 of 1000 (CPU time: 1.988 s)
#> MCMC scan 700 of 1000 (CPU time: 2.296 s)
#> MCMC scan 800 of 1000 (CPU time: 2.623 s)
#> MCMC scan 900 of 1000 (CPU time: 2.950 s)
#> MCMC scan 1000 of 1000 (CPU time: 3.273 s)
#> 
#> 
#> MCMC scan 100 of 1000 (CPU time: 0.432 s)
#> MCMC scan 200 of 1000 (CPU time: 0.774 s)
#> MCMC scan 300 of 1000 (CPU time: 1.144 s)
#> MCMC scan 400 of 1000 (CPU time: 1.499 s)
#> MCMC scan 500 of 1000 (CPU time: 1.836 s)
#> MCMC scan 600 of 1000 (CPU time: 2.221 s)
#> MCMC scan 700 of 1000 (CPU time: 2.566 s)
#> MCMC scan 800 of 1000 (CPU time: 2.940 s)
#> MCMC scan 900 of 1000 (CPU time: 3.320 s)
#> MCMC scan 1000 of 1000 (CPU time: 3.708 s)
#> 
#> ***** Running bnpmediation
#> 
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#> $Y11
#>    [1] 7.773675 6.993048 8.624499 7.481020 6.866863 6.530911 8.205857
#>    [8] 7.061465 8.044678 6.599416 6.523774 7.052494 7.763620 7.092487
#>   [15] 6.827072 6.932883 7.294010 7.402536 7.067454 7.334946 6.734727
#>   [22] 6.888365 7.440086 6.896419 7.221363 8.328016 6.997745 6.841911
#>   [29] 7.183612 6.327545 6.819923 6.469993 7.052804 6.782449 7.832731
#>   [36] 7.073042 6.988804 6.966057 7.151287 7.207013 6.928021 6.876416
#>   [43] 6.845423 6.671691 6.870281 6.868089 7.871114 7.532270 7.023381
#>   [50] 7.054410 7.354639 7.723036 7.550786 7.641947 7.104509 7.074449
#>   [57] 7.362249 7.649607 7.122009 7.295189 6.836744 6.785060 7.721237
#>   [64] 7.065443 6.960071 6.856241 6.888840 6.551076 6.989307 6.475585
#>   [71] 6.637302 6.715977 7.777858 7.564438 7.321250 7.170706 7.215503
#>   [78] 6.966251 6.970067 6.982928 7.052112 6.685796 7.284711 6.948182
#>   [85] 6.664429 6.881041 7.540977 6.952241 7.263533 7.103741 7.786308
#>   [92] 7.062915 8.287590 7.193470 7.386878 7.811139 6.745865 6.827538
#>   [99] 6.433352 7.077547 7.470062 7.443137 6.500155 6.933023 7.051367
#>  [106] 7.171999 6.961830 6.766189 6.894111 6.646019 6.963567 7.332654
#>  [113] 6.659979 7.291739 6.989772 7.592550 6.916920 6.653401 7.028746
#>  [120] 7.134488 8.151686 7.958638 7.212722 6.295014 6.511080 6.739869
#>  [127] 6.537393 6.898641 6.852085 6.818231 7.054588 7.663107 7.563959
#>  [134] 6.935537 7.019953 6.736165 7.137269 6.753123 7.410780 7.631499
#>  [141] 6.694399 8.050111 8.366753 7.232401 6.798149 6.955127 6.694074
#>  [148] 6.935203 6.825447 7.713388 7.096430 7.488563 7.659321 7.950820
#>  [155] 6.811398 6.615780 7.665870 6.826357 7.109326 7.684675 7.345140
#>  [162] 7.712625 7.112546 7.400998 7.588683 7.165350 7.867233 7.383884
#>  [169] 7.366373 6.696997 7.199291 6.938729 7.820240 7.645170 7.187298
#>  [176] 7.089403 7.744254 7.136230 6.980979 6.629376 6.853326 6.883924
#>  [183] 7.403668 6.621646 7.089875 7.030888 8.059002 7.879050 7.035875
#>  [190] 7.468648 8.031107 6.736316 7.360287 6.797137 6.367527 6.906319
#>  [197] 7.301243 6.765147 7.705439 6.945101 7.172712 6.498698 6.571090
#>  [204] 6.972871 7.681781 7.479021 7.408286 7.918718 6.882366 7.835942
#>  [211] 7.240087 6.868007 7.304146 7.887267 7.857803 7.943837 7.247616
#>  [218] 9.105090 7.391071 7.232010 9.086480 7.626725 6.696195 6.892108
#>  [225] 6.955847 7.233168 8.017392 7.068157 6.662228 6.977606 6.940878
#>  [232] 6.955426 6.884641 6.781602 6.548637 6.602060 6.843557 7.191160
#>  [239] 7.154595 7.094400 7.079782 7.312355 7.129986 7.088516 7.094298
#>  [246] 6.808450 6.339874 6.956202 7.366273 7.456405 6.902237 6.800497
#>  [253] 7.065377 6.630614 6.698606 7.726020 7.540357 7.776586 7.309934
#>  [260] 7.119641 7.592463 7.749829 7.122562 6.598967 6.935121 6.990734
#>  [267] 6.882635 7.158433 6.981848 8.367417 7.270226 7.389863 7.291926
#>  [274] 7.474401 7.362498 7.627564 7.377948 6.892284 6.509773 6.524307
#>  [281] 6.938061 7.213330 6.673066 6.830218 6.816391 6.818801 7.418034
#>  [288] 6.844225 7.072243 7.085264 6.635230 7.178549 7.793486 7.624941
#>  [295] 7.243705 7.775897 6.757770 7.211024 7.629646 6.422488 6.793587
#>  [302] 6.616362 6.905840 6.672316 6.787069 6.772656 6.518412 6.910979
#>  [309] 6.487190 7.301575 7.672304 6.740238 6.973936 6.537248 6.968981
#>  [316] 7.259951 7.811832 6.973119 7.343367 7.932576 7.626121 6.822110
#>  [323] 6.940033 6.866130 7.083628 7.311659 7.072382 7.505795 6.966517
