gọi thư viện

library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.3     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.4     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.0
## ✔ purrr     1.0.2     
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library(table1)
## 
## Attaching package: 'table1'
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##     units, units<-
library(factoextra)
## Warning: package 'factoextra' was built under R version 4.3.2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(ggdendro)
## 
## Attaching package: 'ggdendro'
## 
## The following object is masked from 'package:table1':
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##     label
library(dendextend)
## 
## ---------------------
## Welcome to dendextend version 1.17.1
## Type citation('dendextend') for how to cite the package.
## 
## Type browseVignettes(package = 'dendextend') for the package vignette.
## The github page is: https://github.com/talgalili/dendextend/
## 
## Suggestions and bug-reports can be submitted at: https://github.com/talgalili/dendextend/issues
## You may ask questions at stackoverflow, use the r and dendextend tags: 
##   https://stackoverflow.com/questions/tagged/dendextend
## 
##  To suppress this message use:  suppressPackageStartupMessages(library(dendextend))
## ---------------------
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## 
## Attaching package: 'dendextend'
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## The following object is masked from 'package:ggdendro':
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library(tidyverse)
library(cluster)
library(dplyr)

thuan = read.csv("E:\\OneDrive - UMP\\R - lenh 2016\\bvlvt02112022.csv", header=T)
 attach(thuan)
library(FactoMineR)

pca.ome <- PCA(thuan, graph = T)
## Warning in PCA(thuan, graph = T): Missing values are imputed by the mean of the
## variable: you should use the imputePCA function of the missMDA package

get_eig(pca.ome)
##          eigenvalue variance.percent cumulative.variance.percent
## Dim.1  1.572658e+01     3.083643e+01                    30.83643
## Dim.2  6.091225e+00     1.194358e+01                    42.78001
## Dim.3  3.526289e+00     6.914292e+00                    49.69430
## Dim.4  2.941474e+00     5.767596e+00                    55.46189
## Dim.5  2.437581e+00     4.779570e+00                    60.24146
## Dim.6  2.216688e+00     4.346447e+00                    64.58791
## Dim.7  1.742316e+00     3.416306e+00                    68.00422
## Dim.8  1.488365e+00     2.918364e+00                    70.92258
## Dim.9  1.198734e+00     2.350458e+00                    73.27304
## Dim.10 1.090694e+00     2.138616e+00                    75.41165
## Dim.11 1.053070e+00     2.064843e+00                    77.47650
## Dim.12 8.981883e-01     1.761154e+00                    79.23765
## Dim.13 8.374660e-01     1.642090e+00                    80.87974
## Dim.14 7.852821e-01     1.539769e+00                    82.41951
## Dim.15 7.619128e-01     1.493947e+00                    83.91346
## Dim.16 6.670315e-01     1.307905e+00                    85.22136
## Dim.17 6.443879e-01     1.263506e+00                    86.48487
## Dim.18 6.194712e-01     1.214649e+00                    87.69952
## Dim.19 4.608157e-01     9.035603e-01                    88.60308
## Dim.20 4.550068e-01     8.921701e-01                    89.49525
## Dim.21 4.434991e-01     8.696060e-01                    90.36485
## Dim.22 4.006276e-01     7.855444e-01                    91.15040
## Dim.23 3.852650e-01     7.554215e-01                    91.90582
## Dim.24 3.452121e-01     6.768865e-01                    92.58270
## Dim.25 3.203328e-01     6.281035e-01                    93.21081
## Dim.26 3.057978e-01     5.996035e-01                    93.81041
## Dim.27 2.782583e-01     5.456044e-01                    94.35602
## Dim.28 2.680467e-01     5.255818e-01                    94.88160
## Dim.29 2.512086e-01     4.925660e-01                    95.37416
## Dim.30 2.464986e-01     4.833306e-01                    95.85749
## Dim.31 2.289479e-01     4.489174e-01                    96.30641
## Dim.32 2.163304e-01     4.241772e-01                    96.73059
## Dim.33 1.848280e-01     3.624079e-01                    97.09300
## Dim.34 1.810496e-01     3.549992e-01                    97.44800
## Dim.35 1.675115e-01     3.284539e-01                    97.77645
## Dim.36 1.561930e-01     3.062608e-01                    98.08271
## Dim.37 1.397313e-01     2.739829e-01                    98.35669
## Dim.38 1.388412e-01     2.722376e-01                    98.62893
## Dim.39 1.279358e-01     2.508546e-01                    98.87979
## Dim.40 1.220846e-01     2.393816e-01                    99.11917
## Dim.41 1.123400e-01     2.202746e-01                    99.33944
## Dim.42 9.981139e-02     1.957086e-01                    99.53515
## Dim.43 8.557182e-02     1.677879e-01                    99.70294
## Dim.44 8.148942e-02     1.597832e-01                    99.86272
## Dim.45 7.001167e-02     1.372778e-01                   100.00000
## Dim.46 4.502314e-27     8.828066e-27                   100.00000
## Dim.47 3.101521e-30     6.081413e-30                   100.00000
## Dim.48 8.201051e-31     1.608049e-30                   100.00000
## Dim.49 5.223314e-31     1.024179e-30                   100.00000
## Dim.50 1.996670e-31     3.915040e-31                   100.00000
## Dim.51 1.061922e-31     2.082199e-31                   100.00000
fviz_screeplot(pca.ome, addlabels=T, ylim = c(0, 50))

var <- get_pca_var(pca.ome)
var
## Principal Component Analysis Results for variables
##  ===================================================
##   Name       Description                                    
## 1 "$coord"   "Coordinates for the variables"                
## 2 "$cor"     "Correlations between variables and dimensions"
## 3 "$cos2"    "Cos2 for the variables"                       
## 4 "$contrib" "contributions of the variables"
head(var$coord)
##                Dim.1       Dim.2        Dim.3       Dim.4        Dim.5
## id       -0.04880622  0.06766462 -0.002381938 -0.02978331 -0.004095345
## gioi     -0.12570133 -0.08699425  0.125153165 -0.11087317  0.050399689
## thang     0.03992797 -0.02473749 -0.069547437  0.10578645 -0.070718875
## nam       0.04701565 -0.14160881  0.197359673 -0.05939562  0.126814987
## thamnien -0.01230854 -0.22820993  0.206052905 -0.04712547  0.068243945
## a3       -0.13030023  0.01699582  0.243556920 -0.40215270  0.312276865
head(var$contrib)
##                 Dim.1       Dim.2        Dim.3     Dim.4        Dim.5
## id       0.0151466300 0.075165519 0.0001608951 0.0301565 0.0006880533
## gioi     0.1004720981 0.124244296 0.4441869689 0.4179149 0.1042069607
## thang    0.0101372532 0.010046308 0.1371653452 0.3804478 0.2051689828
## nam      0.0140556405 0.329212213 1.1045845751 0.1199344 0.6597542320
## thamnien 0.0009633377 0.854996705 1.2040364190 0.0754999 0.1910597804
## a3       0.1079583237 0.004742196 1.6822211327 5.4981552 4.0005586319
fviz_pca_var(pca.ome, col.var = "blue")

fviz_pca_var(pca.ome, col.var="contrib",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = T )

fviz_contrib(pca.ome, choice = "var", axes = 1, top = 10)

fviz_contrib(pca.ome, choice = "var", axes = 2, top = 10)

ind <- get_pca_ind(pca.ome)
ind
## Principal Component Analysis Results for individuals
##  ===================================================
##   Name       Description                       
## 1 "$coord"   "Coordinates for the individuals" 
## 2 "$cos2"    "Cos2 for the individuals"        
## 3 "$contrib" "contributions of the individuals"
head(ind$coord)
##        Dim.1      Dim.2       Dim.3      Dim.4      Dim.5
## 1 -4.8026068 -0.5049304 -0.11961131  1.0568665  1.4066833
## 2 -4.8026869 -0.5047519 -0.11961957  1.0567534  1.4066662
## 3  0.0742801  1.2296056  1.48707116 -0.3760771 -0.9909968
## 4 -7.8936346  0.3570179 -0.84545357  0.1515572 -0.1694290
## 5 -3.3204308 -1.1039399  0.05008929  1.2022377 -3.2076433
## 6 -2.2520869 -1.0708266  0.05830314 -1.6595463  0.8614978

Đọc

fviz_pca_ind(pca.ome, col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = T)

fviz_pca_biplot(pca.ome, repel = TRUE)

fviz_pca_ind(pca.ome, label = "none", palette = c("#00AFBB", "#E7B800", "#FC4E07"),addEllipses = T)

goi thư viện

library(lavaan)
## This is lavaan 0.6-16
## lavaan is FREE software! Please report any bugs.
library(lavaanPlot)
library(OpenMx)
m1a  <- ' UWES = ~ uwes1+ uwes2+ uwes3+ uwes4+ uwes5+ uwes6+ uwes7+ uwes8+ uwes9
          GJS = ~ gjs1+ gjs2+ gjs3+ gjs4+ gjs5+ gjs6+ gjs7+ gjs8+ gjs9+ gjs10
          WSS = ~ wss1+ wss2+ wss3+ wss4+ wss5+ wss6+ wss7+ wss8
          BRCS = ~ brcs1+ brcs2+ brcs3+ brcs4
          BRS = ~ brs1+ brs2+ brs3+ brs4+ brs5+ brs6 
          CH = ~ gioi*congviec + gioi*thamnien + congviec*thamnien ' 

 m1a.1 <- cfa(m1a, data=thuan, std.lv=T) 
 summary(m1a.1, std=T) 
## lavaan 0.6.16 ended normally after 54 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        93
##   Number of equality constraints                     1
## 
##   Number of observations                           532
## 
## Model Test User Model:
##                                                       
##   Test statistic                              4576.818
##   Degrees of freedom                               688
##   P-value (Chi-square)                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   UWES =~                                                               
##     uwes1             1.257    0.050   25.195    0.000    1.257    0.868
##     uwes2             1.188    0.045   26.685    0.000    1.188    0.899
##     uwes3             1.293    0.046   28.268    0.000    1.293    0.929
##     uwes4             1.342    0.048   28.133    0.000    1.342    0.926
##     uwes5             1.433    0.055   26.104    0.000    1.433    0.887
##     uwes6             1.276    0.049   26.267    0.000    1.276    0.890
##     uwes7             1.166    0.050   23.375    0.000    1.166    0.828
##     uwes8             1.164    0.053   21.799    0.000    1.164    0.791
##     uwes9             1.169    0.061   19.090    0.000    1.169    0.720
##   GJS =~                                                                
##     gjs1              0.618    0.031   19.813    0.000    0.618    0.744
##     gjs2              0.354    0.028   12.667    0.000    0.354    0.522
##     gjs3              0.681    0.030   22.789    0.000    0.681    0.818
##     gjs4              0.819    0.034   24.091    0.000    0.819    0.848
##     gjs5              0.849    0.034   25.249    0.000    0.849    0.873
##     gjs6              0.830    0.035   23.637    0.000    0.830    0.838
##     gjs7              0.884    0.046   19.128    0.000    0.884    0.725
##     gjs8              0.666    0.034   19.842    0.000    0.666    0.745
##     gjs9              0.488    0.029   17.112    0.000    0.488    0.667
##     gjs10             0.715    0.029   24.782    0.000    0.715    0.863
##   WSS =~                                                                
##     wss1              0.780    0.034   22.869    0.000    0.780    0.827
##     wss2              0.926    0.039   23.738    0.000    0.926    0.848
##     wss3              0.848    0.036   23.859    0.000    0.848    0.850
##     wss4              0.816    0.039   20.987    0.000    0.816    0.782
##     wss5              0.885    0.039   22.521    0.000    0.885    0.819
##     wss6              0.361    0.043    8.391    0.000    0.361    0.366
##     wss7              0.204    0.043    4.756    0.000    0.204    0.212
##     wss8              0.277    0.039    7.044    0.000    0.277    0.310
##   BRCS =~                                                               
##     brcs1             0.573    0.026   22.154    0.000    0.573    0.814
##     brcs2             0.562    0.026   22.031    0.000    0.562    0.811
##     brcs3             0.607    0.024   25.053    0.000    0.607    0.881
##     brcs4             0.617    0.027   22.849    0.000    0.617    0.830
##   BRS =~                                                                
##     brs1              0.235    0.032    7.380    0.000    0.235    0.324
##     brs2              0.598    0.034   17.658    0.000    0.598    0.691
##     brs3              0.502    0.035   14.274    0.000    0.502    0.584
##     brs4              0.976    0.038   25.640    0.000    0.976    0.891
##     brs5              0.688    0.035   19.678    0.000    0.688    0.747
##     brs6              0.961    0.036   26.342    0.000    0.961    0.906
##   CH =~                                                                 
##     congvic (gioi)    0.864    0.143    6.025    0.000    0.864    0.754
##     thamnin (gioi)    0.864    0.143    6.025    0.000    0.864    0.171
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   UWES ~~                                                               
##     GJS               0.669    0.026   25.867    0.000    0.669    0.669
##     WSS              -0.250    0.043   -5.772    0.000   -0.250   -0.250
##     BRCS              0.545    0.033   16.279    0.000    0.545    0.545
##     BRS               0.225    0.044    5.146    0.000    0.225    0.225
##     CH                0.068    0.059    1.156    0.248    0.068    0.068
##   GJS ~~                                                                
##     WSS              -0.227    0.044   -5.120    0.000   -0.227   -0.227
##     BRCS              0.569    0.033   17.300    0.000    0.569    0.569
##     BRS               0.251    0.044    5.737    0.000    0.251    0.251
##     CH                0.100    0.060    1.655    0.098    0.100    0.100
##   WSS ~~                                                                
##     BRCS             -0.071    0.047   -1.490    0.136   -0.071   -0.071
##     BRS               0.290    0.044    6.644    0.000    0.290    0.290
##     CH               -0.176    0.065   -2.725    0.006   -0.176   -0.176
##   BRCS ~~                                                               
##     BRS               0.348    0.042    8.208    0.000    0.348    0.348
##     CH                0.155    0.064    2.421    0.015    0.155    0.155
##   BRS ~~                                                                
##     CH                0.173    0.065    2.684    0.007    0.173    0.173
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .uwes1             0.516    0.035   14.784    0.000    0.516    0.246
##    .uwes2             0.336    0.024   14.211    0.000    0.336    0.192
##    .uwes3             0.266    0.020   13.158    0.000    0.266    0.137
##    .uwes4             0.298    0.022   13.277    0.000    0.298    0.142
##    .uwes5             0.556    0.038   14.467    0.000    0.556    0.213
##    .uwes6             0.426    0.030   14.400    0.000    0.426    0.207
##    .uwes7             0.623    0.041   15.225    0.000    0.623    0.314
##    .uwes8             0.813    0.053   15.482    0.000    0.813    0.375
##    .uwes9             1.271    0.081   15.777    0.000    1.271    0.482
##    .gjs1              0.308    0.020   15.233    0.000    0.308    0.447
##    .gjs2              0.334    0.021   15.985    0.000    0.334    0.727
##    .gjs3              0.229    0.016   14.541    0.000    0.229    0.330
##    .gjs4              0.262    0.019   14.073    0.000    0.262    0.281
##    .gjs5              0.225    0.017   13.509    0.000    0.225    0.238
##    .gjs6              0.293    0.021   14.253    0.000    0.293    0.298
##    .gjs7              0.704    0.046   15.346    0.000    0.704    0.474
##    .gjs8              0.356    0.023   15.228    0.000    0.356    0.446
##    .gjs9              0.297    0.019   15.613    0.000    0.297    0.555
##    .gjs10             0.175    0.013   13.758    0.000    0.175    0.255
##    .wss1              0.280    0.021   13.163    0.000    0.280    0.315
##    .wss2              0.336    0.027   12.607    0.000    0.336    0.282
##    .wss3              0.276    0.022   12.520    0.000    0.276    0.277
##    .wss4              0.424    0.030   14.049    0.000    0.424    0.389
##    .wss5              0.384    0.029   13.355    0.000    0.384    0.329
##    .wss6              0.843    0.052   16.091    0.000    0.843    0.866
##    .wss7              0.877    0.054   16.243    0.000    0.877    0.955
##    .wss8              0.722    0.045   16.159    0.000    0.722    0.904
##    .brcs1             0.168    0.013   13.063    0.000    0.168    0.338
##    .brcs2             0.165    0.013   13.135    0.000    0.165    0.343
##    .brcs3             0.107    0.010   10.554    0.000    0.107    0.224
##    .brcs4             0.171    0.014   12.609    0.000    0.171    0.311
##    .brs1              0.472    0.029   16.144    0.000    0.472    0.895
##    .brs2              0.392    0.026   15.000    0.000    0.392    0.523
##    .brs3              0.487    0.031   15.573    0.000    0.487    0.659
##    .brs4              0.246    0.024   10.257    0.000    0.246    0.205
##    .brs5              0.374    0.026   14.474    0.000    0.374    0.441
##    .brs6              0.201    0.022    9.265    0.000    0.201    0.178
##    .congviec          0.566    0.245    2.306    0.021    0.566    0.431
##    .thamnien         24.862    1.544   16.106    0.000   24.862    0.971
##     UWES              1.000                               1.000    1.000
##     GJS               1.000                               1.000    1.000
##     WSS               1.000                               1.000    1.000
##     BRCS              1.000                               1.000    1.000
##     BRS               1.000                               1.000    1.000
##     CH                1.000                               1.000    1.000
 library(semPlot)
  
 fit <- sem(m1a, data = thuan)
 lavaanPlot(model = fit, coefs = T, stand = T, covs = T,
           edge_options = list(color="red"),
           node_options = list(color="blue"),
           sig = .05, digits = 2,
           stars = c("regress","latent", "covs"))
### Phân tích khác
library(BayesFactor)
## Loading required package: coda
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:OpenMx':
## 
##     %&%, expm
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## ************
## Welcome to BayesFactor 0.9.12-4.5. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
## 
## Type BFManual() to open the manual.
## ************
bf = ttestBF(formula = uwes_tol ~ gioi, data=thuan)
bf
## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 0.2293691 ±0.08%
## 
## Against denominator:
##   Null, mu1-mu2 = 0 
## ---
## Bayes factor type: BFindepSample, JZS
mcmc = posterior(bf, iter =10)
summary(mcmc)
## 
## Iterations = 1:10
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                  Mean      SD Naive SE Time-series SE
## mu            40.1111 0.49901  0.15780        0.16700
## beta (1 - 2)   1.2952 0.42674  0.13495        0.08089
## sig2         130.7485 6.84357  2.16413        2.16413
## delta          0.1131 0.03686  0.01166        0.00642
## g              3.3530 9.24151  2.92242        2.92242
## 
## 2. Quantiles for each variable:
## 
##                   2.5%       25%      50%      75%   97.5%
## mu            39.20097  39.82513  40.3437  40.4032  40.642
## beta (1 - 2)   0.68218   1.08987   1.1813   1.4806   2.013
## sig2         120.45701 127.62974 129.7631 137.1886 139.417
## delta          0.06091   0.09555   0.1034   0.1318   0.176
## g              0.06145   0.15187   0.3440   0.8540  23.254
table(mcmc [, 2] <0) # nam nho hon nu
## 
## FALSE 
##    10
# hoi qui tuyen tinh
library(rstanarm)
## Loading required package: Rcpp
## This is rstanarm version 2.26.1
## - See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!
## - Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.
## - For execution on a local, multicore CPU with excess RAM we recommend calling
##   options(mc.cores = parallel::detectCores())
library(BAS)
library(broom)
library(GGally)
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
m1 = stan_glm(uwes_tol ~ congviec, data=thuan)
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## Also defined by 'MatrixModels'
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## Also defined by 'MatrixModels'
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## Also defined by 'MatrixModels'
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## Also defined by 'MatrixModels'
## 
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m1
## stan_glm
##  family:       gaussian [identity]
##  formula:      uwes_tol ~ congviec
##  observations: 532
##  predictors:   2
## ------
##             Median MAD_SD
## (Intercept) 39.1    1.1  
## congviec     0.5    0.4  
## 
## Auxiliary parameter(s):
##       Median MAD_SD
## sigma 11.5    0.4  
## 
## ------
## * For help interpreting the printed output see ?print.stanreg
## * For info on the priors used see ?prior_summary.stanreg
summary(m1)
## 
## Model Info:
##  function:     stan_glm
##  family:       gaussian [identity]
##  formula:      uwes_tol ~ congviec
##  algorithm:    sampling
##  sample:       4000 (posterior sample size)
##  priors:       see help('prior_summary')
##  observations: 532
##  predictors:   2
## 
## Estimates:
##               mean   sd   10%   50%   90%
## (Intercept) 39.1    1.1 37.6  39.1  40.5 
## congviec     0.5    0.4 -0.1   0.5   1.0 
## sigma       11.5    0.4 11.1  11.5  12.0 
## 
## Fit Diagnostics:
##            mean   sd   10%   50%   90%
## mean_PPD 40.2    0.7 39.2  40.2  41.1 
## 
## The mean_ppd is the sample average posterior predictive distribution of the outcome variable (for details see help('summary.stanreg')).
## 
## MCMC diagnostics
##               mcse Rhat n_eff
## (Intercept)   0.0  1.0  3965 
## congviec      0.0  1.0  3750 
## sigma         0.0  1.0  3751 
## mean_PPD      0.0  1.0  3913 
## log-posterior 0.0  1.0  1627 
## 
## For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
prior_summary(m1)
## Priors for model 'm1' 
## ------
## Intercept (after predictors centered)
##   Specified prior:
##     ~ normal(location = 40, scale = 2.5)
##   Adjusted prior:
##     ~ normal(location = 40, scale = 29)
## 
## Coefficients
##   Specified prior:
##     ~ normal(location = 0, scale = 2.5)
##   Adjusted prior:
##     ~ normal(location = 0, scale = 25)
## 
## Auxiliary (sigma)
##   Specified prior:
##     ~ exponential(rate = 1)
##   Adjusted prior:
##     ~ exponential(rate = 0.087)
## ------
## See help('prior_summary.stanreg') for more details
post.r2 = bayes_R2(m1)
summary(post.r2)
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000000 0.0006088 0.0023688 0.0041031 0.0058689 0.0441478
## Da bien cho outcom dịnh luong 

m.da = stan_glm(uwes_tol ~ congviec + gioi*thamnien*congviec + tuoi, data=thuan,
                prior = default_prior_coef(family),
                prior_intercept = default_prior_intercept(family),
                prior_aux = exponential(autoscale = T),
                prior_PD = T,
                adapt_delta = NULL,
                QR = F)
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## 
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summary(m.da)
## 
## Model Info:
##  function:     stan_glm
##  family:       gaussian [identity]
##  formula:      uwes_tol ~ congviec + gioi * thamnien * congviec + tuoi
##  algorithm:    sampling
##  sample:       4000 (posterior sample size)
##  priors:       see help('prior_summary')
##  observations: 532
##  predictors:   9
## 
## Estimates:
##                          mean   sd     10%    50%    90% 
## (Intercept)              42.9  191.5 -204.6   43.1  281.2
## congviec                 -0.1   25.8  -33.5   -0.5   33.3
## gioi                     -0.6   57.7  -75.3   -0.2   73.6
## thamnien                  0.2    5.8   -7.1    0.1    7.4
## tuoi                      0.0    4.4   -5.6   -0.1    5.4
## gioi:thamnien             0.0    3.1   -4.0    0.0    4.0
## congviec:gioi            -0.2   13.8  -17.9   -0.3   17.1
## congviec:thamnien         0.0    1.4   -1.8    0.0    1.8
## congviec:gioi:thamnien    0.0    0.7   -0.9    0.0    0.9
## sigma                    11.7   12.1    1.2    7.9   26.9
## 
## MCMC diagnostics
##                        mcse Rhat n_eff
## (Intercept)            2.7  1.0  5067 
## congviec               0.4  1.0  4864 
## gioi                   0.8  1.0  4657 
## thamnien               0.1  1.0  5131 
## tuoi                   0.1  1.0  5007 
## gioi:thamnien          0.0  1.0  5026 
## congviec:gioi          0.2  1.0  4965 
## congviec:thamnien      0.0  1.0  5015 
## congviec:gioi:thamnien 0.0  1.0  4705 
## sigma                  0.2  1.0  6435 
## log-posterior          0.1  1.0  1946 
## 
## For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
prior_summary(m.da)
## Priors for model 'm.da' 
## ------
## Intercept (after predictors centered)
##   Specified prior:
##     ~ normal(location = 40, scale = 2.5)
##   Adjusted prior:
##     ~ normal(location = 40, scale = 29)
## 
## Coefficients
##   Specified prior:
##     ~ normal(location = [0,0,0,...], scale = [2.5,2.5,2.5,...])
##   Adjusted prior:
##     ~ normal(location = [0,0,0,...], scale = [25.08,58.51, 5.73,...])
## 
## Auxiliary (sigma)
##   Specified prior:
##     ~ exponential(rate = 1)
##   Adjusted prior:
##     ~ exponential(rate = 0.087)
## ------
## See help('prior_summary.stanreg') for more details
post.r2.m.da = bayes_R2(m.da)
summary(post.r2.m.da)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2001  0.9489  0.9885  0.9461  0.9980  1.0000
#exp(coefficients(m.da))
# exp(confint(m.da))

