Last updated: 2022-02-02

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Knit directory: Padgett-Dissertation/

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# Load packages & utility functions
source("code/load_packages.R")
source("code/load_utility_functions.R")
# environment options
options(scipen = 999, digits=3)

POOLS Data

library(readxl)
mydata <- read_excel("data/pools/POOLS_data_2020-11-16.xlsx")

use.var <- c(paste0("Q4_",c(3:5,9,11,15,18)), 
             paste0("Q5_",c(1:3,5:6,12)), 
             paste0("Q6_",c(2,5:8, 11)), 
             paste0("Q7_",c(2, 4:5, 7:8, 14))) 

# trichotomize
f <- function(x){
  y=numeric(length(x))
  for(i in 1:length(x)){
      if(x[i] < 3){
        y[i] = 1
      }
      if(x[i] == 3){
        y[i] = 2
      }
      if(x[i] > 3){
        y[i] = 3
      }
  }
  return(y)
}

mydata <- na.omit(mydata[, use.var]) 
mydata <- apply(mydata, 2, f) %>%
  as.data.frame()

psych::describe(
  mydata
)
      vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
Q4_3     1 490 1.62 0.65      2    1.53 1.48   1   3     2  0.57    -0.68 0.03
Q4_4     2 490 1.64 0.65      2    1.56 1.48   1   3     2  0.51    -0.71 0.03
Q4_5     3 490 1.52 0.68      1    1.40 0.00   1   3     2  0.92    -0.36 0.03
Q4_9     4 490 1.65 0.76      1    1.56 0.00   1   3     2  0.69    -0.96 0.03
Q4_11    5 490 1.64 0.72      1    1.55 0.00   1   3     2  0.66    -0.85 0.03
Q4_15    6 490 1.58 0.68      1    1.47 0.00   1   3     2  0.74    -0.59 0.03
Q4_18    7 490 1.52 0.63      1    1.43 0.00   1   3     2  0.81    -0.38 0.03
Q5_1     8 490 1.73 0.77      2    1.66 1.48   1   3     2  0.50    -1.16 0.03
Q5_2     9 490 2.00 0.86      2    2.00 1.48   1   3     2  0.00    -1.64 0.04
Q5_3    10 490 1.79 0.81      2    1.73 1.48   1   3     2  0.41    -1.37 0.04
Q5_5    11 490 2.33 0.81      3    2.41 0.00   1   3     2 -0.67    -1.18 0.04
Q5_6    12 490 1.94 0.77      2    1.93 1.48   1   3     2  0.09    -1.33 0.03
Q5_12   13 490 1.92 0.78      2    1.90 1.48   1   3     2  0.14    -1.36 0.04
Q6_2    14 490 1.40 0.67      1    1.24 0.00   1   3     2  1.42     0.64 0.03
Q6_5    15 490 1.66 0.80      1    1.58 0.00   1   3     2  0.68    -1.11 0.04
Q6_6    16 490 1.22 0.52      1    1.09 0.00   1   3     2  2.29     4.28 0.02
Q6_7    17 490 1.45 0.66      1    1.32 0.00   1   3     2  1.17     0.14 0.03
Q6_8    18 490 1.43 0.65      1    1.31 0.00   1   3     2  1.21     0.27 0.03
Q6_11   19 490 1.85 0.76      2    1.81 1.48   1   3     2  0.26    -1.22 0.03
Q7_2    20 490 1.74 0.69      2    1.67 1.48   1   3     2  0.39    -0.89 0.03
Q7_4    21 490 1.89 0.79      2    1.86 1.48   1   3     2  0.20    -1.37 0.04
Q7_5    22 490 1.89 0.76      2    1.86 1.48   1   3     2  0.19    -1.24 0.03
Q7_7    23 490 2.43 0.78      3    2.54 0.00   1   3     2 -0.91    -0.76 0.04
Q7_8    24 490 1.87 0.75      2    1.84 1.48   1   3     2  0.21    -1.21 0.03
Q7_14   25 490 2.39 0.76      3    2.49 0.00   1   3     2 -0.78    -0.85 0.03

DWLS

mod <- '
EL =~ 1*Q4_3 + lam44*Q4_4 + lam45*Q4_5 + lam49*Q4_9 + lam411*Q4_11 + lam415*Q4_15 + lam418*Q4_18
SC =~ 1*Q5_1 + lam52*Q5_2 + lam53*Q5_3 + lam55*Q5_5 + lam56*Q5_6 + lam512*Q5_12
IN =~ 1*Q6_2 + lam65*Q6_5 + lam66*Q6_6 + lam67*Q6_7 + lam68*Q6_8 + lam611*Q6_11
EN =~ 1*Q7_2 + lam74*Q7_4 + lam75*Q7_5 + lam77*Q7_7 + lam78*Q7_8 + lam714*Q7_14

# Factor covarainces
EL ~~ EL + SC + IN + EN
SC ~~ SC + IN + EN
IN ~~ IN + EN
EN ~~ EN

# Factor Reliabilities
rEL := ((1 + lam44 + lam45 + lam49 + lam411 + lam415 + lam418)**2)/((1 + lam44 + lam45 + lam49 + lam411 + lam415 + lam418)**2 + 7)
rSC := ((1 + lam52 + lam53 + lam55 + lam56 + lam512)**2)/((1 + lam52 + lam53 + lam55 + lam56 + lam512)**2 + 6)
rIN := ((1 + lam65 + lam66 + lam67 + lam68 + lam611)**2)/((1 + lam65 + lam66 + lam67 + lam68 + lam611)**2 + 6)
rEN := ((1 + lam74 + lam75 + lam77 + lam78 + lam714)**2)/((1 + lam74 + lam75 + lam77 + lam78 + lam714)**2 + 6)
'
fit.dwls <- lavaan::cfa(mod, data=mydata, ordered=T, parameterization="theta")
summary(fit.dwls, standardized=T, fit.measures=T)
lavaan 0.6-7 ended normally after 66 iterations