#>  [330] 6.857284 7.081949 7.088575 6.854921 6.827440 7.086346 6.580764
#>  [337] 6.782769 6.840817 7.763892 7.637699 7.792326 9.103766 7.019944
#>  [344] 7.176734 6.743917 6.676663 6.939893 7.150784 6.436434 6.761987
#>  [351] 6.830529 6.691985 7.002390 7.845166 7.079568 6.687823 6.877492
#>  [358] 6.911390 7.119199 6.894470 7.060122 7.298292 6.986777 6.770445
#>  [365] 6.726139 7.230547 6.952726 7.463969 7.630539 6.953819 7.313608
#>  [372] 6.721147 7.094905 7.333882 7.099648 6.774037 6.974669 6.347847
#>  [379] 6.501327 6.637127 7.303418 7.541230 7.702958 6.993160 7.996939
#>  [386] 7.426971 7.817686 7.306467 7.094809 7.720268 6.881102 7.941977
#>  [393] 8.484485 6.939190 6.631196 6.903156 7.299885 6.664019 7.151875
#>  [400] 7.240689 7.152146 7.615455 7.480706 7.190567 7.002781 6.587207
#>  [407] 7.707821 7.568188 7.423006 6.626725 7.043238 7.857212 7.654918
#>  [414] 7.164688 7.373175 7.407217 7.445985 7.223233 7.552603 7.359087
#>  [421] 6.914750 6.669558 7.344145 7.084986 7.134536 6.797750 7.110225
#>  [428] 7.035000 7.411634 6.841539 7.066611 6.923465 6.566245 6.698794
#>  [435] 7.087307 6.867642 7.071023 6.686716 6.852866 7.215900 6.500505
#>  [442] 7.002610 7.380047 7.352709 7.648800 7.620404 7.360999 7.457208
#>  [449] 8.520533 7.364726 7.112849 7.035661 6.843302 7.296735 6.841409
#>  [456] 6.917166 6.874335 6.698309 7.567837 7.895895 7.027005 6.910646
#>  [463] 7.670304 7.772271 6.847500 6.990862 7.220974 7.734904 7.019930
#>  [470] 6.694371 6.949850 6.718034 7.219640 7.142378 6.927717 7.000957
#>  [477] 7.448232 6.807280 7.873821 7.122530 6.962374 7.898967 7.791275
#>  [484] 6.649076 6.952423 8.035597 7.395658 6.729295 6.561352 7.803202
#>  [491] 7.646185 7.622771 6.835874 6.927067 6.354892 6.316263 6.414939
#>  [498] 7.125370 6.984005 6.664807 6.608841 6.959035 6.344361 6.790003
#>  [505] 6.729269 7.153985 6.689187 6.728574 6.462129 7.174593 6.632621
#>  [512] 7.351308 7.849415 6.946050 6.716368 6.666855 6.895639 7.181399
#>  [519] 6.851630 6.946843 7.447002 6.895909 6.534252 7.120803 6.754108
#>  [526] 6.718094 6.694441 7.062498 7.297792 6.913705 6.927362 7.232492
#>  [533] 7.803843 8.452261 7.668234 7.059250 7.788484 6.733652 7.075230
#>  [540] 6.975059 6.574955 6.737802 7.031578 6.560848 6.525034 7.437329
#>  [547] 7.107544 7.109493 6.884279 7.150628 6.936238 6.434178 6.638905
#>  [554] 9.310885 8.048864 7.117916 6.833691 6.825911 7.136443 7.847917
#>  [561] 7.102652 6.823204 6.814392 7.009387 6.577049 6.945147 7.236196
#>  [568] 7.355542 6.761728 7.091379 7.830576 7.471873 7.751685 7.590113
#>  [575] 7.505020 7.083655 7.630955 7.217464 7.249208 7.124530 7.396304
#>  [582] 6.703606 6.780802 6.709021 7.046769 7.348807 7.372185 8.057786
#>  [589] 8.142077 6.956201 6.977935 6.647104 6.659226 7.225919 7.845615
#>  [596] 6.938136 6.680927 7.167303 6.816104 6.731677 6.971721 6.556555
#>  [603] 6.790351 6.763130 6.599151 7.462858 7.894746 7.262919 6.848325
#>  [610] 6.737212 6.727477 6.720964 6.559949 7.012214 6.707818 7.149090
#>  [617] 7.168250 7.033664 6.742855 6.958710 6.758736 6.871032 7.078749
#>  [624] 6.842615 7.449347 7.593280 7.085837 7.899775 7.273110 7.457483
#>  [631] 7.378911 7.801647 8.314701 7.604834 6.964851 6.512745 7.053832
#>  [638] 7.751636 7.690451 7.514632 7.698423 7.558380 7.930319 6.568632
#>  [645] 7.448089 7.645119 7.300637 7.281999 7.595367 7.205575 6.703362
#>  [652] 6.696777 6.811870 7.225066 6.899242 7.056525 6.934511 6.974060
#>  [659] 6.589444 6.653121 7.178537 7.072632 7.311815 7.055959 7.203259
#>  [666] 6.800452 6.894136 7.169515 7.522479 8.039468 7.329948 7.130078
#>  [673] 7.353075 8.829174 8.843065 7.352216 6.567817 7.103341 7.522707
#>  [680] 6.912625 7.934886 6.748421 6.781574 6.696497 7.421211 7.140330
#>  [687] 6.846535 7.065720 6.697908 7.210211 6.874946 7.328602 6.672074
#>  [694] 7.987365 7.146565 7.876483 7.153137 6.975016 6.496152 6.827531
#>  [701] 7.052489 7.765700 7.265492 7.169324 7.275093 7.086445 7.449105
#>  [708] 7.432243 6.993264 7.286355 6.961813 7.239357 7.198898 7.231424
#>  [715] 7.139748 7.034521 6.977987 7.143793 7.723539 6.746894 6.697212
#>  [722] 6.730855 6.546526 8.371927 6.857512 7.117103 7.509464 7.175118
#>  [729] 6.578131 6.817016 7.285623 7.487155 7.251765 6.848283 7.085146