# Tương tự có thể dùng cách khác
library(MCMCpack)
## Loading required package: MASS
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
## ##
## ## Markov Chain Monte Carlo Package (MCMCpack)
## ## Copyright (C) 2003-2023 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
## ##
## ## Support provided by the U.S. National Science Foundation
## ## (Grants SES-0350646 and SES-0350613)
## ##
## 
## Attaching package: 'MCMCpack'
## The following object is masked from 'package:OpenMx':
## 
##     vech
library(broom)
posterior = MCMCregress(formula= uwes_tol ~ congviec, b0=0, B0=0.01,
                        data=thuan, verbose=10)
## 
## 
## MCMCregress iteration 1 of 11000 
## beta = 
##   40.14947
##    0.22861
## sigma2 =  137.35576
## 
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##   38.21983
##    0.50558
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##   37.26388
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##   38.66012
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##   39.17425
##    0.14075
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##   40.49207
##   -0.28163
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##   38.86229
##    0.45005
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##   37.28149
##    1.04308
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##   39.00709
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##   40.71760
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##   38.22100
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##   39.28809
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##   38.68942
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##   39.44279
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##   39.60378
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##   39.25086
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##   37.89237
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##   38.36414
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##   40.01701
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##   36.86543
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##   37.38563
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## beta = 
##   36.31538
##    1.55292
## sigma2 =  140.28296
## 
## 
## MCMCregress iteration 401 of 11000 
## beta = 
##   38.87566
##    0.75053
## sigma2 =  137.42896
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## 
## MCMCregress iteration 411 of 11000 
## beta = 
##   38.30935
##    0.57255
## sigma2 =  140.82059
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## 
## MCMCregress iteration 421 of 11000 
## beta = 
##   37.88812
##    0.84710
## sigma2 =  135.42299
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## MCMCregress iteration 431 of 11000 
## beta = 
##   39.13727
##    0.19338
## sigma2 =  134.12925
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## MCMCregress iteration 441 of 11000 
## beta = 
##   37.99118
##    0.49388
## sigma2 =  134.63372
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## MCMCregress iteration 451 of 11000 
## beta = 
##   39.04019
##    0.66271
## sigma2 =  129.18784
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## MCMCregress iteration 461 of 11000 
## beta = 
##   37.78190
##    0.75649
## sigma2 =  131.22014
## 
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## MCMCregress iteration 471 of 11000 
## beta = 
##   37.84130
##    0.61408
## sigma2 =  126.31379
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## 
## MCMCregress iteration 481 of 11000 
## beta = 
##   40.91336
##   -0.44798
## sigma2 =  138.15905
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## 
## MCMCregress iteration 491 of 11000 
## beta = 
##   38.43882
##    0.90510
## sigma2 =  136.90045
## 
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## MCMCregress iteration 501 of 11000 
## beta = 
##   38.98673
##    0.40176
## sigma2 =  130.29040
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## MCMCregress iteration 511 of 11000 
## beta = 
##   39.86838
##   -0.21363
## sigma2 =  139.97622
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## MCMCregress iteration 521 of 11000 
## beta = 
##   37.56614
##    1.10591
## sigma2 =  132.84610
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## 
## MCMCregress iteration 531 of 11000 
## beta = 
##   39.92889
##    0.06452
## sigma2 =  128.21401
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## MCMCregress iteration 541 of 11000 
## beta = 
##   37.28849
##    1.27962
## sigma2 =  128.45372
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## MCMCregress iteration 551 of 11000 
## beta = 
##   39.48298
##    0.47966
## sigma2 =  145.20574
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## 
## MCMCregress iteration 561 of 11000 
## beta = 
##   37.33979
##    1.19544
## sigma2 =  130.22336
## 
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## MCMCregress iteration 571 of 11000 
## beta = 
##   38.08282
##    0.75225
## sigma2 =  143.68412
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## 
## MCMCregress iteration 581 of 11000 
## beta = 
##   38.73716
##    0.50026
## sigma2 =  135.31846
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## 
## MCMCregress iteration 591 of 11000 
## beta = 
##   38.21992
##    0.69910
## sigma2 =  119.74317
## 
## 
## MCMCregress iteration 601 of 11000 
## beta = 
##   36.75148
##    1.17842
## sigma2 =  128.72087
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## 
## MCMCregress iteration 611 of 11000 
## beta = 
##   38.33614
##    0.66948
## sigma2 =  135.28226
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## 
## MCMCregress iteration 621 of 11000 
## beta = 
##   37.68968
##    1.07421
## sigma2 =  126.39310
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## MCMCregress iteration 631 of 11000 
## beta = 
##   37.42721
##    1.31916
## sigma2 =  141.22365
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## MCMCregress iteration 641 of 11000 
## beta = 
##   40.09611
##    0.11606
## sigma2 =  128.86108
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## 
## MCMCregress iteration 651 of 11000 
## beta = 
##   36.51567
##    1.11816
## sigma2 =  136.54449
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## 
## MCMCregress iteration 661 of 11000 
## beta = 
##   38.38878
##    0.64696
## sigma2 =  131.09784
## 
## 
## MCMCregress iteration 671 of 11000 
## beta = 
##   39.07994
##    0.19154
## sigma2 =  136.90922
## 
## 
## MCMCregress iteration 681 of 11000 
## beta = 
##   40.16161
##    0.06398
## sigma2 =  139.68566
## 
## 
## MCMCregress iteration 691 of 11000 
## beta = 
##   37.24248
##    1.32120
## sigma2 =  120.90898
## 
## 
## MCMCregress iteration 701 of 11000 
## beta = 
##   39.05100
##    0.64192
## sigma2 =  138.06348
## 
## 
## MCMCregress iteration 711 of 11000 
## beta = 
##   38.98352
##    0.48274
## sigma2 =  139.81599
## 
## 
## MCMCregress iteration 721 of 11000 
## beta = 
##   38.88624
##    0.56875
## sigma2 =  125.84624
## 
## 
## MCMCregress iteration 731 of 11000 
## beta = 
##   37.40257
##    0.98380
## sigma2 =  119.12916
## 
## 
## MCMCregress iteration 741 of 11000 
## beta = 
##   37.11079
##    0.98184
## sigma2 =  135.59363
## 
## 
## MCMCregress iteration 751 of 11000 
## beta = 
##   39.75928
##    0.52134
## sigma2 =  131.70690
## 
## 
## MCMCregress iteration 761 of 11000 
## beta = 
##   41.26304
##   -0.11435
## sigma2 =  120.94362
## 
## 
## MCMCregress iteration 771 of 11000 
## beta = 
##   39.78486
##   -0.00494
## sigma2 =  144.55643
## 
## 
## MCMCregress iteration 781 of 11000 
## beta = 
##   37.19253
##    0.89705
## sigma2 =  128.05924
## 
## 
## MCMCregress iteration 791 of 11000 
## beta = 
##   39.17227
##    0.59941
## sigma2 =  130.92452
## 
## 
## MCMCregress iteration 801 of 11000 
## beta = 
##   35.96489
##    1.42963
## sigma2 =  137.19070
## 
## 
## MCMCregress iteration 811 of 11000 
## beta = 
##   39.72507
##    0.57422
## sigma2 =  134.27447
## 
## 
## MCMCregress iteration 821 of 11000 
## beta = 
##   38.16305
##    0.70897
## sigma2 =  129.83460
## 
## 
## MCMCregress iteration 831 of 11000 
## beta = 
##   40.34922
##    0.57369
## sigma2 =  120.68201
## 
## 
## MCMCregress iteration 841 of 11000 
## beta = 
##   37.40128
##    1.05913
## sigma2 =  131.67798
## 
## 
## MCMCregress iteration 851 of 11000 
## beta = 
##   38.39178
##    0.54557
## sigma2 =  134.07171
## 
## 
## MCMCregress iteration 861 of 11000 
## beta = 
##   37.06474
##    1.25433
## sigma2 =  139.95301
## 
## 
## MCMCregress iteration 871 of 11000 
## beta = 
##   38.34501
##    0.98172
## sigma2 =  132.00199
## 
## 
## MCMCregress iteration 881 of 11000 
## beta = 
##   39.75708
##    0.48151
## sigma2 =  140.86694
## 
## 
## MCMCregress iteration 891 of 11000 
## beta = 
##   40.48641
##    0.00570
## sigma2 =  119.37332
## 
## 
## MCMCregress iteration 901 of 11000 
## beta = 
##   41.30087
##   -0.04424
## sigma2 =  142.43019
## 
## 
## MCMCregress iteration 911 of 11000 
## beta = 
##   39.27044
##    0.56932
## sigma2 =  152.60481
## 
## 
## MCMCregress iteration 921 of 11000 
## beta = 
##   38.81117
##    0.73244
## sigma2 =  126.77390
## 
## 
## MCMCregress iteration 931 of 11000 
## beta = 
##   37.62781
##    0.91160
## sigma2 =  123.41498
## 
## 
## MCMCregress iteration 941 of 11000 
## beta = 
##   37.83309
##    1.22585
## sigma2 =  129.41708
## 
## 
## MCMCregress iteration 951 of 11000 
## beta = 
##   39.68103
##    0.26496
## sigma2 =  141.74696
## 
## 
## MCMCregress iteration 961 of 11000 
## beta = 
##   39.02745
##    0.37268
## sigma2 =  133.78579
## 
## 
## MCMCregress iteration 971 of 11000 
## beta = 
##   39.64571
##    0.14641
## sigma2 =  129.99150
## 
## 
## MCMCregress iteration 981 of 11000 
## beta = 
##   38.67649
##    0.56418
## sigma2 =  116.54102
## 
## 
## MCMCregress iteration 991 of 11000 
## beta = 
##   39.15344
##    0.52137
## sigma2 =  129.24121
## 
## 
## MCMCregress iteration 1001 of 11000 
## beta = 
##   39.50623
##   -0.22457
## sigma2 =  133.13164
## 
## 
## MCMCregress iteration 1011 of 11000 
## beta = 
##   37.49115
##    0.96900
## sigma2 =  125.03844
## 
## 
## MCMCregress iteration 1021 of 11000 
## beta = 
##   38.48769
##    0.69573
## sigma2 =  131.62856
## 
## 
## MCMCregress iteration 1031 of 11000 
## beta = 
##   38.43881
##    0.48604
## sigma2 =  136.11033
## 
## 
## MCMCregress iteration 1041 of 11000 
## beta = 
##   38.36714
##    0.78372
## sigma2 =  137.45906
## 
## 
## MCMCregress iteration 1051 of 11000 
## beta = 
##   38.30277
##    0.76350
## sigma2 =  125.59302
## 
## 
## MCMCregress iteration 1061 of 11000 
## beta = 
##   36.82119
##    0.96587
## sigma2 =  136.85259
## 
## 
## MCMCregress iteration 1071 of 11000 
## beta = 
##   38.33397
##    0.57302
## sigma2 =  125.96008
## 
## 
## MCMCregress iteration 1081 of 11000 
## beta = 
##   39.58601
##    0.44253
## sigma2 =  131.43219
## 
## 
## MCMCregress iteration 1091 of 11000 
## beta = 
##   37.64593
##    1.53163
## sigma2 =  140.39828
## 
## 
## MCMCregress iteration 1101 of 11000 
## beta = 
##   39.29842
##    0.41848
## sigma2 =  143.89614
## 
## 
## MCMCregress iteration 1111 of 11000 
## beta = 
##   39.11533
##    0.36825
## sigma2 =  128.15188
## 
## 
## MCMCregress iteration 1121 of 11000 
## beta = 
##   39.41513
##    0.08492
## sigma2 =  135.67256
## 
## 
## MCMCregress iteration 1131 of 11000 
## beta = 
##   36.90828
##    1.25245
## sigma2 =  126.96162
## 
## 
## MCMCregress iteration 1141 of 11000 
## beta = 
##   38.34075
##    0.54554
## sigma2 =  142.17433
## 
## 
## MCMCregress iteration 1151 of 11000 
## beta = 
##   37.18912
##    1.04335
## sigma2 =  123.03683
## 
## 
## MCMCregress iteration 1161 of 11000 
## beta = 
##   39.25496
##    0.58902
## sigma2 =  122.19891
## 
## 
## MCMCregress iteration 1171 of 11000 
## beta = 
##   37.87551
##    1.05406
## sigma2 =  137.73188
## 
## 
## MCMCregress iteration 1181 of 11000 
## beta = 
##   38.87686
##    0.80209
## sigma2 =  122.38451
## 
## 
## MCMCregress iteration 1191 of 11000 
## beta = 
##   37.95526
##    0.92923
## sigma2 =  131.86457
## 
## 
## MCMCregress iteration 1201 of 11000 
## beta = 
##   35.99306
##    1.88014
## sigma2 =  142.92453
## 
## 
## MCMCregress iteration 1211 of 11000 
## beta = 
##   37.12370
##    1.02269
## sigma2 =  132.70822
## 
## 
## MCMCregress iteration 1221 of 11000 
## beta = 
##   39.21482
##    0.51930
## sigma2 =  118.59560
## 
## 
## MCMCregress iteration 1231 of 11000 
## beta = 
##   37.41081
##    1.22712
## sigma2 =  122.87236
## 
## 
## MCMCregress iteration 1241 of 11000 
## beta = 
##   37.80150
##    1.02328
## sigma2 =  129.99485
## 
## 
## MCMCregress iteration 1251 of 11000 
## beta = 
##   40.24198
##    0.11857
## sigma2 =  135.61487
## 
## 
## MCMCregress iteration 1261 of 11000 
## beta = 
##   39.07815
##    0.21329
## sigma2 =  129.40673
## 
## 
## MCMCregress iteration 1271 of 11000 
## beta = 
##   40.33634
##   -0.27790
## sigma2 =  135.02237
## 
## 
## MCMCregress iteration 1281 of 11000 
## beta = 
##   37.80626
##    1.03660
## sigma2 =  119.10507
## 
## 
## MCMCregress iteration 1291 of 11000 
## beta = 
##   39.33488
##   -0.07501
## sigma2 =  135.65729
## 
## 
## MCMCregress iteration 1301 of 11000 
## beta = 
##   40.11513
##    0.05110
## sigma2 =  145.10500
## 
## 
## MCMCregress iteration 1311 of 11000 
## beta = 
##   35.46880
##    1.64444
## sigma2 =  123.41603
## 
## 
## MCMCregress iteration 1321 of 11000 
## beta = 
##   37.94134
##    0.82867
## sigma2 =  124.77659
## 
## 
## MCMCregress iteration 1331 of 11000 
## beta = 
##   37.90313
##    0.93942
## sigma2 =  134.25354
## 
## 
## MCMCregress iteration 1341 of 11000 
## beta = 
##   38.21845
##    0.79771
## sigma2 =  137.37548
## 
## 
## MCMCregress iteration 1351 of 11000 
## beta = 
##   39.15306
##    0.28469
## sigma2 =  146.91814
## 
## 
## MCMCregress iteration 1361 of 11000 
## beta = 
##   39.73260
##    0.32274
## sigma2 =  122.16805
## 
## 
## MCMCregress iteration 1371 of 11000 
## beta = 
##   39.89364
##    0.20375
## sigma2 =  127.06388
## 
## 
## MCMCregress iteration 1381 of 11000 
## beta = 
##   38.07182
##    0.84393
## sigma2 =  125.80307
## 
## 
## MCMCregress iteration 1391 of 11000 
## beta = 
##   38.34319
##    0.42309
## sigma2 =  132.62828
## 
## 
## MCMCregress iteration 1401 of 11000 
## beta = 
##   38.77507
##    0.51877
## sigma2 =  132.60558
## 
## 
## MCMCregress iteration 1411 of 11000 
## beta = 
##   38.41159
##    0.64267
## sigma2 =  133.26620
## 
## 
## MCMCregress iteration 1421 of 11000 
## beta = 
##   37.92690
##    0.72095
## sigma2 =  129.10131
## 
## 
## MCMCregress iteration 1431 of 11000 
## beta = 
##   39.24876
##    0.00131
## sigma2 =  127.09465
## 
## 
## MCMCregress iteration 1441 of 11000 
## beta = 
##   37.70569
##    1.05135
## sigma2 =  133.30763
## 
## 
## MCMCregress iteration 1451 of 11000 
## beta = 
##   38.55133
##    0.43922
## sigma2 =  141.73574
## 
## 
## MCMCregress iteration 1461 of 11000 
## beta = 
##   38.74321
##    0.60275
## sigma2 =  120.96288
## 
## 
## MCMCregress iteration 1471 of 11000 
## beta = 
##   39.52580
##   -0.05905
## sigma2 =  131.65821
## 
## 
## MCMCregress iteration 1481 of 11000 
## beta = 
##   38.78894
##    0.54174
## sigma2 =  134.14076
## 
## 
## MCMCregress iteration 1491 of 11000 
## beta = 
##   37.77151
##    0.85696
## sigma2 =  119.35726
## 
## 
## MCMCregress iteration 1501 of 11000 
## beta = 
##   37.81239
##    1.06035
## sigma2 =  123.64710
## 
## 
## MCMCregress iteration 1511 of 11000 
## beta = 
##   41.79296
##   -0.81118
## sigma2 =  130.93304
## 
## 
## MCMCregress iteration 1521 of 11000 
## beta = 
##   38.49496
##    0.55011
## sigma2 =  115.05278
## 
## 
## MCMCregress iteration 1531 of 11000 
## beta = 
##   37.16952
##    0.92577
## sigma2 =  135.92992
## 
## 
## MCMCregress iteration 1541 of 11000 
## beta = 
##   38.96128
##    0.42330
## sigma2 =  123.38644
## 
## 
## MCMCregress iteration 1551 of 11000 
## beta = 
##   39.00225
##    0.63750
## sigma2 =  143.67720
## 
## 
## MCMCregress iteration 1561 of 11000 
## beta = 
##   38.09013
##    0.96675
## sigma2 =  135.22284
## 
## 
## MCMCregress iteration 1571 of 11000 
## beta = 
##   37.91040
##    0.66665
## sigma2 =  129.00351
## 
## 
## MCMCregress iteration 1581 of 11000 
## beta = 
##   38.81695
##    0.52968
## sigma2 =  137.46096
## 
## 
## MCMCregress iteration 1591 of 11000 
## beta = 
##   38.04795
##    0.84959
## sigma2 =  132.43822
## 
## 
## MCMCregress iteration 1601 of 11000 
## beta = 
##   37.85692
##    0.65339
## sigma2 =  132.15723
## 
## 
## MCMCregress iteration 1611 of 11000 
## beta = 
##   37.15486
##    1.42620
## sigma2 =  121.52382
## 
## 
## MCMCregress iteration 1621 of 11000 
## beta = 
##   37.84601
##    0.91423
## sigma2 =  118.21874
## 
## 
## MCMCregress iteration 1631 of 11000 
## beta = 
##   40.77478
##    0.08202
## sigma2 =  140.33167
## 
## 
## MCMCregress iteration 1641 of 11000 
## beta = 
##   39.18061
##    0.57345
## sigma2 =  122.35921
## 
## 
## MCMCregress iteration 1651 of 11000 
## beta = 
##   38.85010
##    0.32723
## sigma2 =  133.92970
## 
## 
## MCMCregress iteration 1661 of 11000 
## beta = 
##   39.70137
##   -0.00475
## sigma2 =  137.33746
## 
## 
## MCMCregress iteration 1671 of 11000 
## beta = 
##   37.36571
##    1.01476
## sigma2 =  134.32605
## 
## 
## MCMCregress iteration 1681 of 11000 
## beta = 
##   36.81313
##    0.95764
## sigma2 =  127.40520
## 
## 
## MCMCregress iteration 1691 of 11000 
## beta = 
##   39.15817
##    0.42848
## sigma2 =  138.75822
## 
## 
## MCMCregress iteration 1701 of 11000 
## beta = 
##   37.76032
##    0.77264
## sigma2 =  120.12268
## 
## 
## MCMCregress iteration 1711 of 11000 
## beta = 
##   37.99743
##    0.56541
## sigma2 =  135.90500
## 
## 
## MCMCregress iteration 1721 of 11000 
## beta = 
##   38.18878
##    0.77517
## sigma2 =  131.86724
## 
## 
## MCMCregress iteration 1731 of 11000 
## beta = 
##   39.71321
##    0.34877
## sigma2 =  117.68795
## 
## 
## MCMCregress iteration 1741 of 11000 
## beta = 
##   37.47380
##    0.73390
## sigma2 =  133.79396
## 
## 
## MCMCregress iteration 1751 of 11000 
## beta = 
##   38.77859
##    0.50288
## sigma2 =  126.65472
## 
## 
## MCMCregress iteration 1761 of 11000 
## beta = 
##   39.03062
##    0.33035
## sigma2 =  140.92389
## 
## 
## MCMCregress iteration 1771 of 11000 
## beta = 
##   38.26516
##    0.81700
## sigma2 =  126.68253
## 
## 
## MCMCregress iteration 1781 of 11000 
## beta = 
##   37.22884
##    1.28701
## sigma2 =  147.28096
## 
## 
## MCMCregress iteration 1791 of 11000 
## beta = 
##   39.05472
##    0.34080
## sigma2 =  132.46123
## 
## 
## MCMCregress iteration 1801 of 11000 
## beta = 
##   39.31119
##    0.20386
## sigma2 =  133.09013
## 
## 
## MCMCregress iteration 1811 of 11000 
## beta = 
##   37.25195
##    1.41919
## sigma2 =  130.46178
## 
## 
## MCMCregress iteration 1821 of 11000 
## beta = 
##   37.21566
##    1.22342
## sigma2 =  126.92582
## 
## 
## MCMCregress iteration 1831 of 11000 
## beta = 
##   39.48053
##    0.41031
## sigma2 =  146.82104
## 
## 
## MCMCregress iteration 1841 of 11000 
## beta = 
##   38.81918
##    0.58162
## sigma2 =  130.47731
## 
## 
## MCMCregress iteration 1851 of 11000 
## beta = 
##   36.58730
##    1.00054
## sigma2 =  131.93643
## 
## 
## MCMCregress iteration 1861 of 11000 
## beta = 
##   38.37008
##    0.89149
## sigma2 =  142.24997
## 
## 
## MCMCregress iteration 1871 of 11000 
## beta = 
##   38.50095
##    0.68459
## sigma2 =  146.82653
## 
## 
## MCMCregress iteration 1881 of 11000 
## beta = 
##   38.31844
##    0.89533
## sigma2 =  122.94543
## 
## 
## MCMCregress iteration 1891 of 11000 
## beta = 
##   38.72889
##    0.78058
## sigma2 =  141.05784
## 
## 
## MCMCregress iteration 1901 of 11000 
## beta = 
##   37.81523
##    0.81678
## sigma2 =  129.01271
## 
## 
## MCMCregress iteration 1911 of 11000 
## beta = 
##   37.58876
##    0.80774
## sigma2 =  123.83752
## 
## 
## MCMCregress iteration 1921 of 11000 
## beta = 
##   39.42157
##    0.36896
## sigma2 =  129.32430
## 
## 
## MCMCregress iteration 1931 of 11000 
## beta = 
##   38.51493
##    0.72860
## sigma2 =  143.67092
## 
## 
## MCMCregress iteration 1941 of 11000 
## beta = 
##   39.49322
##    0.44487
## sigma2 =  124.00525
## 
## 
## MCMCregress iteration 1951 of 11000 
## beta = 
##   37.61075
##    0.67867
## sigma2 =  123.79095
## 
## 
## MCMCregress iteration 1961 of 11000 
## beta = 
##   38.13231
##    0.81309
## sigma2 =  123.98272
## 
## 
## MCMCregress iteration 1971 of 11000 
## beta = 
##   37.74561
##    0.87624
## sigma2 =  131.27354
## 
## 
## MCMCregress iteration 1981 of 11000 
## beta = 
##   40.07345
##    0.03629
## sigma2 =  132.70083
## 
## 
## MCMCregress iteration 1991 of 11000 
## beta = 
##   40.11257
##    0.19567
## sigma2 =  139.36015
## 
## 
## MCMCregress iteration 2001 of 11000 
## beta = 
##   37.60384
##    1.05476
## sigma2 =  141.20417
## 
## 
## MCMCregress iteration 2011 of 11000 
## beta = 
##   39.35994
##    0.55171
## sigma2 =  146.62665
## 
## 
## MCMCregress iteration 2021 of 11000 
## beta = 
##   39.65173
##    0.23835
## sigma2 =  130.94320
## 
## 
## MCMCregress iteration 2031 of 11000 
## beta = 
##   38.31874
##    0.92134
## sigma2 =  136.54383
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## 
## MCMCregress iteration 2041 of 11000 
## beta = 
##   39.10286
##    0.55831
## sigma2 =  145.49820
## 
## 
## MCMCregress iteration 2051 of 11000 
## beta = 
##   36.79581
##    1.00828
## sigma2 =  138.83442
## 
## 
## MCMCregress iteration 2061 of 11000 
## beta = 
##   39.14723
##    0.40900
## sigma2 =  134.21202
## 
## 
## MCMCregress iteration 2071 of 11000 
## beta = 
##   38.66939
##    0.83683
## sigma2 =  146.85167
## 
## 
## MCMCregress iteration 2081 of 11000 
## beta = 
##   38.10940
##    0.96762
## sigma2 =  143.66511
## 
## 
## MCMCregress iteration 2091 of 11000 
## beta = 
##   38.29739
##    0.72068
## sigma2 =  136.89393
## 
## 
## MCMCregress iteration 2101 of 11000 
## beta = 
##   37.04538
##    1.49620
## sigma2 =  154.80561
## 
## 
## MCMCregress iteration 2111 of 11000 
## beta = 
##   38.30096
##    0.80312
## sigma2 =  133.01999
## 
## 
## MCMCregress iteration 2121 of 11000 
## beta = 
##   41.36077
##   -0.67722
## sigma2 =  135.62048
## 
## 
## MCMCregress iteration 2131 of 11000 
## beta = 
##   36.86037
##    1.48916
## sigma2 =  121.11987
## 
## 
## MCMCregress iteration 2141 of 11000 
## beta = 
##   37.89083
##    1.28021
## sigma2 =  134.99865
## 
## 
## MCMCregress iteration 2151 of 11000 
## beta = 
##   38.43011
##    0.86981
## sigma2 =  134.07405
## 
## 
## MCMCregress iteration 2161 of 11000 
## beta = 
##   38.95592
##    0.49439
## sigma2 =  130.41277
## 
## 
## MCMCregress iteration 2171 of 11000 
## beta = 
##   38.45198
##    1.03149
## sigma2 =  131.53542
## 
## 
## MCMCregress iteration 2181 of 11000 
## beta = 
##   38.10693
##    0.89821
## sigma2 =  121.32851
## 
## 
## MCMCregress iteration 2191 of 11000 
## beta = 
##   38.01985
##    0.86253
## sigma2 =  139.29581
## 
## 
## MCMCregress iteration 2201 of 11000 
## beta = 
##   37.90996
##    0.77296
## sigma2 =  136.82314
## 
## 
## MCMCregress iteration 2211 of 11000 
## beta = 
##   38.75925
##    0.59659
## sigma2 =  124.38679
## 
## 
## MCMCregress iteration 2221 of 11000 
## beta = 
##   37.83500
##    1.02317
## sigma2 =  125.49062
## 
## 
## MCMCregress iteration 2231 of 11000 
## beta = 
##   37.12943
##    1.27492
## sigma2 =  122.77898
## 
## 
## MCMCregress iteration 2241 of 11000 
## beta = 
##   39.02967
##    0.52465
## sigma2 =  133.41075
## 
## 
## MCMCregress iteration 2251 of 11000 
## beta = 
##   39.06321
##    0.92943
## sigma2 =  134.64734
## 
## 
## MCMCregress iteration 2261 of 11000 
## beta = 
##   39.21901
##    0.32174
## sigma2 =  137.75997
## 
## 
## MCMCregress iteration 2271 of 11000 
## beta = 
##   38.64254
##    0.58937
## sigma2 =  127.01297
## 
## 
## MCMCregress iteration 2281 of 11000 
## beta = 
##   38.39761
##    0.75218
## sigma2 =  133.20148
## 
## 
## MCMCregress iteration 2291 of 11000 
## beta = 
##   39.36769
##    0.76692
## sigma2 =  146.65696
## 
## 
## MCMCregress iteration 2301 of 11000 
## beta = 
##   39.65500
##    0.33333
## sigma2 =  148.38847
## 
## 
## MCMCregress iteration 2311 of 11000 
## beta = 
##   39.36287
##    0.22234
## sigma2 =  135.71541
## 
## 
## MCMCregress iteration 2321 of 11000 
## beta = 
##   37.16332
##    1.03861
## sigma2 =  114.69326
## 
## 
## MCMCregress iteration 2331 of 11000 
## beta = 
##   36.87338
##    1.11257
## sigma2 =  139.38591
## 
## 
## MCMCregress iteration 2341 of 11000 
## beta = 
##   39.34741
##    0.10853
## sigma2 =  140.95608
## 
## 
## MCMCregress iteration 2351 of 11000 
## beta = 
##   38.80726
##    0.61491
## sigma2 =  153.87810
## 
## 
## MCMCregress iteration 2361 of 11000 
## beta = 
##   38.18175
##    0.68120
## sigma2 =  129.58959
## 
## 
## MCMCregress iteration 2371 of 11000 
## beta = 
##   39.40714
##    0.34715
## sigma2 =  140.06999
## 
## 
## MCMCregress iteration 2381 of 11000 
## beta = 
##   40.75209
##    0.06478
## sigma2 =  140.52713
## 
## 
## MCMCregress iteration 2391 of 11000 
## beta = 
##   38.52391
##    0.80919
## sigma2 =  121.96867
## 
## 
## MCMCregress iteration 2401 of 11000 
## beta = 
##   38.05394
##    0.62799
## sigma2 =  128.86422
## 
## 
## MCMCregress iteration 2411 of 11000 
## beta = 
##   38.81457
##    0.57989
## sigma2 =  153.80114
## 
## 
## MCMCregress iteration 2421 of 11000 
## beta = 
##   37.82580
##    0.90595
## sigma2 =  148.91471
## 
## 
## MCMCregress iteration 2431 of 11000 
## beta = 
##   37.84372
##    1.05529
## sigma2 =  128.69915
## 
## 
## MCMCregress iteration 2441 of 11000 
## beta = 
##   38.77773
##    0.45067
## sigma2 =  112.88032
## 
## 
## MCMCregress iteration 2451 of 11000 
## beta = 
##   40.30035
##   -0.13301
## sigma2 =  136.90765
## 
## 
## MCMCregress iteration 2461 of 11000 
## beta = 
##   39.13895
##    0.25787
## sigma2 =  134.40133
## 
## 
## MCMCregress iteration 2471 of 11000 
## beta = 
##   37.57564
##    1.18641
## sigma2 =  148.35909
## 
## 
## MCMCregress iteration 2481 of 11000 
## beta = 
##   40.88239
##    0.01057
## sigma2 =  140.73062
## 
## 
## MCMCregress iteration 2491 of 11000 
## beta = 
##   39.08188
##   -0.08675
## sigma2 =  134.23536
## 
## 
## MCMCregress iteration 2501 of 11000 
## beta = 
##   39.65186
##    0.65728
## sigma2 =  143.94436
## 
## 
## MCMCregress iteration 2511 of 11000 
## beta = 
##   39.10545
##    0.58275
## sigma2 =  129.82355
## 
## 
## MCMCregress iteration 2521 of 11000 
## beta = 
##   39.50510
##    0.52435
## sigma2 =  137.79940
## 
## 
## MCMCregress iteration 2531 of 11000 
## beta = 
##   37.44608
##    1.26268
## sigma2 =  135.86642
## 
## 
## MCMCregress iteration 2541 of 11000 
## beta = 
##   38.82072
##    0.51082
## sigma2 =  131.62028
## 
## 
## MCMCregress iteration 2551 of 11000 
## beta = 
##   37.23786
##    1.07220
## sigma2 =  127.12560
## 
## 
## MCMCregress iteration 2561 of 11000 
## beta = 
##   38.42179
##    0.84531
## sigma2 =  140.51165
## 
## 
## MCMCregress iteration 2571 of 11000 
## beta = 
##   37.91588
##    0.88837
## sigma2 =  131.18586
## 
## 
## MCMCregress iteration 2581 of 11000 
## beta = 
##   39.96491
##    0.14552
## sigma2 =  136.18621
## 
## 
## MCMCregress iteration 2591 of 11000 
## beta = 
##   37.62852
##    0.94003
## sigma2 =  137.64566
## 
## 
## MCMCregress iteration 2601 of 11000 
## beta = 
##   37.29939
##    1.00279
## sigma2 =  130.62010
## 
## 
## MCMCregress iteration 2611 of 11000 
## beta = 
##   38.97842
##    0.71021
## sigma2 =  133.76386
## 
## 
## MCMCregress iteration 2621 of 11000 
## beta = 
##   38.40059
##    0.79792
## sigma2 =  137.88396
## 
## 
## MCMCregress iteration 2631 of 11000 
## beta = 
##   38.26668
##    0.42965
## sigma2 =  129.81774
## 
## 
## MCMCregress iteration 2641 of 11000 
## beta = 
##   38.56139
##    0.48048
## sigma2 =  128.87570
## 
## 
## MCMCregress iteration 2651 of 11000 
## beta = 
##   38.82174
##    0.10898
## sigma2 =  122.56096
## 
## 
## MCMCregress iteration 2661 of 11000 
## beta = 
##   39.25735
##    0.81574
## sigma2 =  136.39687
## 
## 
## MCMCregress iteration 2671 of 11000 
## beta = 
##   39.71256
##    0.41829
## sigma2 =  126.27557
## 
## 
## MCMCregress iteration 2681 of 11000 
## beta = 
##   39.55764
##    0.46328
## sigma2 =  146.05961
## 
## 
## MCMCregress iteration 2691 of 11000 
## beta = 
##   40.20223
##   -0.13049
## sigma2 =  143.11932
## 
## 
## MCMCregress iteration 2701 of 11000 
## beta = 
##   38.96805
##    0.49905
## sigma2 =  123.63305
## 
## 
## MCMCregress iteration 2711 of 11000 
## beta = 
##   39.34745
##    0.20866
## sigma2 =  144.47167
## 
## 
## MCMCregress iteration 2721 of 11000 
## beta = 
##   37.39656
##    1.10014
## sigma2 =  132.51045
## 
## 
## MCMCregress iteration 2731 of 11000 
## beta = 
##   38.61295
##    0.43421
## sigma2 =  145.22632
## 
## 
## MCMCregress iteration 2741 of 11000 
## beta = 
##   36.11595
##    1.49858
## sigma2 =  131.52878
## 
## 
## MCMCregress iteration 2751 of 11000 
## beta = 
##   39.49294
##    0.42986
## sigma2 =  138.06493
## 
## 
## MCMCregress iteration 2761 of 11000 
## beta = 
##   38.54898
##    0.79159
## sigma2 =  137.64147
## 
## 
## MCMCregress iteration 2771 of 11000 
## beta = 
##   39.82360
##    0.09414
## sigma2 =  128.31118
## 
## 
## MCMCregress iteration 2781 of 11000 
## beta = 
##   38.84347
##    0.53783
## sigma2 =  137.80193
## 
## 
## MCMCregress iteration 2791 of 11000 
## beta = 
##   38.73256
##    0.52681
## sigma2 =  124.72445
## 
## 
## MCMCregress iteration 2801 of 11000 
## beta = 
##   39.12888
##    0.54311
## sigma2 =  133.74091
## 
## 
## MCMCregress iteration 2811 of 11000 
## beta = 
##   38.41611
##    0.91468
## sigma2 =  133.80988
## 
## 
## MCMCregress iteration 2821 of 11000 
## beta = 
##   38.01369
##    0.59280
## sigma2 =  140.81525
## 
## 
## MCMCregress iteration 2831 of 11000 
## beta = 
##   36.83263
##    1.48052
## sigma2 =  130.70297
## 
## 
## MCMCregress iteration 2841 of 11000 
## beta = 
##   38.99309
##    0.60359
## sigma2 =  127.13253
## 
## 
## MCMCregress iteration 2851 of 11000 
## beta = 
##   36.86782
##    1.10244
## sigma2 =  134.47538
## 
## 
## MCMCregress iteration 2861 of 11000 
## beta = 
##   38.42494
##    0.78161
## sigma2 =  123.06630
## 
## 
## MCMCregress iteration 2871 of 11000 
## beta = 
##   39.58557
##    0.62119
## sigma2 =  133.46761
## 
## 
## MCMCregress iteration 2881 of 11000 
## beta = 
##   40.37444
##   -0.05062
## sigma2 =  138.57658
## 
## 
## MCMCregress iteration 2891 of 11000 
## beta = 
##   37.74441
##    0.71383
## sigma2 =  132.03627
## 
## 
## MCMCregress iteration 2901 of 11000 
## beta = 
##   37.41777
##    0.92167
## sigma2 =  140.10368
## 
## 
## MCMCregress iteration 2911 of 11000 
## beta = 
##   37.74871
##    1.01844
## sigma2 =  127.35026
## 
## 
## MCMCregress iteration 2921 of 11000 
## beta = 
##   38.43063
##    0.86981
## sigma2 =  146.49347
## 
## 
## MCMCregress iteration 2931 of 11000 
## beta = 
##   37.57384
##    0.88137
## sigma2 =  126.90943
## 
## 
## MCMCregress iteration 2941 of 11000 
## beta = 
##   37.36226
##    1.26610
## sigma2 =  127.84477
## 
## 
## MCMCregress iteration 2951 of 11000 
## beta = 
##   37.91540
##    0.64457
## sigma2 =  142.71192
## 
## 
## MCMCregress iteration 2961 of 11000 
## beta = 
##   38.06125
##    0.79889
## sigma2 =  138.61806
## 
## 
## MCMCregress iteration 2971 of 11000 
## beta = 
##   39.69989
##   -0.14277
## sigma2 =  130.40348
## 
## 
## MCMCregress iteration 2981 of 11000 
## beta = 
##   37.92425
##    0.69028
## sigma2 =  144.90924
## 
## 
## MCMCregress iteration 2991 of 11000 
## beta = 
##   39.73304
##   -0.14674
## sigma2 =  142.19990
## 
## 
## MCMCregress iteration 3001 of 11000 
## beta = 
##   37.18171
##    0.99984
## sigma2 =  133.32028
## 
## 
## MCMCregress iteration 3011 of 11000 
## beta = 
##   37.01096
##    1.26768
## sigma2 =  148.71071
## 
## 
## MCMCregress iteration 3021 of 11000 
## beta = 
##   38.23809
##    0.53269
## sigma2 =  132.80897
## 
## 
## MCMCregress iteration 3031 of 11000 
## beta = 
##   39.01099
##    0.33315
## sigma2 =  146.12386
## 
## 
## MCMCregress iteration 3041 of 11000 
## beta = 
##   38.99931
##    0.70230
## sigma2 =  149.06655