  Estimator                                       DWLS
  Optimization method                           NLMINB
  Number of free parameters                         81
                                                      
  Number of observations                           490
                                                      
Model Test User Model:
                                              Standard      Robust
  Test Statistic                               593.869     765.951
  Degrees of freedom                               269         269
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  0.883
  Shift parameter                                           93.760
       simple second-order correction                             

Model Test Baseline Model:

  Test statistic                             32729.962   10489.239
  Degrees of freedom                               300         300
  P-value                                        0.000       0.000
  Scaling correction factor                                  3.183

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.990       0.951
  Tucker-Lewis Index (TLI)                       0.989       0.946
                                                                  
  Robust Comparative Fit Index (CFI)                            NA
  Robust Tucker-Lewis Index (TLI)                               NA

Root Mean Square Error of Approximation:

  RMSEA                                          0.050       0.061
  90 Percent confidence interval - lower         0.044       0.056
  90 Percent confidence interval - upper         0.055       0.067
  P-value RMSEA <= 0.05                          0.529       0.000
                                                                  
  Robust RMSEA                                                  NA
  90 Percent confidence interval - lower                        NA
  90 Percent confidence interval - upper                        NA

Standardized Root Mean Square Residual:

  SRMR                                           0.065       0.065

Parameter Estimates:

  Standard errors                           Robust.sem
  Information                                 Expected
  Information saturated (h1) model        Unstructured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EL =~                                                                 
    Q4_3              1.000                               1.234    0.777
    Q4_4    (lm44)    1.445    0.145    9.972    0.000    1.783    0.872
    Q4_5    (lm45)    0.949    0.101    9.390    0.000    1.171    0.760
    Q4_9    (lm49)    0.763    0.084    9.048    0.000    0.942    0.686
    Q4_11   (l411)    1.048    0.110    9.536    0.000    1.293    0.791
    Q4_15   (l415)    0.994    0.107    9.309    0.000    1.227    0.775
    Q4_18   (l418)    1.272    0.137    9.295    0.000    1.569    0.843
  SC =~                                                                 
    Q5_1              1.000                               1.082    0.734
    Q5_2    (lm52)    0.976    0.119    8.171    0.000    1.056    0.726
    Q5_3    (lm53)    0.944    0.124    7.587    0.000    1.021    0.714
    Q5_5    (lm55)    0.803    0.114    7.052    0.000    0.869    0.656
    Q5_6    (lm56)    1.224    0.162    7.549    0.000    1.324    0.798
    Q5_12   (l512)    1.188    0.160    7.446    0.000    1.286    0.789
  IN =~                                                                 
    Q6_2              1.000                               1.054    0.725
    Q6_5    (lm65)    0.618    0.095    6.522    0.000    0.651    0.546
    Q6_6    (lm66)    1.704    0.290    5.882    0.000    1.796    0.874
    Q6_7    (lm67)    1.518    0.220    6.893    0.000    1.600    0.848
    Q6_8    (lm68)    1.234    0.157    7.839    0.000    1.301    0.793
    Q6_11   (l611)    1.602    0.256    6.258    0.000    1.688    0.860
  EN =~                                                                 
    Q7_2              1.000                               1.243    0.779
    Q7_4    (lm74)    0.800    0.088    9.095    0.000    0.994    0.705
    Q7_5    (lm75)    1.108    0.132    8.392    0.000    1.378    0.809
    Q7_7    (lm77)    0.875    0.125    6.996    0.000    1.087    0.736
    Q7_8    (lm78)    0.867    0.095    9.155    0.000    1.078    0.733
    Q7_14   (l714)    0.672    0.088    7.626    0.000    0.835    0.641

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EL ~~                                                                 
    SC                0.915    0.139    6.573    0.000    0.685    0.685
    IN                0.973    0.152    6.402    0.000    0.748    0.748
    EN                1.193    0.161    7.417    0.000    0.778    0.778
  SC ~~                                                                 
    IN                0.740    0.129    5.718    0.000    0.649    0.649
    EN                1.080    0.161    6.691    0.000    0.803    0.803
  IN ~~                                                                 
    EN                0.979    0.156    6.265    0.000    0.747    0.747

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .Q4_3              0.000                               0.000    0.000
   .Q4_4              0.000                               0.000    0.000
   .Q4_5              0.000                               0.000    0.000
   .Q4_9              0.000                               0.000    0.000
   .Q4_11             0.000                               0.000    0.000
   .Q4_15             0.000                               0.000    0.000
   .Q4_18             0.000                               0.000    0.000
   .Q5_1              0.000                               0.000    0.000
   .Q5_2              0.000                               0.000    0.000
   .Q5_3              0.000                               0.000    0.000
   .Q5_5              0.000                               0.000    0.000
   .Q5_6              0.000                               0.000    0.000
   .Q5_12             0.000                               0.000    0.000
   .Q6_2              0.000                               0.000    0.000
   .Q6_5              0.000                               0.000    0.000
   .Q6_6              0.000                               0.000    0.000
   .Q6_7              0.000                               0.000    0.000
   .Q6_8              0.000                               0.000    0.000
   .Q6_11             0.000                               0.000    0.000
   .Q7_2              0.000                               0.000    0.000
   .Q7_4              0.000                               0.000    0.000
   .Q7_5              0.000                               0.000    0.000
   .Q7_7              0.000                               0.000    0.000
   .Q7_8              0.000                               0.000    0.000
   .Q7_14             0.000                               0.000    0.000
    EL                0.000                               0.000    0.000
    SC                0.000                               0.000    0.000
    IN                0.000                               0.000    0.000
    EN                0.000                               0.000    0.000