#>  [736] 7.613751 7.025014 7.776691 7.224281 7.354887 7.051443 6.482014
#>  [743] 6.631644 6.959831 7.106100 6.852790 6.836386 6.717843 8.404492
#>  [750] 7.366016 7.403038 6.756423 7.421600 7.059103 6.593291 7.259171
#>  [757] 7.761386 7.570292 6.929315 6.828610 6.617779 6.944788 8.224893
#>  [764] 7.243087 7.140541 6.949968 7.779705 7.196549 8.197759 7.332103
#>  [771] 7.431086 7.252171 7.382179 6.803621 7.368051 7.178135 6.548322
#>  [778] 7.059404 6.849926 6.907300 6.867931 6.958434 6.566403 7.039871
#>  [785] 6.702990 6.959075 7.266296 7.469984 7.702411 7.925776 7.877035
#>  [792] 7.378743 7.171173 6.850787 6.453226 7.020134 6.855256 7.064054
#>  [799] 6.586436 6.806764 6.440416 7.048945 7.410327 7.219404 7.262425
#>  [806] 7.638446 7.139285 7.134531 7.609118 8.282219 7.114747 7.176487
#>  [813] 7.063397 7.916830 7.235873 7.347789 6.705613 6.851099 6.519579
#>  [820] 6.977587 6.714543 6.696795 7.321292 6.552497 7.079582 6.688195
#>  [827] 7.070752 6.993564 7.365078 6.967388 7.125666 6.895108 7.651166
#>  [834] 7.466643 7.064771 7.091904 7.868025 6.760389 6.780382 7.176462
#>  [841] 7.313387 7.176776 7.122262 7.396825 7.160457 7.002358 7.417490
#>  [848] 7.694113 7.230568 7.205979 7.323080 6.811915 6.681276 6.934278
#>  [855] 7.084038 7.267067 7.284940 7.778567 8.129461 7.116314 7.253182
#>  [862] 7.094905 6.879678 6.934654 6.690898 6.684993 7.595025 7.438817
#>  [869] 6.914738 7.070475 6.970860 6.786781 6.801368 7.416155 7.386941
#>  [876] 7.093992 6.737276 6.441030 6.818197 6.291027 6.893370 7.601153
#>  [883] 7.054569 6.737089 6.688633 7.297737 6.520070 6.718160 6.857455
#>  [890] 8.046756 6.749411 7.191356 7.011583 6.914087 6.504979 7.246912
#>  [897] 6.855135 6.709106 6.712481 7.779586 7.028198 7.160210 7.073518
#>  [904] 6.418391 6.826642 6.921275 8.318988 6.688432 6.722906 6.536334
#>  [911] 6.733586 7.005795 7.691462 6.662637 6.672198 7.073587 6.481127
#>  [918] 6.687015 6.583382 6.892979 6.918733 8.254890 7.485340 7.262523
#>  [925] 7.409641 7.255016 7.244960 6.997436 7.158149 6.971744 6.835649
#>  [932] 6.947363 6.856750 6.894780 6.611409 6.736569 7.109899 6.876805
#>  [939] 6.630869 7.145523 6.868581 6.928340 7.505460 7.608022 6.575040
#>  [946] 6.596073 7.096323 6.364231 7.587116 6.965383 6.612505 6.796084
#>  [953] 6.518908 6.796253 6.716029 6.608965 7.540961 6.634679 7.371143
#>  [960] 6.820785 8.012535 7.138201 6.610551 7.595268 7.011500 6.870174
#>  [967] 7.259014 6.908480 7.422939 6.820730 6.870641 7.013223 6.718734
#>  [974] 6.514376 6.814241 7.457872 7.195205 6.865625 6.750600 6.700279
#>  [981] 7.337165 6.671139 6.763794 6.575994 7.623664 7.500963 6.968622
#>  [988] 7.566725 6.731278 6.958346 7.280047 6.904240 7.000238 7.019967
#>  [995] 6.875924 7.844162 6.931375 7.242636 7.577927 7.870819
#> 
#> $Y00
#>    [1] 5.228763 4.978343 4.795500 4.711087 4.988305 4.695599 4.704602
#>    [8] 4.886986 5.208229 5.073764 4.731635 4.695943 4.868534 4.952728
#>   [15] 4.708619 4.989160 4.928166 5.132929 5.283567 5.223050 4.787690
#>   [22] 5.815131 4.977847 4.984932 5.063374 4.813045 4.902737 4.689526
#>   [29] 5.069739 5.070093 4.667069 5.206000 5.433653 5.610305 4.675753
#>   [36] 4.716392 5.995226 5.645892 5.872214 5.350029 4.792785 5.997640
#>   [43] 5.062407 4.920562 4.717853 5.142808 4.712093 5.016675 4.603550
#>   [50] 6.219019 4.733169 4.693046 4.889631 5.000393 4.894343 4.539436
#>   [57] 4.939910 4.945511 4.768618 4.970778 5.032438 5.278024 4.869921
#>   [64] 5.471998 4.764693 4.903612 5.412140 5.117263 5.067665 4.624221
#>   [71] 4.842438 5.081279 4.697374 4.547133 4.747898 4.882697 4.574871
#>   [78] 4.642264 4.780677 5.261282 4.940558 5.771699 4.873745 4.785553
#>   [85] 4.810997 5.040413 5.017274 5.313902 4.699598 5.262194 4.590946
#>   [92] 4.644121 4.602081 4.729970 4.712841 5.085022 5.073537 4.867733
#>   [99] 5.695504 5.984171 5.266083 4.725469 5.192948 4.868463 5.083285
#>  [106] 5.031887 4.924222 5.370063 4.878767 4.974337 4.739423 5.048475
#>  [113] 5.151718 5.540495 6.155799 4.758407 4.945121 4.910412 4.806277
#>  [120] 4.976519 5.334275 5.283002 4.906510 5.105955 5.031047 5.118751
#>  [127] 4.821777 4.832039 4.801659 4.739601 4.932952 4.722290 4.703196
#>  [134] 5.033448 5.071734 6.018100 5.167992 4.801575 4.873949 4.788408