## 
## 
## MCMCregress iteration 3051 of 11000 
## beta = 
##   38.60359
##    0.58530
## sigma2 =  133.01013
## 
## 
## MCMCregress iteration 3061 of 11000 
## beta = 
##   36.65826
##    1.34227
## sigma2 =  135.99528
## 
## 
## MCMCregress iteration 3071 of 11000 
## beta = 
##   36.12365
##    1.00761
## sigma2 =  149.60224
## 
## 
## MCMCregress iteration 3081 of 11000 
## beta = 
##   38.87592
##    0.74419
## sigma2 =  138.28555
## 
## 
## MCMCregress iteration 3091 of 11000 
## beta = 
##   39.39197
##   -0.03245
## sigma2 =  133.64590
## 
## 
## MCMCregress iteration 3101 of 11000 
## beta = 
##   39.26984
##    0.14354
## sigma2 =  129.15921
## 
## 
## MCMCregress iteration 3111 of 11000 
## beta = 
##   40.60388
##   -0.31683
## sigma2 =  134.69071
## 
## 
## MCMCregress iteration 3121 of 11000 
## beta = 
##   38.07693
##    0.56210
## sigma2 =  143.29141
## 
## 
## MCMCregress iteration 3131 of 11000 
## beta = 
##   38.78759
##    0.54675
## sigma2 =  122.27705
## 
## 
## MCMCregress iteration 3141 of 11000 
## beta = 
##   39.96436
##    0.11468
## sigma2 =  145.50374
## 
## 
## MCMCregress iteration 3151 of 11000 
## beta = 
##   39.61048
##    0.09093
## sigma2 =  138.45694
## 
## 
## MCMCregress iteration 3161 of 11000 
## beta = 
##   38.70723
##    0.50113
## sigma2 =  131.38515
## 
## 
## MCMCregress iteration 3171 of 11000 
## beta = 
##   38.21902
##    0.47184
## sigma2 =  133.11060
## 
## 
## MCMCregress iteration 3181 of 11000 
## beta = 
##   39.05681
##    0.58960
## sigma2 =  124.49051
## 
## 
## MCMCregress iteration 3191 of 11000 
## beta = 
##   38.79648
##    0.65964
## sigma2 =  126.17682
## 
## 
## MCMCregress iteration 3201 of 11000 
## beta = 
##   40.68633
##   -0.07113
## sigma2 =  151.61139
## 
## 
## MCMCregress iteration 3211 of 11000 
## beta = 
##   37.96304
##    0.80050
## sigma2 =  128.99904
## 
## 
## MCMCregress iteration 3221 of 11000 
## beta = 
##   37.88679
##    1.19618
## sigma2 =  128.03303
## 
## 
## MCMCregress iteration 3231 of 11000 
## beta = 
##   38.04095
##    0.94553
## sigma2 =  125.31542
## 
## 
## MCMCregress iteration 3241 of 11000 
## beta = 
##   36.11943
##    1.55083
## sigma2 =  129.30185
## 
## 
## MCMCregress iteration 3251 of 11000 
## beta = 
##   40.55439
##    0.32917
## sigma2 =  126.51475
## 
## 
## MCMCregress iteration 3261 of 11000 
## beta = 
##   38.19320
##    0.62753
## sigma2 =  122.48889
## 
## 
## MCMCregress iteration 3271 of 11000 
## beta = 
##   39.41650
##    0.23797
## sigma2 =  125.19070
## 
## 
## MCMCregress iteration 3281 of 11000 
## beta = 
##   39.27323
##    0.69792
## sigma2 =  126.83005
## 
## 
## MCMCregress iteration 3291 of 11000 
## beta = 
##   39.86167
##    0.53187
## sigma2 =  135.29611
## 
## 
## MCMCregress iteration 3301 of 11000 
## beta = 
##   39.15611
##    0.56286
## sigma2 =  130.67370
## 
## 
## MCMCregress iteration 3311 of 11000 
## beta = 
##   39.87544
##    0.56383
## sigma2 =  131.11324
## 
## 
## MCMCregress iteration 3321 of 11000 
## beta = 
##   36.97229
##    1.29377
## sigma2 =  146.39390
## 
## 
## MCMCregress iteration 3331 of 11000 
## beta = 
##   38.67895
##    0.46127
## sigma2 =  118.52748
## 
## 
## MCMCregress iteration 3341 of 11000 
## beta = 
##   37.68720
##    0.91919
## sigma2 =  124.12543
## 
## 
## MCMCregress iteration 3351 of 11000 
## beta = 
##   36.90616
##    1.29624
## sigma2 =  139.79918
## 
## 
## MCMCregress iteration 3361 of 11000 
## beta = 
##   38.50391
##    0.70183
## sigma2 =  125.01181
## 
## 
## MCMCregress iteration 3371 of 11000 
## beta = 
##   38.99835
##    0.20028
## sigma2 =  138.56839
## 
## 
## MCMCregress iteration 3381 of 11000 
## beta = 
##   37.75987
##    0.81430
## sigma2 =  132.76973
## 
## 
## MCMCregress iteration 3391 of 11000 
## beta = 
##   36.98803
##    1.42473
## sigma2 =  129.61107
## 
## 
## MCMCregress iteration 3401 of 11000 
## beta = 
##   40.98736
##   -0.41534
## sigma2 =  143.82446
## 
## 
## MCMCregress iteration 3411 of 11000 
## beta = 
##   38.52121
##    0.87611
## sigma2 =  139.81692
## 
## 
## MCMCregress iteration 3421 of 11000 
## beta = 
##   36.95282
##    1.04386
## sigma2 =  123.92754
## 
## 
## MCMCregress iteration 3431 of 11000 
## beta = 
##   38.89571
##    0.34877
## sigma2 =  131.21897
## 
## 
## MCMCregress iteration 3441 of 11000 
## beta = 
##   37.48882
##    1.04497
## sigma2 =  130.12543
## 
## 
## MCMCregress iteration 3451 of 11000 
## beta = 
##   40.08730
##    0.05668
## sigma2 =  136.34429
## 
## 
## MCMCregress iteration 3461 of 11000 
## beta = 
##   38.73902
##    0.35136
## sigma2 =  126.36164
## 
## 
## MCMCregress iteration 3471 of 11000 
## beta = 
##   39.90786
##    0.21789
## sigma2 =  134.68700
## 
## 
## MCMCregress iteration 3481 of 11000 
## beta = 
##   40.10501
##   -0.06199
## sigma2 =  130.78007
## 
## 
## MCMCregress iteration 3491 of 11000 
## beta = 
##   38.43903
##    0.62856
## sigma2 =  129.01675
## 
## 
## MCMCregress iteration 3501 of 11000 
## beta = 
##   39.41884
##    0.76040
## sigma2 =  136.40219
## 
## 
## MCMCregress iteration 3511 of 11000 
## beta = 
##   35.81645
##    2.13901
## sigma2 =  140.53644
## 
## 
## MCMCregress iteration 3521 of 11000 
## beta = 
##   38.24694
##    1.05554
## sigma2 =  139.88649
## 
## 
## MCMCregress iteration 3531 of 11000 
## beta = 
##   38.73115
##    0.29997
## sigma2 =  148.21601
## 
## 
## MCMCregress iteration 3541 of 11000 
## beta = 
##   39.90109
##    0.29441
## sigma2 =  126.90389
## 
## 
## MCMCregress iteration 3551 of 11000 
## beta = 
##   39.19016
##    0.71326
## sigma2 =  133.38471
## 
## 
## MCMCregress iteration 3561 of 11000 
## beta = 
##   38.95972
##    0.42478
## sigma2 =  128.37324
## 
## 
## MCMCregress iteration 3571 of 11000 
## beta = 
##   37.86511
##    0.72899
## sigma2 =  141.98186
## 
## 
## MCMCregress iteration 3581 of 11000 
## beta = 
##   39.67866
##    0.36131
## sigma2 =  130.73509
## 
## 
## MCMCregress iteration 3591 of 11000 
## beta = 
##   39.21555
##    0.54524
## sigma2 =  129.86921
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## MCMCregress iteration 3601 of 11000 
## beta = 
##   39.43516
##    0.41425
## sigma2 =  128.67233
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## MCMCregress iteration 3611 of 11000 
## beta = 
##   38.63430
##    0.80252
## sigma2 =  130.04777
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## MCMCregress iteration 3621 of 11000 
## beta = 
##   36.23457
##    1.05777
## sigma2 =  137.84980
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## MCMCregress iteration 3631 of 11000 
## beta = 
##   37.42383
##    1.00452
## sigma2 =  132.20509
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## MCMCregress iteration 3641 of 11000 
## beta = 
##   39.00714
##    0.52465
## sigma2 =  126.17905
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## MCMCregress iteration 3651 of 11000 
## beta = 
##   37.39352
##    0.90454
## sigma2 =  136.89923
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## MCMCregress iteration 3661 of 11000 
## beta = 
##   39.44694
##    0.16697
## sigma2 =  127.44900
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## MCMCregress iteration 3671 of 11000 
## beta = 
##   37.70466
##    0.82732
## sigma2 =  149.90892
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## MCMCregress iteration 3681 of 11000 
## beta = 
##   39.51307
##    0.59096
## sigma2 =  140.94350
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## MCMCregress iteration 3691 of 11000 
## beta = 
##   39.25296
##    0.34615
## sigma2 =  122.67656
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## MCMCregress iteration 3701 of 11000 
## beta = 
##   38.61424
##    0.78644
## sigma2 =  129.36622
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## MCMCregress iteration 3711 of 11000 
## beta = 
##   38.16168
##    0.97834
## sigma2 =  140.94639
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## MCMCregress iteration 3721 of 11000 
## beta = 
##   38.03043
##    0.88887
## sigma2 =  141.70791
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## MCMCregress iteration 3731 of 11000 
## beta = 
##   38.95013
##    0.18638
## sigma2 =  142.06035
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## MCMCregress iteration 3741 of 11000 
## beta = 
##   37.33539
##    1.36753
## sigma2 =  126.62758
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## MCMCregress iteration 3751 of 11000 
## beta = 
##   37.55213
##    0.88756
## sigma2 =  148.25167
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## MCMCregress iteration 3761 of 11000 
## beta = 
##   39.03354
##    0.76874
## sigma2 =  124.71996
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## MCMCregress iteration 3771 of 11000 
## beta = 
##   39.46550
##    0.69541
## sigma2 =  142.53356
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## MCMCregress iteration 3781 of 11000 
## beta = 
##   36.07524
##    1.52310
## sigma2 =  132.89026
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## MCMCregress iteration 3791 of 11000 
## beta = 
##   40.48108
##    0.26157
## sigma2 =  137.93048
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## MCMCregress iteration 3801 of 11000 
## beta = 
##   37.91919
##    0.69509
## sigma2 =  136.93480
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## MCMCregress iteration 3811 of 11000 
## beta = 
##   36.80500
##    1.18739
## sigma2 =  131.95745
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## MCMCregress iteration 3821 of 11000 
## beta = 
##   39.14611
##    0.51143
## sigma2 =  117.64715
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## MCMCregress iteration 3831 of 11000 
## beta = 
##   41.05681
##   -0.13067
## sigma2 =  117.68831
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## MCMCregress iteration 3841 of 11000 
## beta = 
##   39.02680
##    0.56273
## sigma2 =  128.01279
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## MCMCregress iteration 3851 of 11000 
## beta = 
##   37.72240
##    0.55787
## sigma2 =  125.17343
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## MCMCregress iteration 3861 of 11000 
## beta = 
##   40.30188
##   -0.14120
## sigma2 =  136.48525
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## MCMCregress iteration 3871 of 11000 
## beta = 
##   37.24281
##    1.19237
## sigma2 =  138.27359
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## MCMCregress iteration 3881 of 11000 
## beta = 
##   40.33941
##    0.05757
## sigma2 =  121.57483
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## MCMCregress iteration 3891 of 11000 
## beta = 
##   40.81947
##   -0.14108
## sigma2 =  129.84243
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## MCMCregress iteration 3901 of 11000 
## beta = 
##   38.48439
##    0.49018
## sigma2 =  147.19211
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## MCMCregress iteration 3911 of 11000 
## beta = 
##   37.86495
##    0.91546
## sigma2 =  132.73351
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## MCMCregress iteration 3921 of 11000 
## beta = 
##   41.05127
##   -0.25116
## sigma2 =  135.52443
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## MCMCregress iteration 3931 of 11000 
## beta = 
##   38.78209
##    0.57852
## sigma2 =  138.38601
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## MCMCregress iteration 3941 of 11000 
## beta = 
##   39.63219
##    0.12521
## sigma2 =  120.28876
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## MCMCregress iteration 3951 of 11000 
## beta = 
##   41.31752
##   -0.16121
## sigma2 =  140.54827
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## MCMCregress iteration 3961 of 11000 
## beta = 
##   38.74514
##    0.65196
## sigma2 =  132.52192
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## MCMCregress iteration 3971 of 11000 
## beta = 
##   37.95885
##    1.05900
## sigma2 =  138.30168
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## MCMCregress iteration 3981 of 11000 
## beta = 
##   40.21692
##   -0.27555
## sigma2 =  128.90689
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## MCMCregress iteration 3991 of 11000 
## beta = 
##   38.11100
##    0.64891
## sigma2 =  134.80383
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## MCMCregress iteration 4001 of 11000 
## beta = 
##   39.60998
##    0.46928
## sigma2 =  133.66264
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## MCMCregress iteration 4011 of 11000 
## beta = 
##   39.72036
##    0.36632
## sigma2 =  137.15031
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## MCMCregress iteration 4021 of 11000 
## beta = 
##   38.53684
##    0.41400
## sigma2 =  120.47248
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## MCMCregress iteration 4031 of 11000 
## beta = 
##   37.95884
##    0.72706
## sigma2 =  128.28045
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## MCMCregress iteration 4041 of 11000 
## beta = 
##   38.13061
##    0.94040
## sigma2 =  115.51323
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## MCMCregress iteration 4051 of 11000 
## beta = 
##   38.11594
##    1.34195
## sigma2 =  144.93121
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## MCMCregress iteration 4061 of 11000 
## beta = 
##   38.84455
##    0.61657
## sigma2 =  143.90157
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## MCMCregress iteration 4071 of 11000 
## beta = 
##   39.60390
##    0.21928
## sigma2 =  128.00365
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## MCMCregress iteration 4081 of 11000 
## beta = 
##   37.17444
##    0.92712
## sigma2 =  122.21342
## 
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## MCMCregress iteration 4091 of 11000 
## beta = 
##   37.06821
##    1.12956
## sigma2 =  133.26787
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## MCMCregress iteration 4101 of 11000 
## beta = 
##   37.98621
##    0.77136
## sigma2 =  140.57772
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## MCMCregress iteration 4111 of 11000 
## beta = 
##   39.73024
##    0.53111
## sigma2 =  135.58767
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## MCMCregress iteration 4121 of 11000 
## beta = 
##   38.46250
##    0.74863
## sigma2 =  129.58167
## 
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## MCMCregress iteration 4131 of 11000 
## beta = 
##   37.40115
##    0.88411
## sigma2 =  136.68546
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## MCMCregress iteration 4141 of 11000 
## beta = 
##   35.98756
##    1.84773
## sigma2 =  125.64610
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## MCMCregress iteration 4151 of 11000 
## beta = 
##   39.82625
##    0.07781
## sigma2 =  128.98832
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## MCMCregress iteration 4161 of 11000 
## beta = 
##   37.15084
##    0.85020
## sigma2 =  129.97317
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## MCMCregress iteration 4171 of 11000 
## beta = 
##   40.59384
##    0.08054
## sigma2 =  120.19516
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## MCMCregress iteration 4181 of 11000 
## beta = 
##   38.68456
##    0.86066
## sigma2 =  142.74854
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## MCMCregress iteration 4191 of 11000 
## beta = 
##   39.65302
##    0.17949
## sigma2 =  132.10675
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## MCMCregress iteration 4201 of 11000 
## beta = 
##   39.18183
##    0.43343
## sigma2 =  129.08924
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## MCMCregress iteration 4211 of 11000 
## beta = 
##   39.24560
##    0.17749
## sigma2 =  127.69987
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## MCMCregress iteration 4221 of 11000 
## beta = 
##   40.43877
##    0.44220
## sigma2 =  129.85173
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## MCMCregress iteration 4231 of 11000 
## beta = 
##   40.22599
##   -0.25011
## sigma2 =  133.44466
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## MCMCregress iteration 4241 of 11000 
## beta = 
##   39.82612
##    0.10656
## sigma2 =  146.24587
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## MCMCregress iteration 4251 of 11000 
## beta = 
##   38.56085
##    0.43069
## sigma2 =  141.02686
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## MCMCregress iteration 4261 of 11000 
## beta = 
##   38.24101
##    0.69078
## sigma2 =  133.08792
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## MCMCregress iteration 4271 of 11000 
## beta = 
##   38.04817
##    0.68286
## sigma2 =  131.42212
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## MCMCregress iteration 4281 of 11000 
## beta = 
##   37.82141
##    0.86530
## sigma2 =  134.14765
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## MCMCregress iteration 4291 of 11000 
## beta = 
##   38.12040
##    0.91829
## sigma2 =  126.91875
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## MCMCregress iteration 4301 of 11000 
## beta = 
##   39.53724
##    0.49181
## sigma2 =  126.60792
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## MCMCregress iteration 4311 of 11000 
## beta = 
##   39.59863
##    0.47986
## sigma2 =  140.00470
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## MCMCregress iteration 4321 of 11000 
## beta = 
##   40.26096
##    0.17693
## sigma2 =  141.04616
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## MCMCregress iteration 4331 of 11000 
## beta = 
##   38.06922
##    0.67359
## sigma2 =  123.60866
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## MCMCregress iteration 4341 of 11000 
## beta = 
##   40.12032
##    0.16193
## sigma2 =  122.82774
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## MCMCregress iteration 4351 of 11000 
## beta = 
##   39.23726
##    0.35551
## sigma2 =  116.57000
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## MCMCregress iteration 4361 of 11000 
## beta = 
##   39.97549
##   -0.06564
## sigma2 =  127.36280
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## MCMCregress iteration 4371 of 11000 
## beta = 
##   38.17580
##    0.74090
## sigma2 =  134.32938
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## MCMCregress iteration 4381 of 11000 
## beta = 
##   36.57519
##    1.19317
## sigma2 =  128.40988
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## MCMCregress iteration 4391 of 11000 
## beta = 
##   36.79496
##    1.33668
## sigma2 =  128.47451
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## MCMCregress iteration 4401 of 11000 
## beta = 
##   39.52158
##    0.56790
## sigma2 =  130.14511
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## MCMCregress iteration 4411 of 11000 
## beta = 
##   38.96150
##    0.66770
## sigma2 =  140.93311
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## MCMCregress iteration 4421 of 11000 
## beta = 
##   38.75175
##    0.77359
## sigma2 =  137.02506
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## MCMCregress iteration 4431 of 11000 
## beta = 
##   38.06572
##    0.93776
## sigma2 =  140.76862
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## MCMCregress iteration 4441 of 11000 
## beta = 
##   40.08045
##    0.06319
## sigma2 =  127.11306
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## MCMCregress iteration 4451 of 11000 
## beta = 
##   38.42267
##    0.72981
## sigma2 =  141.10365
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## MCMCregress iteration 4461 of 11000 
## beta = 
##   37.64529
##    0.91510
## sigma2 =  135.24574
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## MCMCregress iteration 4471 of 11000 
## beta = 
##   37.55676
##    1.14977
## sigma2 =  142.22506
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## MCMCregress iteration 4481 of 11000 
## beta = 
##   38.52371
##    0.49500
## sigma2 =  130.17305
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## MCMCregress iteration 4491 of 11000 
## beta = 
##   37.56870
##    1.05464
## sigma2 =  116.73998
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## MCMCregress iteration 4501 of 11000 
## beta = 
##   37.89599
##    0.74026
## sigma2 =  137.75408
## 
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## MCMCregress iteration 4511 of 11000 
## beta = 
##   40.83430
##   -0.21695
## sigma2 =  133.81206
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## MCMCregress iteration 4521 of 11000 
## beta = 
##   40.53326
##    0.23553
## sigma2 =  130.73950
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## MCMCregress iteration 4531 of 11000 
## beta = 
##   37.74264
##    1.29418
## sigma2 =  123.12199
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## MCMCregress iteration 4541 of 11000 
## beta = 
##   39.55411
##    0.45254
## sigma2 =  131.52763
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## MCMCregress iteration 4551 of 11000 
## beta = 
##   39.82683
##    0.49005
## sigma2 =  134.31328
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## MCMCregress iteration 4561 of 11000 
## beta = 
##   37.27426
##    1.11856
## sigma2 =  136.33586
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## MCMCregress iteration 4571 of 11000 
## beta = 
##   40.07673
##    0.09193
## sigma2 =  138.27552
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## MCMCregress iteration 4581 of 11000 
## beta = 
##   38.65941
##    0.83964
## sigma2 =  127.87058
## 
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## MCMCregress iteration 4591 of 11000 
## beta = 
##   39.03411
##    0.68856
## sigma2 =  112.79364
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## MCMCregress iteration 4601 of 11000 
## beta = 
##   39.62804
##    0.54436
## sigma2 =  132.39824
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## MCMCregress iteration 4611 of 11000 
## beta = 
##   39.39363
##   -0.12825
## sigma2 =  125.22059
## 
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## MCMCregress iteration 4621 of 11000 
## beta = 
##   37.93723
##    0.82585
## sigma2 =  131.77431
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## MCMCregress iteration 4631 of 11000 
## beta = 
##   38.20107
##    0.44048
## sigma2 =  135.07914
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## MCMCregress iteration 4641 of 11000 
## beta = 
##   39.61578
##    0.18011
## sigma2 =  125.43391
## 
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## MCMCregress iteration 4651 of 11000 
## beta = 
##   39.12624
##    0.39327
## sigma2 =  124.42105
## 
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## MCMCregress iteration 4661 of 11000 
## beta = 
##   39.12070
##    0.45610
## sigma2 =  128.41404
## 
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## MCMCregress iteration 4671 of 11000 
## beta = 
##   38.57816
##    0.81776
## sigma2 =  128.86319
## 
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## MCMCregress iteration 4681 of 11000 
## beta = 
##   41.45622
##   -0.28947
## sigma2 =  120.09371
## 
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## MCMCregress iteration 4691 of 11000 
## beta = 
##   39.34863
##    0.31169
## sigma2 =  139.39648
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## MCMCregress iteration 4701 of 11000 
## beta = 
##   36.37592
##    0.98063
## sigma2 =  123.74137
## 
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## MCMCregress iteration 4711 of 11000 
## beta = 
##   39.03384
##    0.66038
## sigma2 =  138.21303
## 
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## MCMCregress iteration 4721 of 11000 
## beta = 
##   36.78347
##    1.33788
## sigma2 =  133.83970
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## MCMCregress iteration 4731 of 11000 
## beta = 
##   38.80760
##    0.34745
## sigma2 =  132.16122
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## MCMCregress iteration 4741 of 11000 
## beta = 
##   39.46641
##    0.44882
## sigma2 =  123.47798
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## MCMCregress iteration 4751 of 11000 
## beta = 
##   37.42375
##    1.13584
## sigma2 =  131.50197
## 
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## MCMCregress iteration 4761 of 11000 
## beta = 
##   38.34588
##    0.07145
## sigma2 =  119.12901
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## MCMCregress iteration 4771 of 11000 
## beta = 
##   38.03218
##    1.02975
## sigma2 =  136.06011
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## MCMCregress iteration 4781 of 11000 
## beta = 
##   37.57668
##    0.79923
## sigma2 =  129.32952
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## MCMCregress iteration 4791 of 11000 
## beta = 
##   39.20991
##    0.42114
## sigma2 =  138.29831
## 
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## MCMCregress iteration 4801 of 11000 
## beta = 
##   38.88346
##    0.37481
## sigma2 =  136.67030
## 
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## MCMCregress iteration 4811 of 11000 
## beta = 
##   37.54705
##    1.00561
## sigma2 =  118.82509
## 
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## MCMCregress iteration 4821 of 11000 
## beta = 
##   36.97022
##    1.02441
## sigma2 =  131.03873
## 
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## MCMCregress iteration 4831 of 11000 
## beta = 
##   38.85595
##    0.94794
## sigma2 =  141.65914
## 
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## MCMCregress iteration 4841 of 11000 
## beta = 
##   39.41698
##    0.17311
## sigma2 =  129.50204
## 
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## MCMCregress iteration 4851 of 11000 
## beta = 
##   37.92362
##    0.60387
## sigma2 =  135.19949
## 
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## MCMCregress iteration 4861 of 11000 
## beta = 
##   38.62588
##    0.42846
## sigma2 =  132.72866
## 
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## MCMCregress iteration 4871 of 11000 
## beta = 
##   37.13659
##    1.31421
## sigma2 =  127.78363
## 
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## MCMCregress iteration 4881 of 11000 
## beta = 
##   37.88970
##    0.94204
## sigma2 =  134.36277
## 
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## MCMCregress iteration 4891 of 11000 
## beta = 
##   37.99808
##    0.66702
## sigma2 =  134.07968
## 
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## MCMCregress iteration 4901 of 11000 
## beta = 
##   38.55114
##    0.62187
## sigma2 =  135.02981
## 
## 
## MCMCregress iteration 4911 of 11000 
## beta = 
##   37.58976
##    0.83847
## sigma2 =  134.60095
## 
## 
## MCMCregress iteration 4921 of 11000 
## beta = 
##   39.68736
##    0.06993
## sigma2 =  128.15852
## 
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## MCMCregress iteration 4931 of 11000 
## beta = 
##   38.26696
##    1.02181
## sigma2 =  133.59876
## 
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## MCMCregress iteration 4941 of 11000 
## beta = 
##   41.17466
##   -0.37565
## sigma2 =  145.13604
## 
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## MCMCregress iteration 4951 of 11000 
## beta = 
##   36.79148
##    1.54806
## sigma2 =  126.71352
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## MCMCregress iteration 4961 of 11000 
## beta = 
##   37.13706
##    0.96926
## sigma2 =  129.80403
## 
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## MCMCregress iteration 4971 of 11000 
## beta = 
##   39.35085
##    0.33492
## sigma2 =  123.64676
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## MCMCregress iteration 4981 of 11000 
## beta = 
##   37.80859
##    1.12306
## sigma2 =  136.56252
## 
## 
## MCMCregress iteration 4991 of 11000 
## beta = 
##   39.48026
##    0.27458
## sigma2 =  144.03227
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## MCMCregress iteration 5001 of 11000 
## beta = 
##   37.15596
##    1.05132
## sigma2 =  132.41853
## 
## 
## MCMCregress iteration 5011 of 11000 
## beta = 
##   38.41038
##    0.51597
## sigma2 =  128.02229
## 
## 
## MCMCregress iteration 5021 of 11000 
## beta = 
##   38.96820
##    0.55972
## sigma2 =  121.43016
## 
## 
## MCMCregress iteration 5031 of 11000 
## beta = 
##   36.05073
##    1.38839
## sigma2 =  117.82315
## 
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## MCMCregress iteration 5041 of 11000 
## beta = 
##   41.21262
##   -0.29354
## sigma2 =  142.94781
## 
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## MCMCregress iteration 5051 of 11000 
## beta = 
##   41.23966
##   -0.71786
## sigma2 =  132.80309
## 
## 
## MCMCregress iteration 5061 of 11000 
## beta = 
##   37.64325
##    0.76566
## sigma2 =  137.83054
## 
## 
## MCMCregress iteration 5071 of 11000 
## beta = 
##   37.50162
##    0.71164
## sigma2 =  144.64990
## 
## 
## MCMCregress iteration 5081 of 11000 
## beta = 
##   39.22644
##    0.51589
## sigma2 =  136.02770
## 
## 
## MCMCregress iteration 5091 of 11000 
## beta = 
##   39.45106
##    0.55188
## sigma2 =  129.24853
## 
## 
## MCMCregress iteration 5101 of 11000 
## beta = 
##   37.07729
##    1.15577
## sigma2 =  120.30236
## 
## 
## MCMCregress iteration 5111 of 11000 
## beta = 
##   39.78402
##    0.38190
## sigma2 =  140.33158
## 
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## MCMCregress iteration 5121 of 11000 
## beta = 
##   39.04898
##    0.35310
## sigma2 =  141.13466
## 
## 
## MCMCregress iteration 5131 of 11000 
## beta = 
##   38.63099
##    0.51381
## sigma2 =  138.36988
## 
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## MCMCregress iteration 5141 of 11000 
## beta = 
##   38.66443
##    0.65651
## sigma2 =  135.54856
## 
## 
## MCMCregress iteration 5151 of 11000 
## beta = 
##   41.27575
##   -0.43438
## sigma2 =  131.72371
## 
## 
## MCMCregress iteration 5161 of 11000 
## beta = 
##   36.39199
##    1.23977
## sigma2 =  152.38839
## 
## 
## MCMCregress iteration 5171 of 11000 
## beta = 
##   36.86022
##    1.36736
## sigma2 =  154.31152
## 
## 
## MCMCregress iteration 5181 of 11000 
## beta = 
##   38.50899
##    0.93920
## sigma2 =  122.53406
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## 
## MCMCregress iteration 5191 of 11000 
## beta = 
##   37.96461
##    0.67220
## sigma2 =  136.13358
## 
## 
## MCMCregress iteration 5201 of 11000 
## beta = 
##   39.66230
##    0.27253
## sigma2 =  128.87164
## 
## 
## MCMCregress iteration 5211 of 11000 
## beta = 
##   38.57111
##    0.88451
## sigma2 =  124.09817
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## 
## MCMCregress iteration 5221 of 11000 
## beta = 
##   36.88858
##    1.01532
## sigma2 =  125.53128
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## 
## MCMCregress iteration 5231 of 11000 
## beta = 
##   40.57677
##   -0.12060
## sigma2 =  138.01809
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## MCMCregress iteration 5241 of 11000 
## beta = 
##   37.09207
##    1.45006
## sigma2 =  126.41746
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## MCMCregress iteration 5251 of 11000 
## beta = 
##   39.72309
##    0.15689
## sigma2 =  146.96617
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## 
## MCMCregress iteration 5261 of 11000 
## beta = 
##   36.15203
##    1.65976
## sigma2 =  124.07318
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## 
## MCMCregress iteration 5271 of 11000 
## beta = 
##   38.68686
##    0.56417
## sigma2 =  131.80021
## 
## 
## MCMCregress iteration 5281 of 11000 
## beta = 
##   39.46198
##    0.27634
## sigma2 =  133.84824
## 
## 
## MCMCregress iteration 5291 of 11000 
## beta = 
##   40.29870
##    0.29492
## sigma2 =  133.63679
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## 
## MCMCregress iteration 5301 of 11000 
## beta = 
##   38.75028
##    0.19553
## sigma2 =  134.25564
## 
## 
## MCMCregress iteration 5311 of 11000 
## beta = 
##   38.61268
##    0.49981
## sigma2 =  136.23082
## 
## 
## MCMCregress iteration 5321 of 11000 
## beta = 
##   36.96896
##    1.03523
## sigma2 =  140.66412
## 
## 
## MCMCregress iteration 5331 of 11000 
## beta = 
##   39.30430
##    0.14900
## sigma2 =  121.02532
## 
## 
## MCMCregress iteration 5341 of 11000 
## beta = 
##   38.76376
##    0.60126
## sigma2 =  147.40899
## 
## 
## MCMCregress iteration 5351 of 11000 
## beta = 
##   38.76882
##    0.29198
## sigma2 =  133.56222
## 
## 
## MCMCregress iteration 5361 of 11000 
## beta = 
##   38.79708
##    0.33063
## sigma2 =  144.24524
## 
## 
## MCMCregress iteration 5371 of 11000 
## beta = 
##   38.32997
##    0.58106
## sigma2 =  127.24226
## 
## 
## MCMCregress iteration 5381 of 11000 
## beta = 
##   39.28274
##    0.40944
## sigma2 =  141.11525
## 
## 
## MCMCregress iteration 5391 of 11000 
## beta = 
##   35.52192
##    1.64295
## sigma2 =  125.45774
## 
## 
## MCMCregress iteration 5401 of 11000 
## beta = 
##   38.82495
##    0.78083
## sigma2 =  125.22096
## 
## 
## MCMCregress iteration 5411 of 11000 
## beta = 
##   39.75787
##    0.55696
## sigma2 =  128.05429
## 
## 
## MCMCregress iteration 5421 of 11000 
## beta = 
##   39.56825
##    0.12301
## sigma2 =  133.50936
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## 