Thresholds:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    Q4_3|t1          -0.106    0.090   -1.181    0.238   -0.106   -0.067
    Q4_3|t2           2.073    0.136   15.218    0.000    2.073    1.305
    Q4_4|t1          -0.241    0.115   -2.098    0.036   -0.241   -0.118
    Q4_4|t2           2.644    0.185   14.260    0.000    2.644    1.293
    Q4_5|t1           0.317    0.090    3.516    0.000    0.317    0.206
    Q4_5|t2           1.938    0.128   15.163    0.000    1.938    1.259
    Q4_9|t1           0.091    0.078    1.168    0.243    0.091    0.067
    Q4_9|t2           1.292    0.097   13.316    0.000    1.292    0.941
    Q4_11|t1          0.017    0.093    0.180    0.857    0.017    0.010
    Q4_11|t2          1.716    0.126   13.628    0.000    1.716    1.050
    Q4_15|t1          0.105    0.091    1.163    0.245    0.105    0.067
    Q4_15|t2          1.974    0.139   14.200    0.000    1.974    1.247
    Q4_18|t1          0.258    0.109    2.368    0.018    0.258    0.139
    Q4_18|t2          2.672    0.190   14.079    0.000    2.672    1.436
    Q5_1|t1          -0.121    0.083   -1.451    0.147   -0.121   -0.082
    Q5_1|t2           1.251    0.104   12.001    0.000    1.251    0.849
    Q5_2|t1          -0.493    0.085   -5.781    0.000   -0.493   -0.339
    Q5_2|t2           0.501    0.084    5.987    0.000    0.501    0.344
    Q5_3|t1          -0.146    0.081   -1.813    0.070   -0.146   -0.102
    Q5_3|t2           0.987    0.094   10.505    0.000    0.987    0.691
    Q5_5|t1          -1.021    0.090  -11.329    0.000   -1.021   -0.771
    Q5_5|t2          -0.163    0.076   -2.143    0.032   -0.163   -0.123
    Q5_6|t1          -0.737    0.101   -7.317    0.000   -0.737   -0.444
    Q5_6|t2           1.000    0.106    9.460    0.000    1.000    0.602
    Q5_12|t1         -0.641    0.098   -6.572    0.000   -0.641   -0.394
    Q5_12|t2          1.001    0.108    9.310    0.000    1.001    0.615
    Q6_2|t1           0.788    0.098    8.044    0.000    0.788    0.542
    Q6_2|t2           1.845    0.133   13.877    0.000    1.845    1.270
    Q6_5|t1           0.128    0.068    1.886    0.059    0.128    0.108
    Q6_5|t2           0.979    0.079   12.392    0.000    0.979    0.820
    Q6_6|t1           1.934    0.262    7.394    0.000    1.934    0.941
    Q6_6|t2           3.402    0.391    8.706    0.000    3.402    1.655
    Q6_7|t1           0.701    0.126    5.564    0.000    0.701    0.372
    Q6_7|t2           2.509    0.216   11.601    0.000    2.509    1.330
    Q6_8|t1           0.655    0.107    6.131    0.000    0.655    0.399
    Q6_8|t2           2.244    0.170   13.237    0.000    2.244    1.368
    Q6_11|t1         -0.633    0.120   -5.279    0.000   -0.633   -0.323
    Q6_11|t2          1.513    0.156    9.676    0.000    1.513    0.771
    Q7_2|t1          -0.396    0.092   -4.325    0.000   -0.396   -0.248
    Q7_2|t2           1.718    0.125   13.767    0.000    1.718    1.077
    Q7_4|t1          -0.455    0.081   -5.608    0.000   -0.455   -0.323
    Q7_4|t2           0.911    0.087   10.467    0.000    0.911    0.646
    Q7_5|t1          -0.661    0.101   -6.551    0.000   -0.661   -0.388
    Q7_5|t2           1.220    0.107   11.362    0.000    1.220    0.717
    Q7_7|t1          -1.343    0.116  -11.624    0.000   -1.343   -0.909
    Q7_7|t2          -0.421    0.090   -4.696    0.000   -0.421   -0.285
    Q7_8|t1          -0.546    0.086   -6.388    0.000   -0.546   -0.372
    Q7_8|t2           1.103    0.093   11.889    0.000    1.103    0.750
    Q7_14|t1         -1.257    0.095  -13.256    0.000   -1.257   -0.965
    Q7_14|t2         -0.187    0.075   -2.503    0.012   -0.187   -0.144

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    EL                1.522    0.237    6.417    0.000    1.000    1.000
    SC                1.171    0.229    5.119    0.000    1.000    1.000
    IN                1.111    0.234    4.753    0.000    1.000    1.000
    EN                1.545    0.275    5.620    0.000    1.000    1.000
   .Q4_3              1.000                               1.000    0.396
   .Q4_4              1.000                               1.000    0.239
   .Q4_5              1.000                               1.000    0.422
   .Q4_9              1.000                               1.000    0.530
   .Q4_11             1.000                               1.000    0.374
   .Q4_15             1.000                               1.000    0.399
   .Q4_18             1.000                               1.000    0.289
   .Q5_1              1.000                               1.000    0.461
   .Q5_2              1.000                               1.000    0.473
   .Q5_3              1.000                               1.000    0.490
   .Q5_5              1.000                               1.000    0.570
   .Q5_6              1.000                               1.000    0.363
   .Q5_12             1.000                               1.000    0.377
   .Q6_2              1.000                               1.000    0.474
   .Q6_5              1.000                               1.000    0.702
   .Q6_6              1.000                               1.000    0.237
   .Q6_7              1.000                               1.000    0.281
   .Q6_8              1.000                               1.000    0.371
   .Q6_11             1.000                               1.000    0.260
   .Q7_2              1.000                               1.000    0.393
   .Q7_4              1.000                               1.000    0.503
   .Q7_5              1.000                               1.000    0.345
   .Q7_7              1.000                               1.000    0.458
   .Q7_8              1.000                               1.000    0.463
   .Q7_14             1.000                               1.000    0.589