#>  [141] 5.239348 5.248528 4.790149 4.673805 4.918661 4.718793 4.702497
#>  [148] 4.793360 5.042223 4.955576 4.764187 4.719893 4.734648 4.705789
#>  [155] 4.448710 4.574920 4.522700 4.866013 4.874424 5.017354 4.986910
#>  [162] 4.947374 4.972174 4.790603 4.953325 4.714893 4.859126 5.304368
#>  [169] 5.496255 5.615564 5.496460 5.043450 5.234402 4.721389 4.745623
#>  [176] 4.691316 4.850460 4.786614 4.684268 4.697341 4.803578 5.097281
#>  [183] 5.123509 4.591117 4.699328 4.523131 5.070577 4.638785 4.629121
#>  [190] 4.882680 5.015014 4.821675 4.669108 4.860609 4.527376 4.756038
#>  [197] 4.971295 5.001473 4.890345 4.956904 5.037768 5.154675 5.190009
#>  [204] 5.267029 5.163176 5.405445 5.016635 5.735791 5.563644 5.414415
#>  [211] 5.858907 4.752085 4.651214 4.898959 4.830082 4.799818 5.083100
#>  [218] 4.877661 4.957342 4.750219 4.733604 4.873178 4.971318 4.996313
#>  [225] 4.787850 4.885812 4.800785 4.837152 5.120840 4.832838 4.590855
#>  [232] 4.711489 4.839506 4.613555 5.009610 4.779558 4.972739 4.914391
#>  [239] 4.749411 4.719333 4.814599 4.654396 4.777725 4.842675 4.633005
#>  [246] 4.860926 4.765294 5.186814 4.786059 4.941680 5.022806 4.640625
#>  [253] 4.820532 4.776450 4.658563 4.841625 4.879563 4.768387 4.740598
#>  [260] 5.259896 5.055506 4.716257 4.792582 5.029962 5.064012 5.662825
#>  [267] 4.957248 5.236642 4.982162 4.896479 5.043073 5.091620 5.599968
#>  [274] 5.184900 4.946562 5.454700 4.870005 5.083741 4.915541 5.306217
#>  [281] 4.800317 4.738968 4.677865 4.634116 4.798282 4.751193 4.770225
#>  [288] 5.193505 5.115334 5.349785 4.795118 5.044086 4.730664 5.036537
#>  [295] 4.700285 4.706189 4.702134 4.537790 4.481516 4.629211 4.606468
#>  [302] 4.716881 4.821111 4.956918 4.807977 5.186362 4.830857 4.762370
#>  [309] 4.564702 4.775908 4.778375 5.139871 5.351923 5.115882 5.134148
#>  [316] 5.333992 4.876046 4.805299 5.875488 5.067545 5.424956 5.398577
#>  [323] 4.880991 4.961300 4.787113 4.953368 4.633546 4.849423 4.878149
#>  [330] 4.814262 4.801882 4.810402 5.032991 4.789375 5.133013 4.853800
#>  [337] 4.913226 4.957548 4.652761 4.588964 4.691683 4.752766 4.539047
#>  [344] 4.993729 5.240900 4.687135 4.850291 4.616165 4.618147 4.774626
#>  [351] 4.853328 4.757834 5.051969 5.038759 5.552345 5.055694 5.282895
#>  [358] 5.570683 5.112783 4.978329 4.974516 4.965480 4.755459 5.118469
#>  [365] 4.710918 5.137338 4.833107 4.928184 4.988581 4.736726 4.895772
#>  [372] 5.011253 4.945663 4.702966 4.568828 4.826328 4.696510 4.769584
#>  [379] 4.842161 5.459611 4.861328 5.339604 4.966900 4.884761 5.477168
#>  [386] 4.868025 5.175533 5.425587 5.769984 5.552272 4.990233 4.675525
#>  [393] 5.025961 4.963864 4.843521 4.934454 5.332031 5.004127 4.802619
#>  [400] 4.777344 4.630878 4.901784 4.957797 4.982082 5.199854 4.688683
#>  [407] 4.580847 4.855462 5.267948 4.716912 5.340627 4.759332 4.773163
#>  [414] 4.786715 4.731037 4.723643 4.736538 5.202386 4.761502 4.914568
#>  [421] 4.716210 5.023970 5.126767 5.272699 4.965433 4.686357 4.811462
#>  [428] 4.884423 4.696273 4.645883 4.855850 5.024743 4.956548 4.694979
#>  [435] 4.637332 4.952657 4.999030 5.303092 4.896077 4.829267 4.827749
#>  [442] 4.679662 4.763218 5.101035 4.720887 4.953242 4.674922 4.703021
#>  [449] 5.225706 5.522172 4.744499 4.779440 5.479824 5.148351 4.886465
#>  [456] 4.642266 4.622532 4.872811 4.745564 4.699042 4.793326 4.830295
#>  [463] 4.737164 4.569625 4.848345 4.553461 5.187376 5.403635 5.009103
#>  [470] 5.320901 5.268076 4.798819 5.542282 5.718356 5.226199 4.762522
#>  [477] 4.903041 4.859782 4.600965 4.645875 4.719972 4.805870 5.092316
#>  [484] 4.752715 4.930552 5.319474 4.795445 5.090804 4.645901 5.002374
#>  [491] 5.337900 5.170676 5.557663 5.163566 4.830845 5.198031 4.852431
#>  [498] 5.193961 4.907244 5.498198 4.797392 5.591491 5.004709 5.316462
#>  [505] 5.294418 5.405935 4.833015 5.101307 5.091800 4.841746 5.300382
#>  [512] 4.806909 5.991806 4.815492 5.195570 5.265888 4.959754 4.754702
#>  [519] 4.688692 4.984762 5.138279 5.283606 5.079702 5.763983 5.657048
#>  [526] 5.211637 4.745398 4.990523 5.048839 5.735975 5.560643 5.346823
#>  [533] 5.248508 5.063574 4.923953 4.948827 5.254874 5.070889 4.682984
#>  [540] 4.766332 4.730647 4.859912 4.792917 5.189160 4.789586 4.608625