## MCMCregress iteration 5431 of 11000 
## beta = 
##   39.95646
##    0.00538
## sigma2 =  140.03067
## 
## 
## MCMCregress iteration 5441 of 11000 
## beta = 
##   37.36230
##    0.95386
## sigma2 =  138.40681
## 
## 
## MCMCregress iteration 5451 of 11000 
## beta = 
##   39.75392
##    0.44340
## sigma2 =  131.59447
## 
## 
## MCMCregress iteration 5461 of 11000 
## beta = 
##   39.77716
##    0.00073
## sigma2 =  139.02816
## 
## 
## MCMCregress iteration 5471 of 11000 
## beta = 
##   37.14813
##    1.10778
## sigma2 =  147.16683
## 
## 
## MCMCregress iteration 5481 of 11000 
## beta = 
##   38.87217
##    0.49701
## sigma2 =  140.13412
## 
## 
## MCMCregress iteration 5491 of 11000 
## beta = 
##   37.73287
##    0.88055
## sigma2 =  119.45907
## 
## 
## MCMCregress iteration 5501 of 11000 
## beta = 
##   38.69572
##    0.80045
## sigma2 =  137.13218
## 
## 
## MCMCregress iteration 5511 of 11000 
## beta = 
##   37.91382
##    1.16182
## sigma2 =  128.93355
## 
## 
## MCMCregress iteration 5521 of 11000 
## beta = 
##   38.85137
##    0.53579
## sigma2 =  126.50980
## 
## 
## MCMCregress iteration 5531 of 11000 
## beta = 
##   38.00135
##    0.76712
## sigma2 =  130.23025
## 
## 
## MCMCregress iteration 5541 of 11000 
## beta = 
##   39.26373
##    0.21957
## sigma2 =  130.48289
## 
## 
## MCMCregress iteration 5551 of 11000 
## beta = 
##   36.89853
##    1.59899
## sigma2 =  139.35789
## 
## 
## MCMCregress iteration 5561 of 11000 
## beta = 
##   37.68537
##    1.10232
## sigma2 =  141.51792
## 
## 
## MCMCregress iteration 5571 of 11000 
## beta = 
##   38.57344
##    0.72848
## sigma2 =  123.31908
## 
## 
## MCMCregress iteration 5581 of 11000 
## beta = 
##   38.96909
##    0.44671
## sigma2 =  126.40414
## 
## 
## MCMCregress iteration 5591 of 11000 
## beta = 
##   37.64403
##    1.23501
## sigma2 =  137.59077
## 
## 
## MCMCregress iteration 5601 of 11000 
## beta = 
##   39.41363
##    0.48076
## sigma2 =  154.67743
## 
## 
## MCMCregress iteration 5611 of 11000 
## beta = 
##   37.03922
##    1.29652
## sigma2 =  123.21217
## 
## 
## MCMCregress iteration 5621 of 11000 
## beta = 
##   36.57029
##    1.28894
## sigma2 =  131.07659
## 
## 
## MCMCregress iteration 5631 of 11000 
## beta = 
##   35.83592
##    1.60282
## sigma2 =  148.14663
## 
## 
## MCMCregress iteration 5641 of 11000 
## beta = 
##   37.98378
##    0.76427
## sigma2 =  129.39103
## 
## 
## MCMCregress iteration 5651 of 11000 
## beta = 
##   38.39253
##    0.85742
## sigma2 =  125.82435
## 
## 
## MCMCregress iteration 5661 of 11000 
## beta = 
##   39.49203
##    0.33589
## sigma2 =  143.08190
## 
## 
## MCMCregress iteration 5671 of 11000 
## beta = 
##   39.60410
##    0.39799
## sigma2 =  130.24068
## 
## 
## MCMCregress iteration 5681 of 11000 
## beta = 
##   37.89249
##    1.36093
## sigma2 =  141.90921
## 
## 
## MCMCregress iteration 5691 of 11000 
## beta = 
##   39.98699
##   -0.07582
## sigma2 =  125.23956
## 
## 
## MCMCregress iteration 5701 of 11000 
## beta = 
##   39.97421
##   -0.15743
## sigma2 =  120.50374
## 
## 
## MCMCregress iteration 5711 of 11000 
## beta = 
##   37.72722
##    0.76748
## sigma2 =  122.33287
## 
## 
## MCMCregress iteration 5721 of 11000 
## beta = 
##   38.72342
##    0.87815
## sigma2 =  120.67888
## 
## 
## MCMCregress iteration 5731 of 11000 
## beta = 
##   39.63318
##    0.55875
## sigma2 =  125.71162
## 
## 
## MCMCregress iteration 5741 of 11000 
## beta = 
##   35.82128
##    1.72555
## sigma2 =  137.95595
## 
## 
## MCMCregress iteration 5751 of 11000 
## beta = 
##   36.53259
##    1.31662
## sigma2 =  129.34068
## 
## 
## MCMCregress iteration 5761 of 11000 
## beta = 
##   37.79867
##    0.74117
## sigma2 =  132.31277
## 
## 
## MCMCregress iteration 5771 of 11000 
## beta = 
##   37.74812
##    0.72018
## sigma2 =  128.42482
## 
## 
## MCMCregress iteration 5781 of 11000 
## beta = 
##   36.70137
##    1.56683
## sigma2 =  122.00792
## 
## 
## MCMCregress iteration 5791 of 11000 
## beta = 
##   38.62311
##    0.22627
## sigma2 =  126.83153
## 
## 
## MCMCregress iteration 5801 of 11000 
## beta = 
##   37.56811
##    1.40054
## sigma2 =  143.97392
## 
## 
## MCMCregress iteration 5811 of 11000 
## beta = 
##   37.39905
##    0.70700
## sigma2 =  122.81561
## 
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## MCMCregress iteration 5821 of 11000 
## beta = 
##   36.89774
##    1.14223
## sigma2 =  138.49813
## 
## 
## MCMCregress iteration 5831 of 11000 
## beta = 
##   38.11718
##    0.88529
## sigma2 =  136.24192
## 
## 
## MCMCregress iteration 5841 of 11000 
## beta = 
##   39.71094
##    0.15784
## sigma2 =  116.73892
## 
## 
## MCMCregress iteration 5851 of 11000 
## beta = 
##   38.51112
##    0.57810
## sigma2 =  145.89011
## 
## 
## MCMCregress iteration 5861 of 11000 
## beta = 
##   40.24515
##    0.21505
## sigma2 =  139.57933
## 
## 
## MCMCregress iteration 5871 of 11000 
## beta = 
##   38.84120
##    0.16562
## sigma2 =  149.96826
## 
## 
## MCMCregress iteration 5881 of 11000 
## beta = 
##   38.62906
##    0.37388
## sigma2 =  121.50610
## 
## 
## MCMCregress iteration 5891 of 11000 
## beta = 
##   38.61812
##    0.62921
## sigma2 =  139.03466
## 
## 
## MCMCregress iteration 5901 of 11000 
## beta = 
##   36.77653
##    0.98250
## sigma2 =  130.73443
## 
## 
## MCMCregress iteration 5911 of 11000 
## beta = 
##   38.69628
##    0.64353
## sigma2 =  139.38993
## 
## 
## MCMCregress iteration 5921 of 11000 
## beta = 
##   38.94915
##    0.56110
## sigma2 =  151.37851
## 
## 
## MCMCregress iteration 5931 of 11000 
## beta = 
##   36.76636
##    1.42088
## sigma2 =  132.54905
## 
## 
## MCMCregress iteration 5941 of 11000 
## beta = 
##   40.02325
##    0.02351
## sigma2 =  133.09042
## 
## 
## MCMCregress iteration 5951 of 11000 
## beta = 
##   38.39187
##    0.56816
## sigma2 =  139.21538
## 
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## MCMCregress iteration 5961 of 11000 
## beta = 
##   39.61185
##    0.25148
## sigma2 =  123.02131
## 
## 
## MCMCregress iteration 5971 of 11000 
## beta = 
##   39.05724
##    0.74268
## sigma2 =  121.83345
## 
## 
## MCMCregress iteration 5981 of 11000 
## beta = 
##   37.78521
##    0.79786
## sigma2 =  119.63761
## 
## 
## MCMCregress iteration 5991 of 11000 
## beta = 
##   38.26764
##    0.77252
## sigma2 =  135.06496
## 
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## MCMCregress iteration 6001 of 11000 
## beta = 
##   38.55985
##    0.83312
## sigma2 =  128.95288
## 
## 
## MCMCregress iteration 6011 of 11000 
## beta = 
##   40.53149
##    0.03453
## sigma2 =  122.03453
## 
## 
## MCMCregress iteration 6021 of 11000 
## beta = 
##   37.57383
##    1.06610
## sigma2 =  139.47386
## 
## 
## MCMCregress iteration 6031 of 11000 
## beta = 
##   38.82787
##    0.48115
## sigma2 =  129.58273
## 
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## MCMCregress iteration 6041 of 11000 
## beta = 
##   38.69771
##    0.71026
## sigma2 =  138.72922
## 
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## MCMCregress iteration 6051 of 11000 
## beta = 
##   38.06506
##    0.65112
## sigma2 =  136.55922
## 
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## MCMCregress iteration 6061 of 11000 
## beta = 
##   37.21530
##    1.32453
## sigma2 =  139.30901
## 
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## MCMCregress iteration 6071 of 11000 
## beta = 
##   41.39445
##   -0.31596
## sigma2 =  120.37251
## 
## 
## MCMCregress iteration 6081 of 11000 
## beta = 
##   38.26696
##    0.56276
## sigma2 =  138.29162
## 
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## MCMCregress iteration 6091 of 11000 
## beta = 
##   37.62441
##    0.84342
## sigma2 =  137.36228
## 
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## MCMCregress iteration 6101 of 11000 
## beta = 
##   37.52863
##    0.85422
## sigma2 =  109.41597
## 
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## MCMCregress iteration 6111 of 11000 
## beta = 
##   40.59219
##   -0.10161
## sigma2 =  135.78266
## 
## 
## MCMCregress iteration 6121 of 11000 
## beta = 
##   39.67830
##    0.42936
## sigma2 =  137.32912
## 
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## MCMCregress iteration 6131 of 11000 
## beta = 
##   38.87469
##    0.51236
## sigma2 =  129.71829
## 
## 
## MCMCregress iteration 6141 of 11000 
## beta = 
##   40.81123
##    0.02130
## sigma2 =  143.03843
## 
## 
## MCMCregress iteration 6151 of 11000 
## beta = 
##   39.34566
##    0.56376
## sigma2 =  132.86434
## 
## 
## MCMCregress iteration 6161 of 11000 
## beta = 
##   37.11542
##    1.24368
## sigma2 =  125.87944
## 
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## MCMCregress iteration 6171 of 11000 
## beta = 
##   37.13635
##    1.11072
## sigma2 =  145.70585
## 
## 
## MCMCregress iteration 6181 of 11000 
## beta = 
##   36.97446
##    1.23267
## sigma2 =  130.79188
## 
## 
## MCMCregress iteration 6191 of 11000 
## beta = 
##   38.88178
##    0.31282
## sigma2 =  127.94105
## 
## 
## MCMCregress iteration 6201 of 11000 
## beta = 
##   39.10918
##    0.83030
## sigma2 =  127.56029
## 
## 
## MCMCregress iteration 6211 of 11000 
## beta = 
##   41.49100
##   -0.26878
## sigma2 =  129.76213
## 
## 
## MCMCregress iteration 6221 of 11000 
## beta = 
##   36.34827
##    1.31997
## sigma2 =  126.04842
## 
## 
## MCMCregress iteration 6231 of 11000 
## beta = 
##   39.05603
##    0.00530
## sigma2 =  137.98050
## 
## 
## MCMCregress iteration 6241 of 11000 
## beta = 
##   36.59183
##    1.24213
## sigma2 =  124.21057
## 
## 
## MCMCregress iteration 6251 of 11000 
## beta = 
##   38.79514
##    0.51772
## sigma2 =  137.04735
## 
## 
## MCMCregress iteration 6261 of 11000 
## beta = 
##   37.80434
##    1.00405
## sigma2 =  118.32409
## 
## 
## MCMCregress iteration 6271 of 11000 
## beta = 
##   37.92026
##    0.59116
## sigma2 =  141.36401
## 
## 
## MCMCregress iteration 6281 of 11000 
## beta = 
##   38.97902
##    0.73569
## sigma2 =  136.20526
## 
## 
## MCMCregress iteration 6291 of 11000 
## beta = 
##   39.30171
##    0.56981
## sigma2 =  145.76378
## 
## 
## MCMCregress iteration 6301 of 11000 
## beta = 
##   37.67626
##    0.78634
## sigma2 =  137.19115
## 
## 
## MCMCregress iteration 6311 of 11000 
## beta = 
##   37.45433
##    1.69075
## sigma2 =  148.02910
## 
## 
## MCMCregress iteration 6321 of 11000 
## beta = 
##   38.48852
##    0.79325
## sigma2 =  132.24184
## 
## 
## MCMCregress iteration 6331 of 11000 
## beta = 
##   39.47274
##   -0.06769
## sigma2 =  125.09891
## 
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## MCMCregress iteration 6341 of 11000 
## beta = 
##   39.00947
##    0.38886
## sigma2 =  124.77339
## 
## 
## MCMCregress iteration 6351 of 11000 
## beta = 
##   39.68266
##    0.26341
## sigma2 =  135.40515
## 
## 
## MCMCregress iteration 6361 of 11000 
## beta = 
##   38.03057
##    1.01519
## sigma2 =  143.92350
## 
## 
## MCMCregress iteration 6371 of 11000 
## beta = 
##   38.94420
##    0.48420
## sigma2 =  143.96981
## 
## 
## MCMCregress iteration 6381 of 11000 
## beta = 
##   37.46399
##    0.84884
## sigma2 =  131.34031
## 
## 
## MCMCregress iteration 6391 of 11000 
## beta = 
##   39.08587
##    0.55186
## sigma2 =  152.44012
## 
## 
## MCMCregress iteration 6401 of 11000 
## beta = 
##   38.39437
##    0.84916
## sigma2 =  152.73056
## 
## 
## MCMCregress iteration 6411 of 11000 
## beta = 
##   36.68385
##    1.31362
## sigma2 =  137.03213
## 
## 
## MCMCregress iteration 6421 of 11000 
## beta = 
##   37.21224
##    0.95857
## sigma2 =  155.29528
## 
## 
## MCMCregress iteration 6431 of 11000 
## beta = 
##   37.54177
##    1.21705
## sigma2 =  127.63016
## 
## 
## MCMCregress iteration 6441 of 11000 
## beta = 
##   39.10149
##    0.22148
## sigma2 =  128.89955
## 
## 
## MCMCregress iteration 6451 of 11000 
## beta = 
##   39.24137
##    0.32871
## sigma2 =  125.74454
## 
## 
## MCMCregress iteration 6461 of 11000 
## beta = 
##   40.82885
##   -0.19539
## sigma2 =  130.55111
## 
## 
## MCMCregress iteration 6471 of 11000 
## beta = 
##   38.58785
##    0.83067
## sigma2 =  127.75889
## 
## 
## MCMCregress iteration 6481 of 11000 
## beta = 
##   37.57480
##    1.11787
## sigma2 =  137.27010
## 
## 
## MCMCregress iteration 6491 of 11000 
## beta = 
##   38.86612
##    0.77679
## sigma2 =  129.69475
## 
## 
## MCMCregress iteration 6501 of 11000 
## beta = 
##   38.85859
##    0.52152
## sigma2 =  128.49846
## 
## 
## MCMCregress iteration 6511 of 11000 
## beta = 
##   37.72621
##    1.28431
## sigma2 =  128.94868
## 
## 
## MCMCregress iteration 6521 of 11000 
## beta = 
##   38.00783
##    0.87174
## sigma2 =  141.05916
## 
## 
## MCMCregress iteration 6531 of 11000 
## beta = 
##   37.95984
##    1.06321
## sigma2 =  137.20009
## 
## 
## MCMCregress iteration 6541 of 11000 
## beta = 
##   38.12381
##    0.77496
## sigma2 =  135.40254
## 
## 
## MCMCregress iteration 6551 of 11000 
## beta = 
##   39.63357
##    0.18045
## sigma2 =  116.84534
## 
## 
## MCMCregress iteration 6561 of 11000 
## beta = 
##   38.42800
##    0.58734
## sigma2 =  148.90229
## 
## 
## MCMCregress iteration 6571 of 11000 
## beta = 
##   38.31154
##    0.65095
## sigma2 =  135.09797
## 
## 
## MCMCregress iteration 6581 of 11000 
## beta = 
##   37.45367
##    0.97424
## sigma2 =  140.04752
## 
## 
## MCMCregress iteration 6591 of 11000 
## beta = 
##   37.03591
##    1.25776
## sigma2 =  131.75248
## 
## 
## MCMCregress iteration 6601 of 11000 
## beta = 
##   40.10340
##   -0.11358
## sigma2 =  126.56371
## 
## 
## MCMCregress iteration 6611 of 11000 
## beta = 
##   38.30365
##    0.87312
## sigma2 =  121.55557
## 
## 
## MCMCregress iteration 6621 of 11000 
## beta = 
##   38.81631
##    0.40756
## sigma2 =  135.27206
## 
## 
## MCMCregress iteration 6631 of 11000 
## beta = 
##   38.51642
##    0.40634
## sigma2 =  116.86233
## 
## 
## MCMCregress iteration 6641 of 11000 
## beta = 
##   38.08333
##    0.76403
## sigma2 =  139.14294
## 
## 
## MCMCregress iteration 6651 of 11000 
## beta = 
##   38.63666
##    0.94192
## sigma2 =  138.64516
## 
## 
## MCMCregress iteration 6661 of 11000 
## beta = 
##   39.87808
##    0.16124
## sigma2 =  135.53838
## 
## 
## MCMCregress iteration 6671 of 11000 
## beta = 
##   39.49259
##    0.34752
## sigma2 =  135.94966
## 
## 
## MCMCregress iteration 6681 of 11000 
## beta = 
##   38.64766
##    0.69563
## sigma2 =  145.29898
## 
## 
## MCMCregress iteration 6691 of 11000 
## beta = 
##   37.83383
##    0.95008
## sigma2 =  134.87956
## 
## 
## MCMCregress iteration 6701 of 11000 
## beta = 
##   38.63450
##    0.75700
## sigma2 =  117.22446
## 
## 
## MCMCregress iteration 6711 of 11000 
## beta = 
##   38.84070
##    0.39998
## sigma2 =  125.54697
## 
## 
## MCMCregress iteration 6721 of 11000 
## beta = 
##   36.37623
##    1.80480
## sigma2 =  139.36699
## 
## 
## MCMCregress iteration 6731 of 11000 
## beta = 
##   37.45880
##    1.28782
## sigma2 =  141.07194
## 
## 
## MCMCregress iteration 6741 of 11000 
## beta = 
##   37.93402
##    0.78613
## sigma2 =  140.30334
## 
## 
## MCMCregress iteration 6751 of 11000 
## beta = 
##   37.13302
##    0.77691
## sigma2 =  133.43373
## 
## 
## MCMCregress iteration 6761 of 11000 
## beta = 
##   39.40056
##    0.74542
## sigma2 =  128.76316
## 
## 
## MCMCregress iteration 6771 of 11000 
## beta = 
##   39.74322
##    0.22602
## sigma2 =  136.90235
## 
## 
## MCMCregress iteration 6781 of 11000 
## beta = 
##   39.12483
##    0.51327
## sigma2 =  119.42207
## 
## 
## MCMCregress iteration 6791 of 11000 
## beta = 
##   38.52611
##    0.62142
## sigma2 =  115.92001
## 
## 
## MCMCregress iteration 6801 of 11000 
## beta = 
##   37.77955
##    1.01190
## sigma2 =  138.92759
## 
## 
## MCMCregress iteration 6811 of 11000 
## beta = 
##   37.20441
##    1.36328
## sigma2 =  132.83998
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## 
## MCMCregress iteration 6821 of 11000 
## beta = 
##   36.91322
##    1.22188
## sigma2 =  133.41111
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## 
## MCMCregress iteration 6831 of 11000 
## beta = 
##   38.60744
##    0.72713
## sigma2 =  138.55412
## 
## 
## MCMCregress iteration 6841 of 11000 
## beta = 
##   39.06323
##    0.44201
## sigma2 =  128.41612
## 
## 
## MCMCregress iteration 6851 of 11000 
## beta = 
##   36.53364
##    1.10531
## sigma2 =  144.46973
## 
## 
## MCMCregress iteration 6861 of 11000 
## beta = 
##   36.41146
##    1.32453
## sigma2 =  139.35227
## 
## 
## MCMCregress iteration 6871 of 11000 
## beta = 
##   37.22763
##    1.22081
## sigma2 =  145.74882
## 
## 
## MCMCregress iteration 6881 of 11000 
## beta = 
##   39.16350
##    0.42048
## sigma2 =  131.66456
## 
## 
## MCMCregress iteration 6891 of 11000 
## beta = 
##   38.74589
##    0.69849
## sigma2 =  136.17864
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## 
## MCMCregress iteration 6901 of 11000 
## beta = 
##   39.36396
##    0.54540
## sigma2 =  153.40552
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## 
## MCMCregress iteration 6911 of 11000 
## beta = 
##   38.53859
##    0.38797
## sigma2 =  133.24302
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## 
## MCMCregress iteration 6921 of 11000 
## beta = 
##   38.69920
##    0.57600
## sigma2 =  135.59928
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## 
## MCMCregress iteration 6931 of 11000 
## beta = 
##   38.64447
##    0.58231
## sigma2 =  133.82622
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## 
## MCMCregress iteration 6941 of 11000 
## beta = 
##   37.62721
##    0.90379
## sigma2 =  131.51572
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## 
## MCMCregress iteration 6951 of 11000 
## beta = 
##   37.54608
##    0.79337
## sigma2 =  143.74774
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## 
## MCMCregress iteration 6961 of 11000 
## beta = 
##   39.45334
##    0.26824
## sigma2 =  142.38777
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## 
## MCMCregress iteration 6971 of 11000 
## beta = 
##   38.92510
##    0.33558
## sigma2 =  122.75110
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## 
## MCMCregress iteration 6981 of 11000 
## beta = 
##   38.66704
##    0.09708
## sigma2 =  131.32124
## 
## 
## MCMCregress iteration 6991 of 11000 
## beta = 
##   38.49236
##    0.67147
## sigma2 =  128.25134
## 
## 
## MCMCregress iteration 7001 of 11000 
## beta = 
##   38.57418
##    0.66724
## sigma2 =  124.96532
## 
## 
## MCMCregress iteration 7011 of 11000 
## beta = 
##   38.15055
##    0.88320
## sigma2 =  144.04530
## 
## 
## MCMCregress iteration 7021 of 11000 
## beta = 
##   37.27506
##    1.31816
## sigma2 =  132.04225
## 
## 
## MCMCregress iteration 7031 of 11000 
## beta = 
##   38.94649
##    0.57071
## sigma2 =  127.81636
## 
## 
## MCMCregress iteration 7041 of 11000 
## beta = 
##   37.76306
##    1.00399
## sigma2 =  137.84649
## 
## 
## MCMCregress iteration 7051 of 11000 
## beta = 
##   38.34498
##    0.84664
## sigma2 =  133.54989
## 
## 
## MCMCregress iteration 7061 of 11000 
## beta = 
##   39.06526
##    0.42725
## sigma2 =  142.87793
## 
## 
## MCMCregress iteration 7071 of 11000 
## beta = 
##   39.14239
##    0.51246
## sigma2 =  137.79261
## 
## 
## MCMCregress iteration 7081 of 11000 
## beta = 
##   39.14392
##    0.57231
## sigma2 =  138.68738
## 
## 
## MCMCregress iteration 7091 of 11000 
## beta = 
##   38.02329
##    0.98691
## sigma2 =  134.30472
## 
## 
## MCMCregress iteration 7101 of 11000 
## beta = 
##   36.96729
##    1.23621
## sigma2 =  132.88614
## 
## 
## MCMCregress iteration 7111 of 11000 
## beta = 
##   37.39301
##    1.10464
## sigma2 =  127.64705
## 
## 
## MCMCregress iteration 7121 of 11000 
## beta = 
##   36.29492
##    1.45614
## sigma2 =  119.67324
## 
## 
## MCMCregress iteration 7131 of 11000 
## beta = 
##   37.37347
##    0.83807
## sigma2 =  141.41646
## 
## 
## MCMCregress iteration 7141 of 11000 
## beta = 
##   40.33094
##    0.10251
## sigma2 =  131.35966
## 
## 
## MCMCregress iteration 7151 of 11000 
## beta = 
##   38.70461
##    0.55992
## sigma2 =  135.82070
## 
## 
## MCMCregress iteration 7161 of 11000 
## beta = 
##   39.26665
##    0.31145
## sigma2 =  134.42628
## 
## 
## MCMCregress iteration 7171 of 11000 
## beta = 
##   38.24698
##    0.95329
## sigma2 =  132.41292
## 
## 
## MCMCregress iteration 7181 of 11000 
## beta = 
##   39.08092
##    0.62468
## sigma2 =  131.85367
## 
## 
## MCMCregress iteration 7191 of 11000 
## beta = 
##   39.05903
##    0.69593
## sigma2 =  132.26773
## 
## 
## MCMCregress iteration 7201 of 11000 
## beta = 
##   36.64801
##    1.29208
## sigma2 =  128.39449
## 
## 
## MCMCregress iteration 7211 of 11000 
## beta = 
##   37.80115
##    0.83663
## sigma2 =  133.73734
## 
## 
## MCMCregress iteration 7221 of 11000 
## beta = 
##   38.37260
##    0.76485
## sigma2 =  118.93287
## 
## 
## MCMCregress iteration 7231 of 11000 
## beta = 
##   37.25701
##    1.02900
## sigma2 =  125.47352
## 
## 
## MCMCregress iteration 7241 of 11000 
## beta = 
##   38.90416
##    0.62599
## sigma2 =  116.63405
## 
## 
## MCMCregress iteration 7251 of 11000 
## beta = 
##   39.90474
##    0.09122
## sigma2 =  133.62919
## 
## 
## MCMCregress iteration 7261 of 11000 
## beta = 
##   38.16952
##    0.79329
## sigma2 =  125.73708
## 
## 
## MCMCregress iteration 7271 of 11000 
## beta = 
##   38.20653
##    0.52456
## sigma2 =  142.39840
## 
## 
## MCMCregress iteration 7281 of 11000 
## beta = 
##   40.65846
##   -0.15071
## sigma2 =  118.95648
## 
## 
## MCMCregress iteration 7291 of 11000 
## beta = 
##   38.04939
##    0.76683
## sigma2 =  137.15725
## 
## 
## MCMCregress iteration 7301 of 11000 
## beta = 
##   38.66304
##    0.84823
## sigma2 =  135.66282
## 
## 
## MCMCregress iteration 7311 of 11000 
## beta = 
##   37.19638
##    1.05668
## sigma2 =  139.53388
## 
## 
## MCMCregress iteration 7321 of 11000 
## beta = 
##   39.14273
##    0.72675
## sigma2 =  135.25309
## 
## 
## MCMCregress iteration 7331 of 11000 
## beta = 
##   36.53609
##    1.31478
## sigma2 =  139.43745
## 
## 
## MCMCregress iteration 7341 of 11000 
## beta = 
##   38.58694
##    0.66133
## sigma2 =  137.62439
## 
## 
## MCMCregress iteration 7351 of 11000 
## beta = 
##   39.05372
##    0.15246
## sigma2 =  133.91822
## 
## 
## MCMCregress iteration 7361 of 11000 
## beta = 
##   38.33794
##    0.66815
## sigma2 =  153.70712
## 
## 
## MCMCregress iteration 7371 of 11000 
## beta = 
##   37.86717
##    1.12886
## sigma2 =  134.78670
## 
## 
## MCMCregress iteration 7381 of 11000 
## beta = 
##   39.51256
##    0.41885
## sigma2 =  139.76007
## 
## 
## MCMCregress iteration 7391 of 11000 
## beta = 
##   39.53065
##    0.35227
## sigma2 =  133.64969
## 
## 
## MCMCregress iteration 7401 of 11000 
## beta = 
##   38.41002
##    0.53931
## sigma2 =  130.69975
## 
## 
## MCMCregress iteration 7411 of 11000 
## beta = 
##   39.99194
##   -0.36215
## sigma2 =  145.83495
## 
## 
## MCMCregress iteration 7421 of 11000 
## beta = 
##   37.25347
##    1.08125
## sigma2 =  138.60200
## 
## 
## MCMCregress iteration 7431 of 11000 
## beta = 
##   38.27130
##    0.66232
## sigma2 =  141.53338
## 
## 
## MCMCregress iteration 7441 of 11000 
## beta = 
##   39.40465
##    0.79881
## sigma2 =  138.39418
## 
## 
## MCMCregress iteration 7451 of 11000 
## beta = 
##   40.53945
##   -0.14597
## sigma2 =  131.75720
## 
## 
## MCMCregress iteration 7461 of 11000 
## beta = 
##   36.70603
##    1.20124
## sigma2 =  132.86129
## 
## 
## MCMCregress iteration 7471 of 11000 
## beta = 
##   39.22137
##    0.53382
## sigma2 =  138.46746
## 
## 
## MCMCregress iteration 7481 of 11000 
## beta = 
##   38.25479
##    0.95462
## sigma2 =  141.40230
## 
## 
## MCMCregress iteration 7491 of 11000 
## beta = 
##   37.65377
##    0.75417
## sigma2 =  140.72967
## 
## 
## MCMCregress iteration 7501 of 11000 
## beta = 
##   37.25060
##    1.11938
## sigma2 =  126.39571
## 
## 
## MCMCregress iteration 7511 of 11000 
## beta = 
##   38.58396
##    0.66565
## sigma2 =  117.78346
## 
## 
## MCMCregress iteration 7521 of 11000 
## beta = 
##   37.83286
##    0.50030
## sigma2 =  127.28215
## 
## 
## MCMCregress iteration 7531 of 11000 
## beta = 
##   37.50998
##    0.86166
## sigma2 =  143.90538
## 
## 
## MCMCregress iteration 7541 of 11000 
## beta = 
##   38.84782
##    0.69805
## sigma2 =  129.68519
## 
## 
## MCMCregress iteration 7551 of 11000 
## beta = 
##   39.55526
##    0.41595
## sigma2 =  126.18625
## 
## 
## MCMCregress iteration 7561 of 11000 
## beta = 
##   38.66737
##    0.72154
## sigma2 =  124.80570
## 
## 
## MCMCregress iteration 7571 of 11000 
## beta = 
##   39.97214
##    0.44595
## sigma2 =  142.62149
## 
## 
## MCMCregress iteration 7581 of 11000 
## beta = 
##   37.23525
##    1.03319
## sigma2 =  125.22525
## 
## 
## MCMCregress iteration 7591 of 11000 
## beta = 
##   40.39551
##   -0.06755
## sigma2 =  139.20691
## 
## 
## MCMCregress iteration 7601 of 11000 
## beta = 
##   38.63159
##    0.65269
## sigma2 =  140.74905
## 
## 
## MCMCregress iteration 7611 of 11000 
## beta = 
##   38.42913
##    0.45537
## sigma2 =  140.57449
## 
## 
## MCMCregress iteration 7621 of 11000 
## beta = 
##   36.34554
##    1.51257
## sigma2 =  146.97345
## 
## 
## MCMCregress iteration 7631 of 11000 
## beta = 
##   39.30485
##    0.15789
## sigma2 =  140.58201
## 
## 
## MCMCregress iteration 7641 of 11000 
## beta = 
##   39.22974
##    0.32157
## sigma2 =  126.49909
## 
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## MCMCregress iteration 7651 of 11000 
## beta = 
##   38.91787
##    0.79757
## sigma2 =  115.75143
## 
## 
## MCMCregress iteration 7661 of 11000 
## beta = 
##   38.25794
##    0.38855
## sigma2 =  135.68307
## 
## 
## MCMCregress iteration 7671 of 11000 
## beta = 
##   38.26630
##    0.96254
## sigma2 =  140.51364
## 
## 
## MCMCregress iteration 7681 of 11000 
## beta = 
##   37.43425
##    1.13771
## sigma2 =  140.02131
## 
## 
## MCMCregress iteration 7691 of 11000 
## beta = 
##   37.93607
##    0.74254
## sigma2 =  139.25139
## 
## 
## MCMCregress iteration 7701 of 11000 
## beta = 
##   38.59019
##    0.18947
## sigma2 =  144.77135
## 
## 
## MCMCregress iteration 7711 of 11000 
## beta = 
##   38.85370
##    0.35516
## sigma2 =  130.48786
## 
## 
## MCMCregress iteration 7721 of 11000 
## beta = 
##   38.10525
##    1.14981
## sigma2 =  130.14108
## 
## 
## MCMCregress iteration 7731 of 11000 
## beta = 
##   38.87123
##    0.41833
## sigma2 =  134.80169
## 
## 
## MCMCregress iteration 7741 of 11000 
## beta = 
##   39.80230
##   -0.18748
## sigma2 =  134.16615
## 
## 
## MCMCregress iteration 7751 of 11000 
## beta = 
##   38.28869
##    1.09140
## sigma2 =  138.49335
## 
## 
## MCMCregress iteration 7761 of 11000 
## beta = 
##   40.03219
##    0.08582
## sigma2 =  128.06586
## 
## 
## MCMCregress iteration 7771 of 11000 
## beta = 
##   38.46227
##    0.90734
## sigma2 =  141.28956
## 
## 
## MCMCregress iteration 7781 of 11000 
## beta = 
##   38.08149
##    0.67276
## sigma2 =  135.47125
## 
## 
## MCMCregress iteration 7791 of 11000 
## beta = 
##   37.96311
##    0.43073
## sigma2 =  131.33288
## 
## 
## MCMCregress iteration 7801 of 11000 
## beta = 
##   39.86468
##    0.22877
## sigma2 =  130.52219
## 
## 
## MCMCregress iteration 7811 of 11000 
## beta = 
##   40.71386
##   -0.07410
## sigma2 =  115.92652
## 
## 
## MCMCregress iteration 7821 of 11000 
## beta = 
##   36.42520
##    1.56896
## sigma2 =  143.26419
## 
## 
## MCMCregress iteration 7831 of 11000 
## beta = 
##   37.79585
##    1.22223
## sigma2 =  115.69441
## 
## 
## MCMCregress iteration 7841 of 11000 
## beta = 
##   39.14834
##    0.21466
## sigma2 =  130.20026
## 
## 
## MCMCregress iteration 7851 of 11000 
## beta = 
##   36.78161
##    1.54618
## sigma2 =  135.80218
## 
## 
## MCMCregress iteration 7861 of 11000 
## beta = 
##   39.23484
##    0.39462
## sigma2 =  147.10097
## 
## 
## MCMCregress iteration 7871 of 11000 
## beta = 
##   38.96706
##    0.26315
## sigma2 =  135.89572
## 
## 
## MCMCregress iteration 7881 of 11000 
## beta = 
##   37.77708
##    0.94831
## sigma2 =  129.92972
## 
## 
## MCMCregress iteration 7891 of 11000 
## beta = 
##   38.96965
##    0.40012
## sigma2 =  139.77461
## 
## 
## MCMCregress iteration 7901 of 11000 
## beta = 
##   38.86237
##    0.90997
## sigma2 =  131.55349
## 
## 
## MCMCregress iteration 7911 of 11000 
## beta = 
##   38.82799
##    0.99634
## sigma2 =  121.06560
## 
## 
## MCMCregress iteration 7921 of 11000 
## beta = 
##   39.48186
##    0.72254
## sigma2 =  131.36281
## 
## 
## MCMCregress iteration 7931 of 11000 
## beta = 
##   38.85582
##    0.63426
## sigma2 =  144.55073
## 
## 
## MCMCregress iteration 7941 of 11000 
## beta = 
##   39.23265
##    0.50012
## sigma2 =  138.43700
## 
## 
## MCMCregress iteration 7951 of 11000 
## beta = 
##   36.56499
##    1.42361
## sigma2 =  127.92867
## 
## 
## MCMCregress iteration 7961 of 11000 
## beta = 
##   38.09561
##    1.01108
## sigma2 =  129.95342
## 
## 
## MCMCregress iteration 7971 of 11000 
## beta = 
##   38.98737
##    0.39151
## sigma2 =  136.29435
## 
## 
## MCMCregress iteration 7981 of 11000 
## beta = 
##   38.73397
##    0.74975
## sigma2 =  132.58110
## 
## 
## MCMCregress iteration 7991 of 11000 
## beta = 
##   38.76908
##    0.36272
## sigma2 =  131.13582
## 
## 
## MCMCregress iteration 8001 of 11000 
## beta = 
##   37.45724
##    0.77866
## sigma2 =  135.31086
## 
## 
## MCMCregress iteration 8011 of 11000 
## beta = 
##   40.55960
##    0.22761
## sigma2 =  153.10198
## 
## 
## MCMCregress iteration 8021 of 11000 
## beta = 
##   37.04325
##    1.01786
## sigma2 =  134.65803
## 
## 
## MCMCregress iteration 8031 of 11000 
## beta = 
##   37.59755
##    1.03752
## sigma2 =  139.59284
## 
## 
## MCMCregress iteration 8041 of 11000 
## beta = 
##   39.20264
##    0.51666
## sigma2 =  130.76121
## 
## 
## MCMCregress iteration 8051 of 11000 
## beta = 
##   40.19860
##   -0.33338
## sigma2 =  142.93339
## 
## 
## MCMCregress iteration 8061 of 11000 
## beta = 
##   39.21584
##    0.33386
## sigma2 =  133.53229
## 
## 
## MCMCregress iteration 8071 of 11000 
## beta = 
##   38.43343
##    0.70228
## sigma2 =  131.87334
## 
## 
## MCMCregress iteration 8081 of 11000 
## beta = 
##   37.72676
##    0.98768
## sigma2 =  146.86458
## 
## 
## MCMCregress iteration 8091 of 11000 
## beta = 
##   38.35589
##    0.90455
## sigma2 =  139.49935
## 
## 
## MCMCregress iteration 8101 of 11000 
## beta = 
##   40.91103
##   -0.52689
## sigma2 =  123.21363
## 
## 
## MCMCregress iteration 8111 of 11000 
## beta = 
##   40.91618
##    0.14821
## sigma2 =  132.88019
## 
## 
## MCMCregress iteration 8121 of 11000 
## beta = 
##   37.44812
##    0.95007
## sigma2 =  137.76602
## 
## 
## MCMCregress iteration 8131 of 11000 
## beta = 
##   37.97667
##    0.83349
## sigma2 =  132.32315
## 
## 
## MCMCregress iteration 8141 of 11000 
## beta = 
##   41.09184
##   -0.25113
## sigma2 =  140.75105
## 
## 
## MCMCregress iteration 8151 of 11000 
## beta = 
##   37.59745
##    1.31955
## sigma2 =  130.81667
## 
## 
## MCMCregress iteration 8161 of 11000 
## beta = 
##   38.05766
##    0.79317
## sigma2 =  124.77793
## 
## 
## MCMCregress iteration 8171 of 11000 
## beta = 
##   37.19035
##    1.03216
## sigma2 =  130.46395
## 
## 
## MCMCregress iteration 8181 of 11000 
## beta = 
##   38.32652
##    1.05654
## sigma2 =  130.71264
## 
## 
## MCMCregress iteration 8191 of 11000 
## beta = 
##   39.40926
##    0.63155
## sigma2 =  133.35432
## 
## 
## MCMCregress iteration 8201 of 11000 
## beta = 
##   38.55942
##    1.12167
## sigma2 =  133.25400
## 
## 
## MCMCregress iteration 8211 of 11000 
## beta = 
##   39.91466
##   -0.11285
## sigma2 =  128.93802
## 
## 
## MCMCregress iteration 8221 of 11000 
## beta = 
##   39.66208
##    0.15903
## sigma2 =  132.55950
## 
## 
## MCMCregress iteration 8231 of 11000 
## beta = 
##   39.07558
##    0.45935
## sigma2 =  132.67152
## 
## 
## MCMCregress iteration 8241 of 11000 
## beta = 
##   38.64808
##    0.23413
## sigma2 =  143.69132
## 
## 
## MCMCregress iteration 8251 of 11000 
## beta = 
##   38.34187
##    0.81926
## sigma2 =  137.94867
## 
## 
## MCMCregress iteration 8261 of 11000 
## beta = 
##   40.26720
##   -0.11545
## sigma2 =  127.27795
## 
## 
## MCMCregress iteration 8271 of 11000 
## beta = 
##   39.33661
##    0.36974
## sigma2 =  135.78647
## 
## 
## MCMCregress iteration 8281 of 11000 
## beta = 
##   39.51620
##    0.02221
## sigma2 =  126.46209
## 
## 
## MCMCregress iteration 8291 of 11000 
## beta = 
##   39.61945
##    0.36154
## sigma2 =  125.90316
## 
## 
## MCMCregress iteration 8301 of 11000 
## beta = 
##   36.82218
##    1.20667
## sigma2 =  127.00649
## 
## 
## MCMCregress iteration 8311 of 11000 
## beta = 
##   40.09989
##    0.07279
## sigma2 =  148.79798
## 
## 
## MCMCregress iteration 8321 of 11000 
## beta = 
##   37.78523
##    1.22479
## sigma2 =  142.87474
## 
## 
## MCMCregress iteration 8331 of 11000 
## beta = 
##   39.67424
##    0.31755
## sigma2 =  138.46243
## 
## 
## MCMCregress iteration 8341 of 11000 
## beta = 
##   39.78195
##    0.21818
## sigma2 =  140.62158
## 
## 
## MCMCregress iteration 8351 of 11000 
## beta = 
##   39.40998
##    0.29056
## sigma2 =  132.26628
## 
## 
## MCMCregress iteration 8361 of 11000 
## beta = 
##   39.93676
##    0.15617
## sigma2 =  119.27390
## 
## 
## MCMCregress iteration 8371 of 11000 
## beta = 
##   34.96739
##    1.90729
## sigma2 =  134.77356
## 
## 
## MCMCregress iteration 8381 of 11000 
## beta = 
##   35.12608
##    2.08986
## sigma2 =  137.50970
## 
## 
## MCMCregress iteration 8391 of 11000 
## beta = 
##   38.39392
##    0.60553
## sigma2 =  138.93889
## 
## 
## MCMCregress iteration 8401 of 11000 
## beta = 
##   39.13069
##    0.24551
## sigma2 =  133.79228
## 
## 
## MCMCregress iteration 8411 of 11000 
## beta = 
##   36.94337
##    0.99914
## sigma2 =  148.41299
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## 