Scales y*:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    Q4_3              0.630                               0.630    1.000
    Q4_4              0.489                               0.489    1.000
    Q4_5              0.650                               0.650    1.000
    Q4_9              0.728                               0.728    1.000
    Q4_11             0.612                               0.612    1.000
    Q4_15             0.632                               0.632    1.000
    Q4_18             0.537                               0.537    1.000
    Q5_1              0.679                               0.679    1.000
    Q5_2              0.688                               0.688    1.000
    Q5_3              0.700                               0.700    1.000
    Q5_5              0.755                               0.755    1.000
    Q5_6              0.603                               0.603    1.000
    Q5_12             0.614                               0.614    1.000
    Q6_2              0.688                               0.688    1.000
    Q6_5              0.838                               0.838    1.000
    Q6_6              0.486                               0.486    1.000
    Q6_7              0.530                               0.530    1.000
    Q6_8              0.609                               0.609    1.000
    Q6_11             0.510                               0.510    1.000
    Q7_2              0.627                               0.627    1.000
    Q7_4              0.709                               0.709    1.000
    Q7_5              0.587                               0.587    1.000
    Q7_7              0.677                               0.677    1.000
    Q7_8              0.680                               0.680    1.000
    Q7_14             0.768                               0.768    1.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    rEL               0.889    0.013   68.903    0.000    0.920    0.824
    rSC               0.863    0.020   42.191    0.000    0.878    0.785
    rIN               0.908    0.016   56.391    0.000    0.915    0.801
    rEN               0.825    0.022   37.817    0.000    0.871    0.781

Model 2: Misclassification in IFA

Model details

cat(read_file(paste0(w.d, "/code/pools_study/model_misclass_ifa.txt")))
model {
### Model
  for(p in 1:N){
    for(i in 1:nit){
      # data model
      y[p,i] ~ dcat(omega[p,i, ])

      # LRV
      ystar[p,i] ~ dnorm(lambda[i]*ksi[p,map[nit]], 1)

     # Pr(nu = 3)
      pi[p,i,3] = phi(ystar[p,i] - tau[i,2])
      # Pr(nu = 2)
      pi[p,i,2] = phi(ystar[p,i] - tau[i,1]) - phi(ystar[p,i] - tau[i,2])
      # Pr(nu = 1)
      pi[p,i,1] = 1 - phi(ystar[p,i] - tau[i,1])

      # compute misclassificatication based prob
      # observed category prob (Pr(y=c))
      for(c in 1:ncat){
        omega[p,i, c] = gamma[i,c,1]*pi[p,i,1] +
            gamma[i,c,2]*pi[p,i,2] +
            gamma[i,c,3]*pi[p,i,3]
      }
    }
  }
  ### Priors
  # misclassification
  for(i in 1:nit){
    for(c in 1:ncat){
      gamma[i,c,1:ncat] ~ ddirch(xi*alpha[c,1:ncat])
    }
  }

  # person parameters
  for(p in 1:N){
    #eta[p] ~ dnorm(0, 1) # latent ability
    ksi[p, 1:M] ~ dmnorm(kappa[], inv.phi[,])
  }
  for(m in 1:M){
    kappa[m] <- 0              # Means of latent variables
  }
  inv.phi[1:M,1:M] ~ dwish(dxphi.0[ , ], d);    # prior for precision matrix for the latent variables
  phi[1:M,1:M] <- inverse(inv.phi[ , ]);        # the covariance matrix for the latent vars

  for(m in 1:M){
    for(mm in 1:M){
      dxphi.0[m,mm] <- d*phi.0[m,mm];
    }
  }

  # factor correlations
  for(m in 1:M){
    for(mm in 1:M){
      phi.cor[m,mm] = (phi[m,mm])/((pow(phi[m,m], 0.5))*(pow(phi[mm,mm], 0.5)));
    }
  }


  # priors for loadings
  # loadings
  lambda[1] = 1
  lambda[8] = 1
  lambda[13] = 1
  lambda[19] = 1
  for(i in 2:7){
    lambda[i] ~ dnorm(0, 1)T(0,)
  }
  for(i in 9:12){
    lambda[i] ~ dnorm(0, 1)T(0,)
  }
  for(i in 14:18){
    lambda[i] ~ dnorm(0, 1)T(0,)
  }
  for(i in 20:25){
    lambda[i] ~ dnorm(0, 1)T(0,)
  }


  for(i in 1:nit){
    # Thresholds
    tau[i, 1] = 0
    tau[i, 2] ~ dnorm(0, 0.1)T(tau[i, 1],)
    # LRV total variance
    # total variance = residual variance + fact. Var.
    theta[i] = 1 + pow(lambda[i],2)
    # standardized loading
    lambda.std[i] = lambda[i]/pow(theta[i],0.5)
  }

  # compute omega
  lambda_sum1[1] = lambda[1]
  lambda_sum2[1] = lambda[8]
  lambda_sum3[1] = lambda[13]
  lambda_sum4[1] = lambda[19]
  for(i in 2:6){
    #lambda_sum (sum factor loadings)
    lambda_sum1[i] = lambda_sum1[i-1]+lambda[i]
    lambda_sum2[i] = lambda_sum2[i-1]+lambda[i+7]
    lambda_sum3[i] = lambda_sum3[i-1]+lambda[i+12]
    lambda_sum4[i] = lambda_sum4[i-1]+lambda[i+18]
  }
  lambda_sum1[7] = lambda_sum1[6] + lambda[7]
  # compute reliability
  reli.omega[1] = (pow(lambda_sum1[7],2))/(pow(lambda_sum1[7],2)+7)
  reli.omega[2] = (pow(lambda_sum2[6],2))/(pow(lambda_sum2[6],2)+6)
  reli.omega[3] = (pow(lambda_sum3[6],2))/(pow(lambda_sum3[6],2)+6)
  reli.omega[4] = (pow(lambda_sum4[6],2))/(pow(lambda_sum4[6],2)+6)
}

Model results

# Save parameters
jags.params <- c("tau", "lambda", "theta", "reli.omega", "lambda.std",
                 "phi.cor", "inv.phi", "phi", "gamma")
# initial-values
jags.inits <- function(){
    list(
      "inv.phi"=solve(matrix(
    c(1.52, 0.92, 0.97, 1.19,
      0.92, 1.17, 0.74, 1.08,
      0.97, 0.74, 1.11, 0.98,
      1.19, 1.08, 0.98, 1.55), ncol=4, nrow=4, byrow=T
    ))
  )
}