#>  [547] 5.255053 4.682590 4.746587 4.820643 4.829273 4.656487 4.545821
#>  [554] 5.224816 4.931224 4.586746 4.793645 4.746977 5.018805 4.745095
#>  [561] 4.980095 4.983336 4.813887 4.780358 5.166667 4.905687 4.907415
#>  [568] 4.872616 4.830507 5.280446 4.880379 5.087728 4.982066 4.714570
#>  [575] 4.842921 4.937308 4.826836 5.025969 5.271644 5.195389 4.700655
#>  [582] 4.869237 4.967177 5.143798 5.159215 5.592567 4.796729 4.806130
#>  [589] 4.949450 5.317975 5.048924 4.724582 4.661483 4.822561 4.897943
#>  [596] 4.739901 5.097155 4.792634 4.979123 4.982072 4.821560 5.104040
#>  [603] 4.890146 4.716108 4.588605 4.542125 4.779534 4.586928 4.824719
#>  [610] 4.879289 4.958780 4.687936 4.760020 4.717280 5.176647 5.217501
#>  [617] 4.795291 4.672888 4.709307 4.709346 4.804434 4.819149 4.709157
#>  [624] 5.178495 4.844859 5.018393 5.511274 5.206767 4.648112 4.729819
#>  [631] 5.085300 5.106607 5.214671 5.279525 4.863901 4.620257 4.621350
#>  [638] 4.760851 4.785734 4.889072 5.359398 4.861395 5.029709 4.652041
#>  [645] 4.760501 4.604677 4.939318 5.455372 4.783328 4.669595 5.097085
#>  [652] 4.873543 5.048541 5.188844 4.593088 4.694136 4.913540 5.132404
#>  [659] 5.088786 5.149201 5.686508 4.988192 5.777838 4.994654 5.197493
#>  [666] 5.342350 5.115528 4.793126 5.017826 4.920508 4.949253 4.800155
#>  [673] 4.871199 4.856307 4.916939 5.133349 5.020743 5.690765 5.021588
#>  [680] 4.743248 4.637926 5.079745 4.902824 4.926348 4.941388 5.066538
#>  [687] 6.061166 5.544989 6.132555 5.552639 5.087329 5.091180 5.254058
#>  [694] 4.770663 4.497678 4.521148 4.595386 4.642898 4.616698 4.825961
#>  [701] 4.734588 5.037115 4.978509 4.980794 4.841910 8.035920 4.965777
#>  [708] 5.945386 4.898271 4.929872 4.816526 4.895585 4.865528 4.556079
#>  [715] 4.707772 5.091471 5.192264 4.816680 4.742181 4.947286 4.817636
#>  [722] 4.973482 4.710873 4.867415 4.975422 4.659297 4.736178 4.884995
#>  [729] 4.743216 4.936425 4.811440 4.813031 4.738220 4.798793 4.662817
#>  [736] 4.549470 4.916183 4.858720 5.283700 4.625472 4.943701 4.795005
#>  [743] 4.638021 4.541629 5.208172 4.537210 4.865575 5.076079 4.735425
#>  [750] 4.633112 4.689204 4.732006 4.714189 5.122197 4.778845 5.701975
#>  [757] 4.686210 4.874890 4.694133 4.960521 4.751901 4.732551 4.714777
#>  [764] 4.959277 5.421952 4.681750 4.839475 4.916513 5.008378 5.654726
#>  [771] 5.140690 5.230206 4.914545 4.941742 4.669350 4.545210 4.752491
#>  [778] 5.206324 4.889337 4.779193 4.724378 4.913250 4.887144 4.632401
#>  [785] 5.993313 5.268928 5.404651 5.644494 4.979346 5.176312 5.249589
#>  [792] 4.844722 4.765196 4.919343 5.158777 4.945692 4.883167 4.710155
#>  [799] 5.027397 5.066536 4.769843 4.671607 4.812860 4.533153 4.496338
#>  [806] 4.815450 4.636432 4.673706 4.786130 4.772965 4.886042 4.639498
#>  [813] 4.706123 4.762228 4.609312 4.818615 5.341116 4.902594 4.905838
#>  [820] 4.841029 5.330641 4.915683 4.674252 4.546291 4.553654 4.748080
#>  [827] 4.724705 4.577132 4.578409 4.921739 5.151469 5.023109 5.281964
#>  [834] 4.980044 4.977240 5.084393 4.880006 4.869186 4.677458 4.701002
#>  [841] 4.695450 5.017959 5.015533 5.020478 4.997203 5.248994 5.071998
#>  [848] 5.506294 4.851917 5.452370 5.194445 5.136535 5.074107 4.802104
#>  [855] 4.835274 5.048402 5.010951 5.128694 5.427576 4.816115 4.806195
#>  [862] 5.156572 5.022147 5.129236 4.821058 4.791568 5.034344 4.891750
#>  [869] 4.844616 4.604878 4.972339 4.774369 4.901014 4.687501 4.689462
#>  [876] 4.856326 4.771279 4.775940 4.904365 4.595666 4.801538 4.779864
#>  [883] 5.053905 5.373475 4.845289 4.775161 4.871406 4.929036 4.716728
#>  [890] 5.169673 4.910219 5.231293 5.137657 5.203749 4.923512 5.342335
#>  [897] 5.074064 4.851720 5.085887 5.280697 5.101608 4.737978 4.782492
#>  [904] 4.759765 4.702328 4.459059 4.479113 4.520861 4.522885 4.553945
#>  [911] 4.562790 4.614142 4.457084 4.620940 4.640579 4.643019 4.693535
#>  [918] 4.641197 4.749947 4.685121 4.810003 4.892378 4.866342 4.892809
#>  [925] 5.008690 5.183794 5.148454 6.598572 5.226396 4.658101 4.886322
#>  [932] 4.967458 4.785457 4.952332 4.832508 4.688243 4.866875 4.834215
#>  [939] 5.070860 4.826424 4.920745 5.043888 4.786705 4.723389 4.648971
#>  [946] 4.892320 4.680344 4.903799 4.620268 5.121947 4.657650 5.061350