## MCMCregress iteration 8421 of 11000 
## beta = 
##   36.95985
##    1.34297
## sigma2 =  127.06690
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## 
## MCMCregress iteration 8431 of 11000 
## beta = 
##   38.96809
##    0.66597
## sigma2 =  140.63327
## 
## 
## MCMCregress iteration 8441 of 11000 
## beta = 
##   39.53635
##    0.06277
## sigma2 =  123.95693
## 
## 
## MCMCregress iteration 8451 of 11000 
## beta = 
##   37.10246
##    1.39972
## sigma2 =  162.61532
## 
## 
## MCMCregress iteration 8461 of 11000 
## beta = 
##   38.94390
##    0.58174
## sigma2 =  135.59035
## 
## 
## MCMCregress iteration 8471 of 11000 
## beta = 
##   37.69734
##    1.27900
## sigma2 =  149.84624
## 
## 
## MCMCregress iteration 8481 of 11000 
## beta = 
##   38.12126
##    0.58216
## sigma2 =  123.06038
## 
## 
## MCMCregress iteration 8491 of 11000 
## beta = 
##   37.84674
##    0.87864
## sigma2 =  138.43553
## 
## 
## MCMCregress iteration 8501 of 11000 
## beta = 
##   38.85001
##    0.51032
## sigma2 =  125.32921
## 
## 
## MCMCregress iteration 8511 of 11000 
## beta = 
##   39.79136
##   -0.06714
## sigma2 =  112.30914
## 
## 
## MCMCregress iteration 8521 of 11000 
## beta = 
##   38.62599
##    0.55972
## sigma2 =  132.79198
## 
## 
## MCMCregress iteration 8531 of 11000 
## beta = 
##   39.03966
##    0.12402
## sigma2 =  120.74975
## 
## 
## MCMCregress iteration 8541 of 11000 
## beta = 
##   37.41527
##    1.09282
## sigma2 =  128.45430
## 
## 
## MCMCregress iteration 8551 of 11000 
## beta = 
##   35.83229
##    1.74460
## sigma2 =  139.99444
## 
## 
## MCMCregress iteration 8561 of 11000 
## beta = 
##   38.33316
##    0.85411
## sigma2 =  130.92853
## 
## 
## MCMCregress iteration 8571 of 11000 
## beta = 
##   38.28920
##    0.82243
## sigma2 =  122.26048
## 
## 
## MCMCregress iteration 8581 of 11000 
## beta = 
##   39.97455
##    0.44547
## sigma2 =  140.78338
## 
## 
## MCMCregress iteration 8591 of 11000 
## beta = 
##   37.85912
##    0.82532
## sigma2 =  123.12822
## 
## 
## MCMCregress iteration 8601 of 11000 
## beta = 
##   40.92292
##    0.13010
## sigma2 =  126.29133
## 
## 
## MCMCregress iteration 8611 of 11000 
## beta = 
##   38.96665
##    0.45415
## sigma2 =  122.45716
## 
## 
## MCMCregress iteration 8621 of 11000 
## beta = 
##   38.30725
##    1.24974
## sigma2 =  130.21234
## 
## 
## MCMCregress iteration 8631 of 11000 
## beta = 
##   39.01956
##    0.45704
## sigma2 =  132.22919
## 
## 
## MCMCregress iteration 8641 of 11000 
## beta = 
##   37.95518
##    0.79620
## sigma2 =  142.08714
## 
## 
## MCMCregress iteration 8651 of 11000 
## beta = 
##   39.89795
##    0.27495
## sigma2 =  119.74042
## 
## 
## MCMCregress iteration 8661 of 11000 
## beta = 
##   38.97573
##    0.48586
## sigma2 =  134.65370
## 
## 
## MCMCregress iteration 8671 of 11000 
## beta = 
##   37.06848
##    1.21746
## sigma2 =  126.28529
## 
## 
## MCMCregress iteration 8681 of 11000 
## beta = 
##   36.92321
##    1.06017
## sigma2 =  139.02643
## 
## 
## MCMCregress iteration 8691 of 11000 
## beta = 
##   39.58088
##   -0.04660
## sigma2 =  125.65533
## 
## 
## MCMCregress iteration 8701 of 11000 
## beta = 
##   38.14387
##    0.57860
## sigma2 =  127.22370
## 
## 
## MCMCregress iteration 8711 of 11000 
## beta = 
##   38.66102
##    0.35348
## sigma2 =  132.33400
## 
## 
## MCMCregress iteration 8721 of 11000 
## beta = 
##   39.68470
##    0.03644
## sigma2 =  133.26107
## 
## 
## MCMCregress iteration 8731 of 11000 
## beta = 
##   36.57741
##    1.18867
## sigma2 =  133.42372
## 
## 
## MCMCregress iteration 8741 of 11000 
## beta = 
##   39.06376
##    0.05657
## sigma2 =  136.86691
## 
## 
## MCMCregress iteration 8751 of 11000 
## beta = 
##   36.60089
##    1.55027
## sigma2 =  132.41685
## 
## 
## MCMCregress iteration 8761 of 11000 
## beta = 
##   39.78082
##    0.43149
## sigma2 =  126.92335
## 
## 
## MCMCregress iteration 8771 of 11000 
## beta = 
##   37.29867
##    1.22857
## sigma2 =  138.95265
## 
## 
## MCMCregress iteration 8781 of 11000 
## beta = 
##   39.24966
##    0.37408
## sigma2 =  118.44029
## 
## 
## MCMCregress iteration 8791 of 11000 
## beta = 
##   39.04952
##    0.64023
## sigma2 =  116.89196
## 
## 
## MCMCregress iteration 8801 of 11000 
## beta = 
##   38.73966
##    0.40745
## sigma2 =  131.69253
## 
## 
## MCMCregress iteration 8811 of 11000 
## beta = 
##   39.93507
##    0.60777
## sigma2 =  122.26526
## 
## 
## MCMCregress iteration 8821 of 11000 
## beta = 
##   36.99841
##    1.16467
## sigma2 =  160.89480
## 
## 
## MCMCregress iteration 8831 of 11000 
## beta = 
##   39.47171
##    0.63318
## sigma2 =  126.63497
## 
## 
## MCMCregress iteration 8841 of 11000 
## beta = 
##   37.43788
##    1.17974
## sigma2 =  135.46177
## 
## 
## MCMCregress iteration 8851 of 11000 
## beta = 
##   38.31048
##    0.70886
## sigma2 =  138.16530
## 
## 
## MCMCregress iteration 8861 of 11000 
## beta = 
##   38.30059
##    1.02725
## sigma2 =  139.19621
## 
## 
## MCMCregress iteration 8871 of 11000 
## beta = 
##   37.40122
##    0.72296
## sigma2 =  130.48678
## 
## 
## MCMCregress iteration 8881 of 11000 
## beta = 
##   39.06690
##    0.40783
## sigma2 =  117.69512
## 
## 
## MCMCregress iteration 8891 of 11000 
## beta = 
##   38.66063
##    0.35186
## sigma2 =  133.28332
## 
## 
## MCMCregress iteration 8901 of 11000 
## beta = 
##   38.98628
##    0.84418
## sigma2 =  139.10260
## 
## 
## MCMCregress iteration 8911 of 11000 
## beta = 
##   39.39431
##    0.37339
## sigma2 =  131.86489
## 
## 
## MCMCregress iteration 8921 of 11000 
## beta = 
##   38.59778
##    0.93219
## sigma2 =  131.67946
## 
## 
## MCMCregress iteration 8931 of 11000 
## beta = 
##   37.46775
##    0.89861
## sigma2 =  124.26239
## 
## 
## MCMCregress iteration 8941 of 11000 
## beta = 
##   37.34671
##    1.30456
## sigma2 =  129.82971
## 
## 
## MCMCregress iteration 8951 of 11000 
## beta = 
##   38.53589
##    0.24680
## sigma2 =  127.84798
## 
## 
## MCMCregress iteration 8961 of 11000 
## beta = 
##   38.10731
##    0.77768
## sigma2 =  135.67055
## 
## 
## MCMCregress iteration 8971 of 11000 
## beta = 
##   38.73847
##    0.54634
## sigma2 =  137.89149
## 
## 
## MCMCregress iteration 8981 of 11000 
## beta = 
##   38.71139
##    0.87543
## sigma2 =  129.07782
## 
## 
## MCMCregress iteration 8991 of 11000 
## beta = 
##   38.24897
##    0.55275
## sigma2 =  137.00169
## 
## 
## MCMCregress iteration 9001 of 11000 
## beta = 
##   38.02473
##    0.48307
## sigma2 =  142.06941
## 
## 
## MCMCregress iteration 9011 of 11000 
## beta = 
##   37.66692
##    0.87734
## sigma2 =  137.94012
## 
## 
## MCMCregress iteration 9021 of 11000 
## beta = 
##   39.88940
##    0.07696
## sigma2 =  135.97949
## 
## 
## MCMCregress iteration 9031 of 11000 
## beta = 
##   39.08563
##    0.66467
## sigma2 =  136.11979
## 
## 
## MCMCregress iteration 9041 of 11000 
## beta = 
##   39.17553
##    0.27946
## sigma2 =  130.21203
## 
## 
## MCMCregress iteration 9051 of 11000 
## beta = 
##   39.59992
##    0.27493
## sigma2 =  127.88371
## 
## 
## MCMCregress iteration 9061 of 11000 
## beta = 
##   38.88194
##    0.65085
## sigma2 =  121.24702
## 
## 
## MCMCregress iteration 9071 of 11000 
## beta = 
##   38.17678
##    0.70766
## sigma2 =  123.81583
## 
## 
## MCMCregress iteration 9081 of 11000 
## beta = 
##   36.41916
##    1.36372
## sigma2 =  133.56038
## 
## 
## MCMCregress iteration 9091 of 11000 
## beta = 
##   38.27944
##    0.81041
## sigma2 =  137.70053
## 
## 
## MCMCregress iteration 9101 of 11000 
## beta = 
##   39.73718
##    0.51567
## sigma2 =  125.29583
## 
## 
## MCMCregress iteration 9111 of 11000 
## beta = 
##   37.87485
##    0.64720
## sigma2 =  123.92272
## 
## 
## MCMCregress iteration 9121 of 11000 
## beta = 
##   39.18184
##    0.64760
## sigma2 =  131.50826
## 
## 
## MCMCregress iteration 9131 of 11000 
## beta = 
##   37.46106
##    1.24563
## sigma2 =  122.03801
## 
## 
## MCMCregress iteration 9141 of 11000 
## beta = 
##   37.49607
##    0.87125
## sigma2 =  125.19142
## 
## 
## MCMCregress iteration 9151 of 11000 
## beta = 
##   38.24321
##    0.59200
## sigma2 =  148.59749
## 
## 
## MCMCregress iteration 9161 of 11000 
## beta = 
##   37.78579
##    1.23723
## sigma2 =  142.32892
## 
## 
## MCMCregress iteration 9171 of 11000 
## beta = 
##   38.52707
##    0.90736
## sigma2 =  140.20570
## 
## 
## MCMCregress iteration 9181 of 11000 
## beta = 
##   39.95321
##    0.10305
## sigma2 =  133.15899
## 
## 
## MCMCregress iteration 9191 of 11000 
## beta = 
##   37.65864
##    0.70075
## sigma2 =  124.37526
## 
## 
## MCMCregress iteration 9201 of 11000 
## beta = 
##   38.24529
##    0.90275
## sigma2 =  146.92745
## 
## 
## MCMCregress iteration 9211 of 11000 
## beta = 
##   37.10669
##    1.37255
## sigma2 =  147.12121
## 
## 
## MCMCregress iteration 9221 of 11000 
## beta = 
##   40.01673
##    0.29436
## sigma2 =  142.31762
## 
## 
## MCMCregress iteration 9231 of 11000 
## beta = 
##   37.26603
##    1.02512
## sigma2 =  129.68145
## 
## 
## MCMCregress iteration 9241 of 11000 
## beta = 
##   37.67099
##    0.95979
## sigma2 =  133.31514
## 
## 
## MCMCregress iteration 9251 of 11000 
## beta = 
##   38.17319
##    0.56232
## sigma2 =  139.46619
## 
## 
## MCMCregress iteration 9261 of 11000 
## beta = 
##   38.50914
##    0.69669
## sigma2 =  144.47135
## 
## 
## MCMCregress iteration 9271 of 11000 
## beta = 
##   38.37852
##    0.81700
## sigma2 =  145.65634
## 
## 
## MCMCregress iteration 9281 of 11000 
## beta = 
##   38.45848
##    1.22069
## sigma2 =  125.77285
## 
## 
## MCMCregress iteration 9291 of 11000 
## beta = 
##   39.20865
##    0.51901
## sigma2 =  140.64151
## 
## 
## MCMCregress iteration 9301 of 11000 
## beta = 
##   39.71277
##    0.30475
## sigma2 =  141.11769
## 
## 
## MCMCregress iteration 9311 of 11000 
## beta = 
##   38.66330
##    0.83575
## sigma2 =  133.46035
## 
## 
## MCMCregress iteration 9321 of 11000 
## beta = 
##   37.25805
##    1.17268
## sigma2 =  132.22074
## 
## 
## MCMCregress iteration 9331 of 11000 
## beta = 
##   37.52301
##    1.13308
## sigma2 =  132.46038
## 
## 
## MCMCregress iteration 9341 of 11000 
## beta = 
##   39.05702
##    0.77397
## sigma2 =  131.08893
## 
## 
## MCMCregress iteration 9351 of 11000 
## beta = 
##   37.02239
##    1.13894
## sigma2 =  127.81834
## 
## 
## MCMCregress iteration 9361 of 11000 
## beta = 
##   38.18725
##    0.84167
## sigma2 =  141.02205
## 
## 
## MCMCregress iteration 9371 of 11000 
## beta = 
##   36.25010
##    1.46113
## sigma2 =  125.79446
## 
## 
## MCMCregress iteration 9381 of 11000 
## beta = 
##   38.05231
##    1.04367
## sigma2 =  115.43265
## 
## 
## MCMCregress iteration 9391 of 11000 
## beta = 
##   39.01242
##    0.57825
## sigma2 =  131.09214
## 
## 
## MCMCregress iteration 9401 of 11000 
## beta = 
##   39.87900
##   -0.00187
## sigma2 =  128.70482
## 
## 
## MCMCregress iteration 9411 of 11000 
## beta = 
##   37.30860
##    1.36394
## sigma2 =  131.75549
## 
## 
## MCMCregress iteration 9421 of 11000 
## beta = 
##   38.65514
##    0.41469
## sigma2 =  145.99098
## 
## 
## MCMCregress iteration 9431 of 11000 
## beta = 
##   37.88137
##    0.75913
## sigma2 =  127.72226
## 
## 
## MCMCregress iteration 9441 of 11000 
## beta = 
##   39.17051
##    0.44290
## sigma2 =  122.27613
## 
## 
## MCMCregress iteration 9451 of 11000 
## beta = 
##   38.93403
##    0.64284
## sigma2 =  135.92234
## 
## 
## MCMCregress iteration 9461 of 11000 
## beta = 
##   38.92986
##    0.29808
## sigma2 =  125.74726
## 
## 
## MCMCregress iteration 9471 of 11000 
## beta = 
##   39.28359
##    0.55299
## sigma2 =  128.30815
## 
## 
## MCMCregress iteration 9481 of 11000 
## beta = 
##   37.73280
##    0.63693
## sigma2 =  134.04341
## 
## 
## MCMCregress iteration 9491 of 11000 
## beta = 
##   39.03310
##    0.59500
## sigma2 =  130.71428
## 
## 
## MCMCregress iteration 9501 of 11000 
## beta = 
##   37.55732
##    0.88561
## sigma2 =  130.86182
## 
## 
## MCMCregress iteration 9511 of 11000 
## beta = 
##   37.22036
##    1.14208
## sigma2 =  129.43137
## 
## 
## MCMCregress iteration 9521 of 11000 
## beta = 
##   39.31727
##    0.22646
## sigma2 =  133.74349
## 
## 
## MCMCregress iteration 9531 of 11000 
## beta = 
##   38.75153
##    0.37013
## sigma2 =  134.01970
## 
## 
## MCMCregress iteration 9541 of 11000 
## beta = 
##   37.97690
##    0.50422
## sigma2 =  150.68954
## 
## 
## MCMCregress iteration 9551 of 11000 
## beta = 
##   39.85222
##    0.20823
## sigma2 =  130.78552
## 
## 
## MCMCregress iteration 9561 of 11000 
## beta = 
##   38.56250
##    0.28314
## sigma2 =  134.49974
## 
## 
## MCMCregress iteration 9571 of 11000 
## beta = 
##   38.51429
##    0.51435
## sigma2 =  149.48251
## 
## 
## MCMCregress iteration 9581 of 11000 
## beta = 
##   37.77605
##    1.18311
## sigma2 =  130.63587
## 
## 
## MCMCregress iteration 9591 of 11000 
## beta = 
##   36.05409
##    1.55002
## sigma2 =  140.80132
## 
## 
## MCMCregress iteration 9601 of 11000 
## beta = 
##   39.46079
##    0.45251
## sigma2 =  128.31633
## 
## 
## MCMCregress iteration 9611 of 11000 
## beta = 
##   38.39282
##    0.89045
## sigma2 =  132.53181
## 
## 
## MCMCregress iteration 9621 of 11000 
## beta = 
##   38.04489
##    0.97551
## sigma2 =  135.98523
## 
## 
## MCMCregress iteration 9631 of 11000 
## beta = 
##   38.05197
##    0.78948
## sigma2 =  145.46198
## 
## 
## MCMCregress iteration 9641 of 11000 
## beta = 
##   40.68576
##   -0.12340
## sigma2 =  129.69517
## 
## 
## MCMCregress iteration 9651 of 11000 
## beta = 
##   37.74493
##    1.25213
## sigma2 =  136.23071
## 
## 
## MCMCregress iteration 9661 of 11000 
## beta = 
##   39.76858
##   -0.14931
## sigma2 =  134.61637
## 
## 
## MCMCregress iteration 9671 of 11000 
## beta = 
##   38.19865
##    0.44906
## sigma2 =  121.09620
## 
## 
## MCMCregress iteration 9681 of 11000 
## beta = 
##   39.32190
##    0.40906
## sigma2 =  126.17589
## 
## 
## MCMCregress iteration 9691 of 11000 
## beta = 
##   38.53954
##    0.84242
## sigma2 =  124.63752
## 
## 
## MCMCregress iteration 9701 of 11000 
## beta = 
##   37.37832
##    0.98532
## sigma2 =  129.76288
## 
## 
## MCMCregress iteration 9711 of 11000 
## beta = 
##   39.14391
##    0.42605
## sigma2 =  131.42056
## 
## 
## MCMCregress iteration 9721 of 11000 
## beta = 
##   38.26881
##    0.68525
## sigma2 =  138.84838
## 
## 
## MCMCregress iteration 9731 of 11000 
## beta = 
##   38.27314
##    0.61286
## sigma2 =  134.75892
## 
## 
## MCMCregress iteration 9741 of 11000 
## beta = 
##   39.09935
##    0.61833
## sigma2 =  145.89610
## 
## 
## MCMCregress iteration 9751 of 11000 
## beta = 
##   38.79187
##    0.68219
## sigma2 =  127.04556
## 
## 
## MCMCregress iteration 9761 of 11000 
## beta = 
##   37.10156
##    1.11429
## sigma2 =  128.55298
## 
## 
## MCMCregress iteration 9771 of 11000 
## beta = 
##   38.56521
##    0.58355
## sigma2 =  131.51810
## 
## 
## MCMCregress iteration 9781 of 11000 
## beta = 
##   37.55355
##    0.99145
## sigma2 =  162.82102
## 
## 
## MCMCregress iteration 9791 of 11000 
## beta = 
##   39.85959
##    0.02395
## sigma2 =  130.16390
## 
## 
## MCMCregress iteration 9801 of 11000 
## beta = 
##   37.83573
##    1.07737
## sigma2 =  121.40861
## 
## 
## MCMCregress iteration 9811 of 11000 
## beta = 
##   40.78750
##   -0.41501
## sigma2 =  127.83004
## 
## 
## MCMCregress iteration 9821 of 11000 
## beta = 
##   35.94980
##    1.38181
## sigma2 =  129.18135
## 
## 
## MCMCregress iteration 9831 of 11000 
## beta = 
##   39.27091
##    0.83479
## sigma2 =  143.38805
## 
## 
## MCMCregress iteration 9841 of 11000 
## beta = 
##   39.15836
##    0.47769
## sigma2 =  141.97146
## 
## 
## MCMCregress iteration 9851 of 11000 
## beta = 
##   37.28911
##    1.42312
## sigma2 =  130.23473
## 
## 
## MCMCregress iteration 9861 of 11000 
## beta = 
##   37.78280
##    0.64256
## sigma2 =  129.59908
## 
## 
## MCMCregress iteration 9871 of 11000 
## beta = 
##   38.46249
##    0.61656
## sigma2 =  130.74922
## 
## 
## MCMCregress iteration 9881 of 11000 
## beta = 
##   39.77415
##    0.39734
## sigma2 =  135.33543
## 
## 
## MCMCregress iteration 9891 of 11000 
## beta = 
##   36.96320
##    1.09055
## sigma2 =  122.86848
## 
## 
## MCMCregress iteration 9901 of 11000 
## beta = 
##   38.16421
##    0.58476
## sigma2 =  133.62685
## 
## 
## MCMCregress iteration 9911 of 11000 
## beta = 
##   38.23367
##    0.85945
## sigma2 =  137.20151
## 
## 
## MCMCregress iteration 9921 of 11000 
## beta = 
##   37.79066
##    1.05653
## sigma2 =  129.76817
## 
## 
## MCMCregress iteration 9931 of 11000 
## beta = 
##   38.56977
##    0.77260
## sigma2 =  147.37413
## 
## 
## MCMCregress iteration 9941 of 11000 
## beta = 
##   39.40534
##    0.49708
## sigma2 =  138.40222
## 
## 
## MCMCregress iteration 9951 of 11000 
## beta = 
##   37.96092
##    0.88042
## sigma2 =  139.73061
## 
## 
## MCMCregress iteration 9961 of 11000 
## beta = 
##   38.90287
##    0.84257
## sigma2 =  124.52150
## 
## 
## MCMCregress iteration 9971 of 11000 
## beta = 
##   40.00369
##    0.50630
## sigma2 =  125.24078
## 
## 
## MCMCregress iteration 9981 of 11000 
## beta = 
##   40.08552
##    0.17443
## sigma2 =  140.22584
## 
## 
## MCMCregress iteration 9991 of 11000 
## beta = 
##   39.10105
##    0.59007
## sigma2 =  123.62620
## 
## 
## MCMCregress iteration 10001 of 11000 
## beta = 
##   39.76575
##    0.09375
## sigma2 =  141.88600
## 
## 
## MCMCregress iteration 10011 of 11000 
## beta = 
##   41.11425
##   -0.30844
## sigma2 =  149.05810
## 
## 
## MCMCregress iteration 10021 of 11000 
## beta = 
##   38.59270
##    0.57965
## sigma2 =  127.46191
## 
## 
## MCMCregress iteration 10031 of 11000 
## beta = 
##   38.91261
##    0.39800
## sigma2 =  142.87238
## 
## 
## MCMCregress iteration 10041 of 11000 
## beta = 
##   39.22577
##    0.27560
## sigma2 =  138.54038
## 
## 
## MCMCregress iteration 10051 of 11000 
## beta = 
##   38.28463
##    0.48983
## sigma2 =  135.33981
## 
## 
## MCMCregress iteration 10061 of 11000 
## beta = 
##   37.69899
##    0.93208
## sigma2 =  130.54471
## 
## 
## MCMCregress iteration 10071 of 11000 
## beta = 
##   38.50223
##    0.71419
## sigma2 =  127.82217
## 
## 
## MCMCregress iteration 10081 of 11000 
## beta = 
##   37.95019
##    1.32236
## sigma2 =  122.41878
## 
## 
## MCMCregress iteration 10091 of 11000 
## beta = 
##   38.72307
##    0.77133
## sigma2 =  142.58163
## 
## 
## MCMCregress iteration 10101 of 11000 
## beta = 
##   38.50598
##    0.72287
## sigma2 =  139.14341
## 
## 
## MCMCregress iteration 10111 of 11000 
## beta = 
##   39.82232
##    0.39397
## sigma2 =  141.87479
## 
## 
## MCMCregress iteration 10121 of 11000 
## beta = 
##   39.72384
##    0.27544
## sigma2 =  136.80409
## 
## 
## MCMCregress iteration 10131 of 11000 
## beta = 
##   37.75628
##    0.64988
## sigma2 =  135.51166
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## 
## MCMCregress iteration 10141 of 11000 
## beta = 
##   38.45435
##    0.28073
## sigma2 =  132.60433
## 
## 
## MCMCregress iteration 10151 of 11000 
## beta = 
##   38.94691
##    0.26531
## sigma2 =  134.16606
## 
## 
## MCMCregress iteration 10161 of 11000 
## beta = 
##   37.23353
##    1.38029
## sigma2 =  142.72515
## 
## 
## MCMCregress iteration 10171 of 11000 
## beta = 
##   37.00044
##    1.04513
## sigma2 =  134.35088
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## 
## MCMCregress iteration 10181 of 11000 
## beta = 
##   37.46628
##    1.08607
## sigma2 =  132.03779
## 
## 
## MCMCregress iteration 10191 of 11000 
## beta = 
##   39.19829
##    0.65555
## sigma2 =  131.23317
## 
## 
## MCMCregress iteration 10201 of 11000 
## beta = 
##   39.69246
##    0.02587
## sigma2 =  126.03746
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## MCMCregress iteration 10211 of 11000 
## beta = 
##   39.50263
##   -0.07824
## sigma2 =  128.47664
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## 
## MCMCregress iteration 10221 of 11000 
## beta = 
##   38.42777
##    0.64865
## sigma2 =  141.81714
## 
## 
## MCMCregress iteration 10231 of 11000 
## beta = 
##   38.81683
##    0.50362
## sigma2 =  129.34436
## 
## 
## MCMCregress iteration 10241 of 11000 
## beta = 
##   38.08409
##    0.77764
## sigma2 =  135.07010
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## 
## MCMCregress iteration 10251 of 11000 
## beta = 
##   38.59002
##    0.36825
## sigma2 =  136.64103
## 
## 
## MCMCregress iteration 10261 of 11000 
## beta = 
##   39.54700
##    0.41741
## sigma2 =  135.91150
## 
## 
## MCMCregress iteration 10271 of 11000 
## beta = 
##   38.93891
##    0.22238
## sigma2 =  147.81662
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## 
## MCMCregress iteration 10281 of 11000 
## beta = 
##   36.77314
##    1.06870
## sigma2 =  132.69489
## 
## 
## MCMCregress iteration 10291 of 11000 
## beta = 
##   40.58122
##   -0.22175
## sigma2 =  125.70969
## 
## 
## MCMCregress iteration 10301 of 11000 
## beta = 
##   37.67283
##    0.78029
## sigma2 =  123.36979
## 
## 
## MCMCregress iteration 10311 of 11000 
## beta = 
##   38.58365
##    0.70318
## sigma2 =  143.76267
## 
## 
## MCMCregress iteration 10321 of 11000 
## beta = 
##   39.77981
##    0.31577
## sigma2 =  121.85095
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## MCMCregress iteration 10331 of 11000 
## beta = 
##   38.16730
##    0.61439
## sigma2 =  129.63834
## 
## 
## MCMCregress iteration 10341 of 11000 
## beta = 
##   40.35801
##    0.02995
## sigma2 =  133.06988
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## 
## MCMCregress iteration 10351 of 11000 
## beta = 
##   37.45940
##    0.93600
## sigma2 =  139.37637
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## MCMCregress iteration 10361 of 11000 
## beta = 
##   39.07269
##    0.33374
## sigma2 =  115.51074
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## 
## MCMCregress iteration 10371 of 11000 
## beta = 
##   39.64096
##    0.48616
## sigma2 =  127.28064
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## MCMCregress iteration 10381 of 11000 
## beta = 
##   38.78194
##    0.21382
## sigma2 =  136.19705
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## MCMCregress iteration 10391 of 11000 
## beta = 
##   39.57891
##    0.54275
## sigma2 =  135.24572
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## 
## MCMCregress iteration 10401 of 11000 
## beta = 
##   37.46282
##    0.76909
## sigma2 =  136.18094
## 
## 
## MCMCregress iteration 10411 of 11000 
## beta = 
##   38.53841
##    0.88735
## sigma2 =  139.60645
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## MCMCregress iteration 10421 of 11000 
## beta = 
##   40.44766
##    0.03991
## sigma2 =  143.74028
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## MCMCregress iteration 10431 of 11000 
## beta = 
##   39.50803
##    0.37020
## sigma2 =  131.41948
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## 
## MCMCregress iteration 10441 of 11000 
## beta = 
##   38.36085
##    0.93792
## sigma2 =  133.39007
## 
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## MCMCregress iteration 10451 of 11000 
## beta = 
##   38.02156
##    0.71153
## sigma2 =  117.82118
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## MCMCregress iteration 10461 of 11000 
## beta = 
##   40.67877
##    0.06655
## sigma2 =  130.41065
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## 
## MCMCregress iteration 10471 of 11000 
## beta = 
##   38.67601
##    0.79557
## sigma2 =  117.77008
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## 
## MCMCregress iteration 10481 of 11000 
## beta = 
##   37.42186
##    0.64612
## sigma2 =  151.90835
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## MCMCregress iteration 10491 of 11000 
## beta = 
##   38.58524
##    0.58562
## sigma2 =  127.47170
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## MCMCregress iteration 10501 of 11000 
## beta = 
##   38.05282
##    0.91198
## sigma2 =  142.11678
## 
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## MCMCregress iteration 10511 of 11000 
## beta = 
##   37.76698
##    0.60661
## sigma2 =  133.04517
## 
## 
## MCMCregress iteration 10521 of 11000 
## beta = 
##   38.08722
##    0.47563
## sigma2 =  136.80500
## 
## 
## MCMCregress iteration 10531 of 11000 
## beta = 
##   39.07660
##    0.39475
## sigma2 =  130.17235
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## 
## MCMCregress iteration 10541 of 11000 
## beta = 
##   38.79121
##    0.34870
## sigma2 =  129.19188
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## 
## MCMCregress iteration 10551 of 11000 
## beta = 
##   36.96843
##    0.96229
## sigma2 =  136.87840
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## MCMCregress iteration 10561 of 11000 
## beta = 
##   37.60981
##    1.14446
## sigma2 =  134.47584
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## MCMCregress iteration 10571 of 11000 
## beta = 
##   36.07294
##    1.75519
## sigma2 =  149.10486
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## MCMCregress iteration 10581 of 11000 
## beta = 
##   38.91174
##    0.43344
## sigma2 =  122.87050
## 
## 
## MCMCregress iteration 10591 of 11000 
## beta = 
##   38.52900
##    0.97843
## sigma2 =  130.21418
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## 
## MCMCregress iteration 10601 of 11000 
## beta = 
##   39.42976
##    0.28336
## sigma2 =  111.65502
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## 
## MCMCregress iteration 10611 of 11000 
## beta = 
##   39.11843
##    0.52429
## sigma2 =  123.22294
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## 
## MCMCregress iteration 10621 of 11000 
## beta = 
##   40.29229
##   -0.06928
## sigma2 =  121.99847
## 
## 
## MCMCregress iteration 10631 of 11000 
## beta = 
##   38.67114
##    1.05728
## sigma2 =  134.70814
## 
## 
## MCMCregress iteration 10641 of 11000 
## beta = 
##   38.84161
##    0.54834
## sigma2 =  138.25316
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## MCMCregress iteration 10651 of 11000 
## beta = 
##   38.05180
##    0.84808
## sigma2 =  138.71274
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## MCMCregress iteration 10661 of 11000 
## beta = 
##   39.82863
##    0.41544
## sigma2 =  126.39843
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## 
## MCMCregress iteration 10671 of 11000 
## beta = 
##   40.46840
##   -0.11834
## sigma2 =  138.51172
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## MCMCregress iteration 10681 of 11000 
## beta = 
##   38.21153
##    1.22134
## sigma2 =  126.61821
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## 
## MCMCregress iteration 10691 of 11000 
## beta = 
##   39.71723
##    0.09731
## sigma2 =  133.14957
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## 
## MCMCregress iteration 10701 of 11000 
## beta = 
##   36.16148
##    1.58739
## sigma2 =  143.99364
## 
## 
## MCMCregress iteration 10711 of 11000 
## beta = 
##   38.40656
##    0.41974
## sigma2 =  126.81092
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## 
## MCMCregress iteration 10721 of 11000 
## beta = 
##   38.82340
##    0.64726
## sigma2 =  131.52120
## 
## 
## MCMCregress iteration 10731 of 11000 
## beta = 
##   37.89373
##    0.96667
## sigma2 =  124.50003
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## 
## MCMCregress iteration 10741 of 11000 
## beta = 
##   37.55989
##    0.82760
## sigma2 =  128.84470
## 
## 
## MCMCregress iteration 10751 of 11000 
## beta = 
##   39.37078
##    0.20898
## sigma2 =  140.67033
## 
## 
## MCMCregress iteration 10761 of 11000 
## beta = 
##   38.84146
##    0.71447
## sigma2 =  121.77453
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## 
## MCMCregress iteration 10771 of 11000 
## beta = 
##   38.75080
##    1.00771
## sigma2 =  129.68508
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## 
## MCMCregress iteration 10781 of 11000 
## beta = 
##   37.46667
##    0.65264
## sigma2 =  136.63050
## 
## 
## MCMCregress iteration 10791 of 11000 
## beta = 
##   37.36068
##    0.83134
## sigma2 =  121.62215
## 
## 
## MCMCregress iteration 10801 of 11000 
## beta = 
##   38.82190
##    0.73728
## sigma2 =  133.91706
## 
## 
## MCMCregress iteration 10811 of 11000 
## beta = 
##   38.28748
##    0.72061
## sigma2 =  133.61592
## 
## 
## MCMCregress iteration 10821 of 11000 
## beta = 
##   38.34277
##    0.55097
## sigma2 =  126.73940
## 
## 
## MCMCregress iteration 10831 of 11000 
## beta = 
##   38.54855
##    0.57745
## sigma2 =  137.34656
## 
## 
## MCMCregress iteration 10841 of 11000 
## beta = 
##   38.65406
##    0.72098
## sigma2 =  137.57573
## 
## 
## MCMCregress iteration 10851 of 11000 
## beta = 
##   39.51947
##    0.03700
## sigma2 =  131.60430
## 
## 
## MCMCregress iteration 10861 of 11000 
## beta = 
##   37.59779
##    0.88532
## sigma2 =  134.48487
## 
## 
## MCMCregress iteration 10871 of 11000 
## beta = 
##   38.43772
##    0.41710
## sigma2 =  129.98655
## 
## 
## MCMCregress iteration 10881 of 11000 
## beta = 
##   39.55639
##    0.47286
## sigma2 =  134.02380
## 
## 
## MCMCregress iteration 10891 of 11000 
## beta = 
##   38.15379
##    0.73680
## sigma2 =  131.85296
## 
## 
## MCMCregress iteration 10901 of 11000 
## beta = 
##   39.83996
##    0.13125
## sigma2 =  130.02210
## 
## 
## MCMCregress iteration 10911 of 11000 
## beta = 
##   38.20015
##    0.82186
## sigma2 =  133.90803
## 
## 
## MCMCregress iteration 10921 of 11000 
## beta = 
##   40.22437
##    0.00831
## sigma2 =  134.35696
## 
## 
## MCMCregress iteration 10931 of 11000 
## beta = 
##   38.61245
##    0.82235
## sigma2 =  128.19427
## 
## 
## MCMCregress iteration 10941 of 11000 
## beta = 
##   39.01061
##    0.56156
## sigma2 =  141.48396
## 
## 
## MCMCregress iteration 10951 of 11000 
## beta = 
##   38.41508
##    0.94816
## sigma2 =  142.71731
## 
## 
## MCMCregress iteration 10961 of 11000 
## beta = 
##   40.69073
##   -0.22467
## sigma2 =  127.33435
## 
## 
## MCMCregress iteration 10971 of 11000 
## beta = 
##   37.60150
##    0.81172
## sigma2 =  129.53709
## 
## 
## MCMCregress iteration 10981 of 11000 
## beta = 
##   38.49362
##    0.86493
## sigma2 =  120.96099
## 
## 
## MCMCregress iteration 10991 of 11000 
## beta = 
##   37.15306
##    1.07951
## sigma2 =  137.79680
plot(posterior, col= "red")