# data
jags.data <- list(
  y = mydata,
  N = nrow(mydata),
  nit = ncol(mydata),
  map = c(rep(1,7), rep(2,6), rep(3,6), rep(4,6)),
  d = 8,
  M = 4,
  phi.0 = matrix(
    c(1, 0.69, 0.75, 0.78,
      0.69, 1, 0.65, 0.80,
      0.75, 0.65, 1, 0.75,
      0.78, 0.80, 0.75, 1), ncol=4, nrow=4, byrow=T
    ),
  ncat = 3,
  alpha = matrix(
    c(0.90, 0.10, 0,
      0.05, 0.90, 0.05,
      0.0, 0.10, 0.90),
    ncol=3, nrow=3, byrow=T
  ),
  xi = 10
)

model.fit <-  R2jags::jags(
  model = paste0(w.d, "/code/pools_study/model_misclass_ifa.txt"),
  parameters.to.save = jags.params,
  inits = jags.inits,
  data = jags.data,
  n.chains = 4,
  n.burnin = 5000,
  n.iter = 10000
)
module glm loaded
Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 12250
   Unobserved stochastic nodes: 12862
   Total graph size: 269608

Initializing model
print(model.fit, width=1000)
Inference for Bugs model at "C:/Users/noahp/Documents/GitHub/Padgett-Dissertation/code/pools_study/model_misclass_ifa.txt", fit using jags,
 4 chains, each with 10000 iterations (first 5000 discarded), n.thin = 5
 n.sims = 4000 iterations saved
                 mu.vect sd.vect      2.5%       25%       50%       75%     97.5% Rhat n.eff
gamma[1,1,1]       0.767   0.061     0.638     0.729     0.770     0.810     0.877 1.00  1500
gamma[2,1,1]       0.841   0.049     0.733     0.809     0.845     0.876     0.929 1.01   390
gamma[3,1,1]       0.612   0.086     0.441     0.554     0.616     0.674     0.771 1.01   310
gamma[4,1,1]       0.522   0.088     0.353     0.461     0.522     0.580     0.693 1.02   140
gamma[5,1,1]       0.699   0.070     0.554     0.654     0.700     0.748     0.828 1.02   110
gamma[6,1,1]       0.721   0.076     0.566     0.671     0.723     0.773     0.866 1.01   210
gamma[7,1,1]       0.769   0.074     0.613     0.721     0.774     0.820     0.899 1.02   110
gamma[8,1,1]       0.698   0.078     0.534     0.647     0.701     0.753     0.838 1.00  4000
gamma[9,1,1]       0.894   0.101     0.607     0.850     0.925     0.970     0.997 1.00  1700
gamma[10,1,1]      0.805   0.123     0.533     0.724     0.823     0.901     0.987 1.00  1500
gamma[11,1,1]      0.263   0.069     0.146     0.214     0.256     0.307     0.413 1.01   190
gamma[12,1,1]      0.959   0.032     0.877     0.941     0.967     0.984     0.998 1.01   380
gamma[13,1,1]      0.962   0.032     0.882     0.945     0.970     0.987     0.999 1.00   770
gamma[14,1,1]      0.575   0.111     0.356     0.497     0.574     0.650     0.789 1.00   890
gamma[15,1,1]      0.820   0.129     0.538     0.732     0.847     0.925     0.993 1.01   460
gamma[16,1,1]      0.634   0.103     0.422     0.570     0.642     0.704     0.823 1.00   820
gamma[17,1,1]      0.692   0.098     0.491     0.626     0.697     0.763     0.870 1.01   320
gamma[18,1,1]      0.593   0.108     0.368     0.521     0.595     0.669     0.794 1.03   150
gamma[19,1,1]      0.953   0.033     0.873     0.933     0.960     0.978     0.998 1.00  2700
gamma[20,1,1]      0.907   0.047     0.808     0.878     0.910     0.940     0.988 1.02   130
gamma[21,1,1]      0.873   0.075     0.710     0.824     0.879     0.930     0.993 1.02   130
gamma[22,1,1]      0.975   0.022     0.920     0.964     0.981     0.991     0.999 1.00  1400
gamma[23,1,1]      0.192   0.053     0.107     0.155     0.185     0.223     0.315 1.01   610
gamma[24,1,1]      0.956   0.036     0.864     0.937     0.964     0.983     0.998 1.00   990
gamma[25,1,1]      0.152   0.042     0.080     0.123     0.149     0.177     0.245 1.01   340
gamma[1,2,1]       0.015   0.018     0.000     0.002     0.009     0.022     0.063 1.00  3700
gamma[2,2,1]       0.008   0.011     0.000     0.001     0.004     0.012     0.039 1.02   290
gamma[3,2,1]       0.005   0.007     0.000     0.001     0.002     0.007     0.023 1.03   240
gamma[4,2,1]       0.005   0.008     0.000     0.001     0.003     0.007     0.028 1.00   670
gamma[5,2,1]       0.015   0.013     0.000     0.005     0.012     0.022     0.049 1.03   400
gamma[6,2,1]       0.023   0.019     0.000     0.008     0.019     0.034     0.072 1.06    89
gamma[7,2,1]       0.007   0.009     0.000     0.001     0.003     0.009     0.031 1.04   130
gamma[8,2,1]       0.020   0.019     0.000     0.004     0.014     0.028     0.070 1.10    52
gamma[9,2,1]       0.018   0.024     0.000     0.002     0.009     0.025     0.089 1.01   960
gamma[10,2,1]      0.020   0.024     0.000     0.003     0.011     0.028     0.087 1.01   650
gamma[11,2,1]      0.035   0.031     0.000     0.013     0.029     0.050     0.114 1.22    44
gamma[12,2,1]      0.077   0.056     0.001     0.031     0.069     0.115     0.200 1.04   120
gamma[13,2,1]      0.051   0.038     0.001     0.022     0.044     0.072     0.140 1.05   110
gamma[14,2,1]      0.008   0.008     0.000     0.002     0.006     0.012     0.030 1.09    48
gamma[15,2,1]      0.007   0.011     0.000     0.001     0.003     0.010     0.039 1.01   480