#>  [953] 5.464482 5.841249 4.972082 5.003123 5.126240 5.106305 4.608487
#>  [960] 4.619377 4.815398 4.723334 4.966068 5.126282 4.881898 4.823340
#>  [967] 4.769456 4.660539 4.754073 4.936202 5.042556 4.900983 5.066827
#>  [974] 5.050705 4.710723 4.996137 5.573895 4.583561 4.754173 4.875171
#>  [981] 4.760085 4.860151 4.649824 4.671671 4.909889 4.718907 5.215605
#>  [988] 4.841976 4.679359 5.001945 4.843078 5.049004 5.172001 4.851154
#>  [995] 4.757447 4.927041 4.844887 4.806506 4.657697 5.784349
#> 
#> $Y10
#>    [1]  9.582372  8.286290  9.547317 11.190942 11.748658 10.778729
#>    [7] 12.227235  8.973460 11.087169  9.082510 10.915588  8.774650
#>   [13]  7.020994  8.401154  9.916690 10.660697  7.366386  9.294274
#>   [19]  9.000707  7.978389  7.722928 10.709353 10.531579 10.592698
#>   [25] 10.399745  9.020707  7.595816 10.575430  9.293662  3.629424
#>   [31]  9.960092  9.754651 10.553037  8.106724 10.685647  8.517302
#>   [37]  6.773453 11.069569  6.229006  8.764365  8.359807  9.635109
#>   [43]  8.305141  9.337377  9.445274  8.724299 10.461328  9.522269
#>   [49] 10.643082  9.965671 10.696860 11.590481  9.082492 10.588725
#>   [55] 10.938043  9.055285 12.111870  9.426079 11.272755 11.805392
#>   [61]  8.138697 11.402237 12.412215  9.566931 11.222404  9.562958
#>   [67]  8.916800 12.379583  9.301297 10.461059  6.617481  9.552772
#>   [73] 10.264576 11.456695 10.405926  9.929612  8.558682 10.024393
#>   [79]  7.995365 10.972733 11.143730  7.818277 11.072307  8.307418
#>   [85] 10.132246  9.260636  8.149857 10.355323 10.443782 10.399372
#>   [91] 10.214604 10.088316  6.944972 11.622931 10.117797  8.791238
#>   [97]  8.875623 10.814692  6.577234 12.216453  7.560324 10.370006
#>  [103]  7.585143 10.584420  6.567620  8.295046  9.436773  8.145721
#>  [109]  8.641151  7.790173 10.115991 10.485215  7.940852  9.677836
#>  [115] 11.120864 11.384471  8.770543 10.531239  9.311559 11.311988
#>  [121] 11.254332  8.363629 11.042978  9.179573 10.695704  6.521764
#>  [127]  7.865698  5.420796  8.425371 11.589800  7.824765  9.494724
#>  [133]  9.294597  8.577675  8.260006  7.541137  6.653711 10.504514
#>  [139]  9.649055 10.275775 12.144514 11.648650 10.737740 11.454838
#>  [145]  6.786957 10.570939 10.841263  9.062783 11.053177  8.501576
#>  [151]  9.605578  7.333423  8.625032  7.164481 10.872096  9.477885
#>  [157]  9.981516  9.967387 11.084818 10.193455 11.314897 10.034729
#>  [163]  9.666407 10.292139 10.913602 11.150576  9.805234 10.586547
#>  [169]  9.519855  7.164203  9.615080 10.900794 11.800434 11.518086
#>  [175] 11.168387  9.055596 11.170210 10.100200  8.882482 10.394316
#>  [181] 10.906444  8.975278 12.964388 11.089046 10.893325 10.168532
#>  [187] 10.977718  7.624408 10.782742 10.870000 10.214041  9.507359
#>  [193] 11.483030 10.688698 10.197375  8.408369  9.603503 10.059135
#>  [199]  9.309589  8.714336 10.029903  8.851802  9.034916  7.602402
#>  [205]  8.837038  6.707891  8.921026 10.845232 11.008175  8.571035
#>  [211] 10.563664  9.582110 13.102078 10.280545 10.824263  8.867512
#>  [217]  7.352418  6.189613 10.230285  7.470126  9.766444  9.462863
#>  [223]  9.681642 11.815666  7.555394 10.005245 10.194760 15.303544
#>  [229]  8.527175 11.136634  9.689032  8.893326 10.051824 10.657505
#>  [235]  5.408484 10.798680 10.406409 10.056774  8.181411  7.714264
#>  [241]  9.079617 10.388285  8.876086 10.907395 10.470624 10.700959
#>  [247]  9.038477  8.781198  9.962129 10.186688 11.030059  8.117704
#>  [253] 10.253378 12.045678  9.505074  8.554474 11.162925  8.914834
#>  [259]  7.669477  9.173339  9.935810 10.471819 10.243432  9.426597
#>  [265]  8.331944  9.848430 10.721048  8.657681  9.336199 10.846157
#>  [271] 10.358214 10.990856  9.724527 11.894517  9.429313  7.271822
#>  [277] 10.524780  8.509679 10.060365 10.564033 11.411862  9.127453
#>  [283]  8.440427 10.695475 11.163771 10.540046  7.750688  7.713395
#>  [289]  8.339439 10.800680  8.846456  9.043539  7.837468  9.385964
#>  [295] 10.707187 10.248697  9.403196 11.865466  7.768959  9.540433
#>  [301]  8.066960  9.580187 10.848519 10.350464 11.703424 12.591846
#>  [307]  9.457546  9.012733  9.149874 10.583257  8.958535  7.790350
#>  [313]  9.580330  9.546636  9.896671 12.482522 10.418034 11.400816