raftery.diag(posterior)
## 
## Quantile (q) = 0.025
## Accuracy (r) = +/- 0.005
## Probability (s) = 0.95 
##                                                    
##              Burn-in  Total Lower bound  Dependence
##              (M)      (N)   (Nmin)       factor (I)
##  (Intercept) 2        3710  3746         0.990     
##  congviec    2        3636  3746         0.971     
##  sigma2      2        3802  3746         1.010
summary(posterior)                     
## 
## Iterations = 1001:11000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 10000 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                 Mean     SD Naive SE Time-series SE
## (Intercept)  38.5685 1.1081 0.011081       0.011081
## congviec      0.6426 0.4364 0.004364       0.004364
## sigma2      133.6371 8.3022 0.083022       0.083022
## 
## 2. Quantiles for each variable:
## 
##                 2.5%      25%      50%      75%   97.5%
## (Intercept)  36.3920  37.8219  38.5772  39.3126  40.752
## congviec     -0.2028   0.3517   0.6388   0.9274   1.499
## sigma2      118.2541 127.8499 133.3116 139.1302 150.690
apply(posterior, 2, quantile, probs=c(0.025, 0.5, 0.975))
##       (Intercept)   congviec   sigma2
## 2.5%     36.39197 -0.2028191 118.2541
## 50%      38.57717  0.6387640 133.3116
## 97.5%    40.75189  1.4985906 150.6900
library(nnet)
require(brms)
## Loading required package: brms
## Loading 'brms' package (version 2.20.4). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').
## 
## Attaching package: 'brms'
## The following objects are masked from 'package:MCMCpack':
## 
##     ddirichlet, rdirichlet
## The following objects are masked from 'package:rstanarm':
## 
##     dirichlet, exponential, get_y, lasso, ngrps
## The following object is masked from 'package:stats':
## 
##     ar
m.2 = multinom(uwes_tol ~ congviec, data=thuan)
## # weights:  129 (84 variable)
## initial  value 2000.958462 
## iter  10 value 1790.232977
## iter  20 value 1732.824691
## iter  30 value 1703.693118
## iter  40 value 1698.904538
## iter  50 value 1698.099745
## iter  60 value 1696.769044
## iter  70 value 1696.596122
## iter  80 value 1696.569898
## final  value 1696.569837 
## converged
summary(m.2)
## Call:
## multinom(formula = uwes_tol ~ congviec, data = thuan)
## 
## Coefficients:
##    (Intercept)  congviec
## 4   -12.415962  11.92546
## 9   -12.793798  11.59141
## 10   36.474126 -36.47803
## 14  -12.793657  11.59134
## 15  -16.857851  13.34498
## 18   36.478099 -36.47406
## 19  -12.793755  11.59150
## 20  -13.148145  12.06081
## 21  -14.098698  12.40738
## 22  -10.790713  11.09445
## 23  -11.958709  11.85146
## 24  -11.696678  11.59215
## 25  -13.059031  12.18313
## 26   -9.923890  10.72781
## 27   -9.925637  11.50991
## 28  -12.423205  12.13572
## 29  -12.793846  11.59142
## 30  -13.906590  12.56766
## 31  -14.800612  12.40989
## 32   -9.077899  10.53196
## 33   -9.494699  10.21977
## 34  -10.674790  11.32248
## 35  -11.186001  11.59216
## 36  -10.779266  11.88378
## 37  -13.906590  12.56765
## 38  -13.148142  12.06080
## 39   42.716244 -42.02292
## 40  -12.366618  12.18351
## 41  -12.415964  11.92546
## 42  -11.003298  11.59206
## 43   -9.981584  11.32248
## 44  -11.757348  12.00484
## 45  -10.615646  12.20892
## 46  -11.171489  11.74780
## 47   -9.657097  11.24237
## 48  -12.049120  12.06060
## 49  -11.173713  11.74867
## 50  -11.729698  12.13562
## 51  -13.183312  12.40767
## 52   -9.820029  11.52003
## 53  -12.415963  11.92546
## 54  -10.508843  12.06064
## 
## Std. Errors:
##    (Intercept)  congviec
## 4    1.0263387 0.5187729
## 9    1.7029334 0.8281014
## 10   0.5005233 0.5005233
## 14   1.7029445 0.8281278
## 15   1.6701554 0.5127741
## 18   0.4995301 0.4995301
## 19   1.7027531 0.8280026
## 20   1.2426016 0.5594275
## 21   1.3403124 0.5317962
## 22   1.0703094 0.6617628
## 23   0.9059589 0.4935835
## 24   1.0289216 0.5669590
## 25   1.0566020 0.4948242
## 26   0.9761889 0.6670539
## 27   0.5695060 0.4237333
## 28   0.8463756 0.4517729
## 29   1.7029676 0.8281144
## 30   1.0444659 0.4573424
## 31   1.8586796 0.6542475
## 32   0.7917886 0.5878757
## 33   1.1631273 0.8524724
## 34   0.8460814 0.5333055
## 35   0.8309852 0.4986750
## 36   0.5785583 0.4092300
## 37   1.0444699 0.4573433
## 38   1.2426159 0.5594335
## 39   0.4330285 0.4330285
## 40   0.7936886 0.4373673
## 41   1.0263419 0.5187740
## 42   0.7735567 0.4800753
## 43   0.6536432 0.4613450
## 44   0.7326760 0.4362950
## 45   0.4729905 0.3825030
## 46   0.7266969 0.4531362
## 47   0.6191693 0.4542058
## 48   0.7805169 0.4430451
## 49   0.7267884 0.4530952
## 50   0.6554005 0.4134776
## 51   0.8986786 0.4424588
## 52   0.5496932 0.4176981
## 53   1.0263405 0.5187736
## 54   0.4918504 0.3878595
## 
## Residual Deviance: 3393.14 
## AIC: 3561.14