gamma[16,2,1]      0.002   0.004     0.000     0.000     0.001     0.003     0.013 1.01   310
gamma[17,2,1]      0.005   0.006     0.000     0.000     0.002     0.006     0.023 1.17    36
gamma[18,2,1]      0.004   0.005     0.000     0.000     0.002     0.004     0.017 1.04    87
gamma[19,2,1]      0.014   0.019     0.000     0.002     0.007     0.020     0.069 1.01   390
gamma[20,2,1]      0.019   0.023     0.000     0.002     0.010     0.029     0.085 1.02   950
gamma[21,2,1]      0.022   0.028     0.000     0.003     0.011     0.031     0.102 1.02   280
gamma[22,2,1]      0.039   0.035     0.000     0.010     0.031     0.058     0.123 1.01   630
gamma[23,2,1]      0.075   0.039     0.018     0.047     0.068     0.095     0.169 1.01   240
gamma[24,2,1]      0.034   0.036     0.000     0.006     0.022     0.051     0.129 1.04   110
gamma[25,2,1]      0.038   0.028     0.002     0.018     0.034     0.052     0.108 1.07    70
gamma[1,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,1,2]       0.233   0.061     0.123     0.190     0.230     0.271     0.362 1.00  1300
gamma[2,1,2]       0.159   0.049     0.071     0.124     0.155     0.191     0.267 1.01   380
gamma[3,1,2]       0.388   0.086     0.229     0.326     0.384     0.446     0.559 1.01   300
gamma[4,1,2]       0.478   0.088     0.307     0.420     0.478     0.539     0.647 1.03   110
gamma[5,1,2]       0.301   0.070     0.172     0.252     0.300     0.346     0.446 1.02   110
gamma[6,1,2]       0.279   0.076     0.134     0.227     0.277     0.329     0.434 1.02   180
gamma[7,1,2]       0.231   0.074     0.101     0.180     0.226     0.279     0.387 1.02   110
gamma[8,1,2]       0.302   0.078     0.162     0.247     0.299     0.353     0.466 1.00  4000
gamma[9,1,2]       0.106   0.101     0.003     0.030     0.075     0.150     0.393 1.01  1100
gamma[10,1,2]      0.195   0.123     0.013     0.099     0.177     0.276     0.467 1.01  1100
gamma[11,1,2]      0.737   0.069     0.587     0.693     0.744     0.786     0.854 1.02   160
gamma[12,1,2]      0.041   0.032     0.002     0.016     0.033     0.059     0.123 1.01   260
gamma[13,1,2]      0.038   0.032     0.001     0.013     0.030     0.055     0.118 1.00   800
gamma[14,1,2]      0.425   0.111     0.211     0.350     0.426     0.503     0.644 1.01   460
gamma[15,1,2]      0.180   0.129     0.007     0.075     0.153     0.268     0.462 1.01   290
gamma[16,1,2]      0.366   0.103     0.177     0.296     0.358     0.430     0.578 1.00   700
gamma[17,1,2]      0.308   0.098     0.130     0.237     0.303     0.374     0.509 1.01   490
gamma[18,1,2]      0.407   0.108     0.206     0.331     0.405     0.479     0.632 1.02   200
gamma[19,1,2]      0.047   0.033     0.002     0.022     0.040     0.067     0.127 1.01  1100
gamma[20,1,2]      0.093   0.047     0.012     0.060     0.090     0.122     0.192 1.08    90
gamma[21,1,2]      0.127   0.075     0.007     0.070     0.121     0.176     0.290 1.02   260
gamma[22,1,2]      0.025   0.022     0.001     0.009     0.019     0.036     0.080 1.00   980
gamma[23,1,2]      0.808   0.053     0.685     0.777     0.815     0.845     0.893 1.01   390
gamma[24,1,2]      0.044   0.036     0.002     0.017     0.036     0.063     0.136 1.01   470
gamma[25,1,2]      0.848   0.042     0.755     0.823     0.851     0.877     0.920 1.01   340
gamma[1,2,2]       0.946   0.049     0.817     0.925     0.962     0.982     0.998 1.00  4000
gamma[2,2,2]       0.951   0.049     0.820     0.930     0.967     0.987     0.999 1.00  1300
gamma[3,2,2]       0.696   0.118     0.476     0.608     0.690     0.779     0.935 1.02   170
gamma[4,2,2]       0.952   0.055     0.789     0.937     0.972     0.990     0.999 1.02   150
gamma[5,2,2]       0.916   0.076     0.715     0.880     0.941     0.973     0.995 1.02   180
gamma[6,2,2]       0.828   0.122     0.566     0.748     0.843     0.931     0.992 1.00  3500
gamma[7,2,2]       0.679   0.146     0.422     0.569     0.669     0.787     0.966 1.02   170
gamma[8,2,2]       0.932   0.059     0.780     0.906     0.950     0.976     0.997 1.01   280
gamma[9,2,2]       0.871   0.099     0.612     0.826     0.893     0.942     0.991 1.02   270
gamma[10,2,2]      0.953   0.043     0.837     0.933     0.965     0.985     0.998 1.00  2800
gamma[11,2,2]      0.647   0.050     0.549     0.614     0.645     0.680     0.745 1.01   330
gamma[12,2,2]      0.900   0.064     0.760     0.859     0.910     0.952     0.992 1.00   520
gamma[13,2,2]      0.928   0.046     0.824     0.900     0.935     0.963     0.994 1.01   450
gamma[14,2,2]      0.262   0.054     0.165     0.224     0.259     0.297     0.377 1.00  1100
gamma[15,2,2]      0.623   0.159     0.353     0.503     0.611     0.725     0.959 1.00  1900
gamma[16,2,2]      0.106   0.027     0.060     0.087     0.103     0.122     0.169 1.01   390
gamma[17,2,2]      0.372   0.084     0.222     0.312     0.368     0.425     0.549 1.01   460
gamma[18,2,2]      0.409   0.083     0.267     0.352     0.401     0.463     0.592 1.02   180