#>  [319]  9.240365  8.370530  9.305134  8.774338  8.896532 10.954466
#>  [325] 10.317170  9.691758 10.432773 11.429942  8.299824 11.026284
#>  [331]  9.770888  8.180709  9.870354 10.876971  6.393680  8.934209
#>  [337]  7.518748 10.966831  8.113246 10.131153  9.037511  6.793585
#>  [343] 11.125907  8.154456  8.357230  9.843490  9.681644  9.047039
#>  [349]  9.032779 10.247075  9.962503  9.268571  7.799094 10.887234
#>  [355]  6.739053  6.112093  6.582805  6.989508 10.782627  8.002105
#>  [361]  8.802151  8.853082 11.564834  9.040358  9.667341 10.085897
#>  [367] 10.334362 10.696227  9.777783  8.340859 12.929431 11.344447
#>  [373] 11.658443 11.516429  9.803837 10.186097 10.192716  9.756327
#>  [379]  7.239149  6.405822  7.820445  8.546779  8.785556  8.375088
#>  [385]  8.568859  9.022946  9.010954  9.574121  6.999321 10.336127
#>  [391] 10.078939  9.886955  8.638047 10.912848 10.896979  9.632776
#>  [397] 10.172920  9.562134  9.522656 10.588303  9.722882  9.716238
#>  [403] 11.939144  9.410769  9.192738  9.939576  8.676590  9.534435
#>  [409]  8.839670  9.811224 11.294276 10.573066  9.950840 11.496780
#>  [415] 10.401356 10.780372  9.848957 10.706655 10.076252  9.477387
#>  [421]  9.425822  9.886235  9.503002 11.160018 10.952532 10.405124
#>  [427]  8.686444 11.871353 11.569956 11.815767  8.343251 10.063588
#>  [433]  7.613972  9.404316  9.266110  9.510547 11.268717  9.802148
#>  [439]  6.385772  8.651518 10.587486 11.234224 10.266094  9.457338
#>  [445] 11.329676  8.244442 10.342349  7.285047  7.385403 10.832893
#>  [451]  8.718049  7.440722  7.927029  8.597894 10.483066 10.627138
#>  [457] 10.724898  8.787222  9.781421 10.614836  9.671304 10.790688
#>  [463]  9.515575  9.706967  8.673373 11.543026 10.048596 11.452184
#>  [469]  9.585644 10.266567  8.726318  9.712607 10.931177  8.560162
#>  [475] 10.464191 10.425541 10.415494 10.642113  9.456079 11.018899
#>  [481]  8.688760 11.579652 10.123593 10.557773  9.869883 10.661418
#>  [487]  8.275461  9.608211 10.029295  8.269619  9.962669  9.156719
#>  [493] 11.099421  8.871184  7.889361  3.893565 10.573862 10.296199
#>  [499] 10.839472  6.992510  9.207721  6.334472  7.383074 10.581140
#>  [505]  8.323460  8.356589  8.579468  8.933690 10.594139  8.541014
#>  [511]  7.322568 10.979325  8.868419 10.582604  7.770583 10.453589
#>  [517] 10.173494  9.957935 11.424079  9.468986 10.237143  9.248863
#>  [523] 11.822529  9.883460  9.611059  9.541665  7.180021  9.099278
#>  [529]  8.606619 10.012372  7.227394  9.467664  7.960527  8.118650
#>  [535]  9.427206  9.287545  8.640385 10.163703  6.554070  7.797298
#>  [541]  6.744845  8.223011 10.243911  9.013752  6.123270 11.367282
#>  [547]  9.986551 11.101546 12.697445 10.917715  8.179364  9.470735
#>  [553]  9.514366  8.122712 10.970969 10.447082  9.483897 10.800541
#>  [559] 10.974213  9.989949  9.806156  8.614706 11.015560 10.462441
#>  [565]  8.218402  9.777896 11.469187 12.643978 10.628014  9.925406
#>  [571] 11.729759 10.298827  9.058536 10.646162 11.000715  9.987201
#>  [577]  8.487232 10.346519  9.463414 11.035217 10.197552  9.529258
#>  [583] 10.633720 10.756015 10.396271 11.799367 11.392673  8.398155
#>  [589]  9.255729  7.162383  8.564856 10.656210  7.832573 11.302059
#>  [595]  9.952116  8.301494  6.918291 11.804012 11.425416  9.146381
#>  [601] 11.419850  9.402058 12.727209 10.875944 10.821421 10.476206
#>  [607] 11.585363 11.323725 10.695583  8.258162  8.279495  9.450324
#>  [613]  9.331741 10.139530  7.675778  9.913848 10.785649  8.794736
#>  [619] 10.119353  9.844361 12.125773  9.306974  9.473320 10.191739
#>  [625]  7.053519  7.846051  8.893620  9.037062  8.449898 12.066126
#>  [631] 10.724109 10.224691  7.288141 10.489789 10.012738 11.104942
#>  [637] 11.019873 12.200977 12.958395 10.173121 12.354731 12.808078
#>  [643]  9.454838 12.070499  9.154633 10.245075  8.757394 10.323241
#>  [649] 10.025285  9.665167 10.026746  9.677780  7.708918 10.625854
#>  [655] 10.932548  9.347437  9.537789  9.934260  8.754576 11.024092
#>  [661] 11.341267  9.151015 10.039570  9.835229 10.651903  9.964715
#>  [667]  9.845513 10.755526  9.960750 10.040664  9.017961 12.199566
#>  [673] 11.445572  8.217396  9.013253  9.674078  8.363110  8.636267
#>  [679]  8.083588  9.049505  8.648381  8.752221 10.154460  8.899370