#exp(coefficients(m.2)) #exp(confint(m.2))

library(bayesplot)
## This is bayesplot version 1.10.0
## - Online documentation and vignettes at mc-stan.org/bayesplot
## - bayesplot theme set to bayesplot::theme_default()
##    * Does _not_ affect other ggplot2 plots
##    * See ?bayesplot_theme_set for details on theme setting
## 
## Attaching package: 'bayesplot'
## The following object is masked from 'package:brms':
## 
##     rhat
library(ggplot2)

p = ggplot(thuan, aes(x = uwes_tol, group=congviec))
p + geom_density(aes(fill = congviec), alpha=0.5) + theme_light(base_size = 12)

library(rstan)
## Warning: package 'rstan' was built under R version 4.3.2
## Loading required package: StanHeaders
## 
## rstan version 2.32.3 (Stan version 2.26.1)
## For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores()).
## To avoid recompilation of unchanged Stan programs, we recommend calling
## rstan_options(auto_write = TRUE)
## For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,
## change `threads_per_chain` option:
## rstan_options(threads_per_chain = 1)
## Do not specify '-march=native' in 'LOCAL_CPPFLAGS' or a Makevars file
## 
## Attaching package: 'rstan'
## The following object is masked from 'package:coda':
## 
##     traceplot
## The following object is masked from 'package:tidyr':
## 
##     extract
library(shinystan)
## Loading required package: shiny
## 
## This is shinystan version 2.6.0
library(rstanarm)
library(psych)
## 
## Attaching package: 'psych'
## The following object is masked from 'package:rstan':
## 
##     lookup
## The following object is masked from 'package:brms':
## 
##     cs
## The following object is masked from 'package:rstanarm':
## 
##     logit
## The following object is masked from 'package:OpenMx':
## 
##     tr
## The following object is masked from 'package:lavaan':
## 
##     cor2cov
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(brms)
set.seed(123)
# Có Intercept
#  family = "poisson", prior = prior)