gamma[19,2,2]      0.971   0.027     0.900     0.960     0.979     0.991     0.999 1.02   370
gamma[20,2,2]      0.959   0.038     0.866     0.941     0.970     0.987     0.999 1.01   480
gamma[21,2,2]      0.963   0.034     0.869     0.948     0.973     0.988     0.999 1.01   630
gamma[22,2,2]      0.941   0.044     0.832     0.915     0.949     0.975     0.998 1.01   260
gamma[23,2,2]      0.738   0.042     0.650     0.711     0.739     0.766     0.818 1.00  1800
gamma[24,2,2]      0.945   0.046     0.825     0.921     0.957     0.980     0.998 1.01   420
gamma[25,2,2]      0.594   0.052     0.488     0.559     0.595     0.628     0.692 1.00   740
gamma[1,3,2]       0.051   0.023     0.012     0.034     0.048     0.066     0.102 1.00   860
gamma[2,3,2]       0.035   0.019     0.004     0.020     0.032     0.047     0.078 1.01  2900
gamma[3,3,2]       0.033   0.019     0.005     0.018     0.030     0.044     0.079 1.01   410
gamma[4,3,2]       0.171   0.060     0.048     0.132     0.171     0.211     0.291 1.07    57
gamma[5,3,2]       0.118   0.042     0.044     0.088     0.115     0.145     0.207 1.02   140
gamma[6,3,2]       0.041   0.024     0.005     0.024     0.038     0.056     0.095 1.03   240
gamma[7,3,2]       0.024   0.014     0.003     0.014     0.022     0.033     0.057 1.02   260
gamma[8,3,2]       0.230   0.055     0.129     0.192     0.228     0.265     0.345 1.00  1700
gamma[9,3,2]       0.328   0.163     0.028     0.207     0.334     0.451     0.628 1.01   370
gamma[10,3,2]      0.067   0.058     0.001     0.022     0.051     0.099     0.211 1.00  1700
gamma[11,3,2]      0.065   0.059     0.003     0.021     0.049     0.091     0.216 1.01   340
gamma[12,3,2]      0.345   0.079     0.192     0.290     0.344     0.399     0.501 1.00   890
gamma[13,3,2]      0.333   0.069     0.198     0.288     0.332     0.379     0.471 1.00  2300
gamma[14,3,2]      0.055   0.020     0.018     0.041     0.054     0.068     0.098 1.03   160
gamma[15,3,2]      0.105   0.088     0.003     0.033     0.079     0.162     0.308 1.01   590
gamma[16,3,2]      0.006   0.005     0.000     0.003     0.005     0.008     0.018 1.01   350
gamma[17,3,2]      0.032   0.016     0.005     0.020     0.030     0.041     0.066 1.01   810
gamma[18,3,2]      0.048   0.018     0.020     0.036     0.047     0.058     0.090 1.01   180
gamma[19,3,2]      0.127   0.057     0.026     0.084     0.124     0.164     0.242 1.04   110
gamma[20,3,2]      0.064   0.037     0.004     0.035     0.061     0.088     0.146 1.03   150
gamma[21,3,2]      0.294   0.100     0.088     0.226     0.298     0.367     0.476 1.03   110
gamma[22,3,2]      0.262   0.059     0.154     0.220     0.260     0.301     0.380 1.01   490
gamma[23,3,2]      0.057   0.053     0.002     0.018     0.040     0.082     0.197 1.01   850
gamma[24,3,2]      0.272   0.070     0.134     0.225     0.271     0.319     0.406 1.00   680
gamma[25,3,2]      0.069   0.063     0.002     0.022     0.052     0.098     0.229 1.00   780
gamma[1,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,1,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,1,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,2,3]       0.038   0.046     0.000     0.005     0.022     0.056     0.156 1.01   570
gamma[2,2,3]       0.040   0.047     0.000     0.005     0.022     0.061     0.171 1.02   660
gamma[3,2,3]       0.299   0.117     0.062     0.216     0.305     0.385     0.519 1.01   290
gamma[4,2,3]       0.043   0.054     0.000     0.005     0.022     0.058     0.200 1.02   150
gamma[5,2,3]       0.069   0.074     0.000     0.012     0.044     0.103     0.262 1.10    63
gamma[6,2,3]       0.149   0.116     0.001     0.050     0.131     0.228     0.405 1.00  4000
gamma[7,2,3]       0.315   0.146     0.025     0.208     0.326     0.425     0.573 1.14    83
gamma[8,2,3]       0.048   0.053     0.000     0.008     0.030     0.069     0.193 1.00   550
gamma[9,2,3]       0.111   0.091     0.001     0.044     0.090     0.153     0.357 1.07   100
gamma[10,2,3]      0.027   0.035     0.000     0.002     0.013     0.039     0.128 1.02   220
gamma[11,2,3]      0.317   0.054     0.215     0.281     0.316     0.354     0.424 1.01   390
gamma[12,2,3]      0.023   0.027     0.000     0.003     0.013     0.035     0.090 1.05   100
gamma[13,2,3]      0.021   0.026     0.000     0.002     0.011     0.030     0.091 1.01   570
gamma[14,2,3]      0.729   0.053     0.616     0.696     0.732     0.766     0.827 1.00  1300
gamma[15,2,3]      0.370   0.159     0.035     0.267     0.383     0.491     0.642 1.04   360
gamma[16,2,3]      0.892   0.027     0.830     0.875     0.895     0.911     0.938 1.01   470
gamma[17,2,3]      0.623   0.083     0.448     0.570     0.628     0.682     0.771 1.01   480
gamma[18,2,3]      0.587   0.083     0.407     0.534     0.595     0.644     0.730 1.02   200
gamma[19,2,3]      0.015   0.019     0.000     0.002     0.008     0.020     0.065 1.01   310
gamma[20,2,3]      0.022   0.029     0.000     0.003     0.011     0.030     0.106 1.08    69