#>  [685] 12.424942  8.163367  8.386173 11.054278  8.804724 10.089049
#>  [691]  9.259822  8.939944  6.176380  9.603678  8.999121 10.429693
#>  [697] 11.089872  9.577552 10.376345  8.032568  7.432838 11.907707
#>  [703]  9.709681  6.708350 10.929303  9.165371  9.401676  9.349923
#>  [709] 10.777345 11.840427  9.270257 11.277747  9.952448 11.294559
#>  [715] 11.412411  8.921875 10.454634 10.138525 11.684658 10.412604
#>  [721]  9.318036  8.913441  6.193079  9.594224  8.056908  9.030482
#>  [727]  8.848375 10.875166  9.966881  9.602231 11.148074 10.410291
#>  [733] 12.224741  9.879649  9.510502 11.429014 11.413868 11.909807
#>  [739]  8.924805 11.554712 10.500328  7.784206  9.543233 10.466921
#>  [745] 10.576705 10.773581 11.112288  8.312534 11.706475 10.995869
#>  [751] 10.611369  8.793532 10.685432  8.569555  8.983106  9.806364
#>  [757] 10.595757 10.780851 10.425684  9.563714 10.322788 10.511517
#>  [763]  9.694556 11.968079  9.258876 11.655012 12.021388 10.332193
#>  [769]  9.466751 12.233156 10.501295  9.848594  8.132747  9.458487
#>  [775]  8.309760  9.416586  8.950407 10.369366  9.722050  9.829364
#>  [781]  9.317953  8.070696  8.895186 10.154974  5.896469  5.274603
#>  [787] 10.557813 10.662636 10.755070  9.891990 10.209733 11.143043
#>  [793] 10.580617 10.849453  9.483360 10.636180 10.509973  9.559786
#>  [799]  9.272337 10.907532  8.771167  9.195591  9.367227  8.089169
#>  [805] 11.269514 10.484806 10.843433 10.565195 12.198548  9.442001
#>  [811] 10.677962  9.247010 11.702200 10.550737 11.385645  9.680785
#>  [817]  9.944766 11.344780  7.985588  9.913736  8.375597  9.144176
#>  [823] 10.413793 10.962041 12.558761  9.540976 11.586332 11.337177
#>  [829] 10.649039  9.440905  8.433637 12.456596 10.898577 12.001869
#>  [835] 10.285121 11.021671  9.836067  9.804145  9.137375  9.239404
#>  [841]  8.635301 10.611035  7.716600  7.966339 10.857916  9.370972
#>  [847] 11.119622  8.429634 11.086868  9.848494 10.420813  8.906719
#>  [853]  9.306560 10.605568 12.001903 12.480325 10.682390 11.618913
#>  [859] 11.432581  8.813549 12.378291  9.318949 10.175568  6.461989
#>  [865]  9.247761  5.319413  6.584992 10.657908 10.995878  8.415953
#>  [871] 11.994551 11.194957  8.137202  9.128034  9.241652  9.902063
#>  [877] 11.329928  8.787100  9.670600  7.208586  8.773652  9.240583
#>  [883] 10.289809  8.656719  8.904266 10.245809 10.358748  9.544136
#>  [889] 10.283122 10.233617  7.529640 10.021925  9.863273 11.161187
#>  [895] 10.584682  9.172508  8.730139 11.031454  6.766914  8.810735
#>  [901] 11.198958  9.212397 11.000014  9.936482 11.223078 11.207464
#>  [907]  9.899798  9.940672 10.217330 10.278334 11.547793 11.287880
#>  [913] 10.503207  9.177424  9.364388 10.010535  9.402282  7.091392
#>  [919] 10.464028  7.781170 10.353617 10.879603 12.389784  9.908369
#>  [925]  8.908058 11.281745 10.735878  9.867883  9.995849  8.695572
#>  [931]  9.553404  9.172282  9.476889  9.061542  8.256502  9.987123
#>  [937]  9.248848 10.667025 10.655567 10.669765  7.154433  7.352040
#>  [943] 10.496828 10.635179 10.357846 11.088428 10.307637  8.676489
#>  [949] 12.177664 10.002981  9.247853  8.827718  8.440090  8.756152
#>  [955]  7.044217 10.058607 10.468815  8.731020 11.170453  9.334457
#>  [961] 11.535732  9.667567  9.063004  8.014067  6.558392 11.172422
#>  [967] 12.028850 10.423596  9.306574  8.786613  9.748520 11.354558
#>  [973]  8.787617  8.327121  8.373705  9.333729  7.711995  9.174361
#>  [979]  8.080680 10.656454  7.807798  7.655317 12.270739 10.300398
#>  [985] 10.944739 11.072560 10.930406 10.175985 10.282994 10.014402
#>  [991] 11.311171  5.962929  7.617423 11.258817 11.326268  7.695156
#>  [997]  9.102228  7.377585 10.251228 10.189969
#> 
#> $ENIE
#> [1] -2.595363
#> 
#> $ENDE
#> [1] 4.776552
#> 
#> $ETE
#> [1] 2.181189
#> 
#> $TE.c.i
#> [1] 1.218090 3.251656
#> 
#> $IE.c.i
#> [1] -5.023691  0.483747
#> 
#> $DE.c.i
#> [1] 1.403014 7.336307
#> 
#> $call
#> bnpmediation(dataTreatment = dataTreatment, dataControl = dataControl, 
#>     prior = prior, mcmc = mcmc, state = state, status = TRUE, 
#>     na.action = na.action, q = 2, NN = 10, n1 = 10, n0 = 10, 
#>     extra.thin = 0, seed = 12345)
#> 
#> attr(,"class")
#> [1] "bnpmediation"