prior0 = get_prior(uwes_tol ~ congviec + gioi + congviec*gioi, family = gaussian, data=thuan)
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
bf.1 = brm(data=thuan, uwes1 ~ congviec + gioi + congviec*gioi, 
           prior0, family = gaussian, chains = 2, iter = 10)
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## Compiling Stan program...
## Start sampling
## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 3.4e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.34 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: WARNING: No variance estimation is
## Chain 1:          performed for num_warmup < 20
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## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
## Chain 2: 
## Chain 2: Gradient evaluation took 9e-06 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2: 
## Chain 2: 
## Chain 2: WARNING: No variance estimation is
## Chain 2:          performed for num_warmup < 20
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## Chain 2:
## Warning: There were 5 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is NA, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
summary(bf.1)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 5 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: uwes1 ~ congviec + gioi + congviec * gioi 
##    Data: thuan (Number of observations: 532) 
##   Draws: 2 chains, each with iter = 10; warmup = 5; thin = 1;
##          total post-warmup draws = 10
## 
## Population-Level Effects: 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        -0.06      2.23    -2.18     2.06   NA       NA       NA
## congviec          0.77      1.02    -0.20     1.74   NA       NA       NA
## gioi             -0.75      1.14    -1.84     0.34   NA       NA       NA
## congviec:gioi     0.12      1.12    -0.94     1.18   NA       NA       NA
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     4.41      1.12     3.35     5.47  Inf       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
bf.1$fit
## Inference for Stan model: anon_model.
## 2 chains, each with iter=10; warmup=5; thin=1; 
## post-warmup draws per chain=5, total post-warmup draws=10.
## 
##                     mean se_mean     sd     2.5%      25%      50%      75%
## b_Intercept        -0.06     NaN   2.23    -2.18    -2.18    -0.06     2.06
## b_congviec          0.77     NaN   1.02    -0.20    -0.20     0.77     1.74
## b_gioi             -0.75     NaN   1.14    -1.84    -1.84    -0.75     0.34
## b_congviec:gioi     0.12     NaN   1.12    -0.94    -0.94     0.12     1.18
## sigma               4.41     NaN   1.12     3.35     3.35     4.41     5.47
## lprior             -9.71     NaN   0.14    -9.85    -9.85    -9.71    -9.58
## lp__            -1547.87     NaN 111.59 -1653.73 -1653.73 -1547.87 -1442.01
##                    97.5% n_eff Rhat
## b_Intercept         2.06   NaN  Inf
## b_congviec          1.74   NaN  Inf
## b_gioi              0.34   NaN  Inf
## b_congviec:gioi     1.18   NaN  Inf
## sigma               5.47   NaN  Inf
## lprior             -9.58   NaN  Inf
## lp__            -1442.01   NaN  Inf
## 
## Samples were drawn using NUTS(diag_e) at Thu Nov 16 19:32:40 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at 
## convergence, Rhat=1).

Không Intercept

prior1 = get_prior(uwes_tol ~ congviec - 1, family = gaussian, data=thuan)
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
bf.2 = brm(data = thuan, uwes_tol ~ congviec-1, prior1, 
                family = gaussian, chains = 2, iter = 10)
## Found more than one class "family" in cache; using the first, from namespace 'lme4'
## Also defined by 'MatrixModels'
## Compiling Stan program...
## Start sampling
## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 9.9e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.99 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1: 
## Chain 1: 
## Chain 1: WARNING: No variance estimation is
## Chain 1:          performed for num_warmup < 20
## Chain 1: 
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## Chain 1: 
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## Chain 1:                0.002 seconds (Sampling)
## Chain 1:                0.003 seconds (Total)
## Chain 1: 
## 
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
## Chain 2: 
## Chain 2: Gradient evaluation took 2.3e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.23 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2: 
## Chain 2: 
## Chain 2: WARNING: No variance estimation is
## Chain 2:          performed for num_warmup < 20
## Chain 2: 
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## Chain 2: 
## Chain 2:  Elapsed Time: 0.001 seconds (Warm-up)
## Chain 2:                0.001 seconds (Sampling)
## Chain 2:                0.002 seconds (Total)
## Chain 2:
## Warning: There were 10 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is NA, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
summary(bf.2)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 10 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: uwes_tol ~ congviec - 1 
##    Data: thuan (Number of observations: 532) 
##   Draws: 2 chains, each with iter = 10; warmup = 5; thin = 1;
##          total post-warmup draws = 10
## 
## Population-Level Effects: 
##          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## congviec     1.12      0.64     0.51     1.73  Inf       NA       NA
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.45      0.01     0.44     0.46  Inf       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Vẽ biểu đồ

bf.2$fit
## Inference for Stan model: anon_model.
## 2 chains, each with iter=10; warmup=5; thin=1; 
## post-warmup draws per chain=5, total post-warmup draws=10.
## 
##                   mean se_mean       sd        2.5%         25%         50%
## b_congviec        1.12     NaN     0.64        0.51        0.51        1.12
## sigma             0.45    0.01     0.01        0.44        0.44        0.45
## lprior           -2.79     NaN     0.00       -2.79       -2.79       -2.79
## lp__       -2038169.10     NaN 27677.51 -2064426.30 -2064426.30 -2038169.10
##                    75%       97.5% n_eff Rhat
## b_congviec        1.73        1.73   NaN  Inf
## sigma             0.46        0.46     1  Inf
## lprior           -2.79       -2.79   NaN  Inf
## lp__       -2011911.91 -2011911.91   NaN  Inf
## 
## Samples were drawn using NUTS(diag_e) at Thu Nov 16 19:34:20 2023.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at 
## convergence, Rhat=1).
pairs(bf.2)

plot(bf.2, ignore_prior = T, theme = ggplot2::theme())

marginal_effects(bf.2, probs=c(0.05,0.95), conditions=congviec)
## Warning: Method 'marginal_effects' is deprecated. Please use
## 'conditional_effects' instead.
## Warning: Argument 'probs' is deprecated. Please use 'prob' instead.
## Warning: The following variables in 'conditions' are not part of the model:
## 'conditions'

kiểm tra bằng phương pháp khác

# launch_shinystan(bf.1, rstudio = getOption("shinystan.rstudio"))

Kiểm tra giả thuyết

#hypothesis(bf.2, "congviecAA > congviecCC", digits = 4)
#hypothesis(bf.2, "congviecBB > congviecCC", digits = 4)
#hypothesis(bf.2, "congviecEE > congviecCC", digits = 4)

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