gamma[21,2,3]      0.014   0.020     0.000     0.001     0.007     0.019     0.071 1.01   310
gamma[22,2,3]      0.020   0.024     0.000     0.003     0.011     0.029     0.088 1.05   280
gamma[23,2,3]      0.187   0.046     0.104     0.157     0.186     0.217     0.283 1.01   210
gamma[24,2,3]      0.021   0.027     0.000     0.002     0.010     0.030     0.095 1.03   310
gamma[25,2,3]      0.368   0.058     0.258     0.328     0.366     0.406     0.487 1.00  1500
gamma[1,3,3]       0.949   0.023     0.898     0.934     0.952     0.966     0.988 1.00  1100
gamma[2,3,3]       0.965   0.019     0.922     0.953     0.968     0.980     0.996 1.00  1100
gamma[3,3,3]       0.967   0.019     0.921     0.956     0.970     0.982     0.995 1.00   650
gamma[4,3,3]       0.829   0.060     0.709     0.789     0.829     0.868     0.952 1.04    70
gamma[5,3,3]       0.882   0.042     0.793     0.855     0.885     0.912     0.956 1.02   160
gamma[6,3,3]       0.959   0.024     0.905     0.944     0.962     0.976     0.995 1.01   230
gamma[7,3,3]       0.976   0.014     0.943     0.967     0.978     0.986     0.997 1.01   430
gamma[8,3,3]       0.770   0.055     0.655     0.735     0.772     0.808     0.871 1.00  2300
gamma[9,3,3]       0.672   0.163     0.372     0.549     0.666     0.793     0.972 1.01   200
gamma[10,3,3]      0.933   0.058     0.789     0.901     0.949     0.978     0.999 1.00  1400
gamma[11,3,3]      0.935   0.059     0.784     0.909     0.951     0.979     0.997 1.01   340
gamma[12,3,3]      0.655   0.079     0.499     0.601     0.656     0.710     0.808 1.00   660
gamma[13,3,3]      0.667   0.069     0.529     0.621     0.668     0.712     0.802 1.00  2900
gamma[14,3,3]      0.945   0.020     0.902     0.932     0.946     0.959     0.982 1.01   220
gamma[15,3,3]      0.895   0.088     0.692     0.838     0.921     0.967     0.997 1.00   950
gamma[16,3,3]      0.994   0.005     0.982     0.992     0.995     0.997     1.000 1.00   630
gamma[17,3,3]      0.968   0.016     0.934     0.959     0.970     0.980     0.995 1.00  1100
gamma[18,3,3]      0.952   0.018     0.910     0.942     0.953     0.964     0.980 1.02   160
gamma[19,3,3]      0.873   0.057     0.758     0.836     0.876     0.916     0.974 1.02   100
gamma[20,3,3]      0.936   0.037     0.854     0.912     0.939     0.965     0.996 1.01   170
gamma[21,3,3]      0.706   0.100     0.524     0.633     0.702     0.774     0.912 1.03    87
gamma[22,3,3]      0.738   0.059     0.620     0.699     0.740     0.780     0.846 1.01   530
gamma[23,3,3]      0.943   0.053     0.803     0.918     0.960     0.982     0.998 1.01  1500
gamma[24,3,3]      0.728   0.070     0.594     0.681     0.729     0.775     0.866 1.00   590
gamma[25,3,3]      0.931   0.063     0.771     0.902     0.948     0.978     0.998 1.01   450
inv.phi[1,1]       3.368   1.621     0.951     2.208     3.123     4.248     7.213 1.09    35
inv.phi[2,1]      -0.434   1.046    -2.551    -1.127    -0.389     0.292     1.487 1.02   170
inv.phi[3,1]      -1.271   1.144    -3.926    -1.901    -1.155    -0.480     0.566 1.01   220
inv.phi[4,1]      -1.270   1.197    -3.901    -1.972    -1.152    -0.480     0.762 1.01   240
inv.phi[1,2]      -0.434   1.046    -2.551    -1.127    -0.389     0.292     1.487 1.02   170
inv.phi[2,2]       2.938   1.426     0.879     1.881     2.730     3.737     6.381 1.02   270
inv.phi[3,2]      -0.254   1.008    -2.250    -0.892    -0.282     0.371     1.783 1.02   180
inv.phi[4,2]      -1.826   1.412    -5.249    -2.569    -1.605    -0.826     0.326 1.02   150
inv.phi[1,3]      -1.271   1.144    -3.926    -1.901    -1.155    -0.480     0.566 1.01   220
inv.phi[2,3]      -0.254   1.008    -2.250    -0.892    -0.282     0.371     1.783 1.02   180
inv.phi[3,3]       2.641   1.417     0.638     1.597     2.371     3.383     6.162 1.02   260
inv.phi[4,3]      -0.757   1.193    -3.407    -1.501    -0.619     0.110     1.213 1.01   320
inv.phi[1,4]      -1.270   1.197    -3.901    -1.972    -1.152    -0.480     0.762 1.01   240
inv.phi[2,4]      -1.826   1.412    -5.249    -2.569    -1.605    -0.826     0.326 1.02   150
inv.phi[3,4]      -0.757   1.193    -3.407    -1.501    -0.619     0.110     1.213 1.01   320
inv.phi[4,4]       3.537   2.014     0.764     2.051     3.114     4.649     8.520 1.03   120
lambda[1]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[2]          1.367   0.226     1.000     1.197     1.335     1.524     1.827 1.03   110
lambda[3]          1.251   0.209     0.876     1.105     1.236     1.388     1.675 1.02   130
lambda[4]          1.152   0.224     0.736     1.000     1.145     1.304     1.612 1.06    50
lambda[5]          1.475   0.315     0.935     1.254     1.462     1.657     2.203 1.08    39
lambda[6]          1.205   0.244     0.812     1.023     1.171     1.367     1.731 1.09    35
lambda[7]          1.450   0.255     0.933     1.290     1.441     1.618     1.956 1.09    33
lambda[8]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[9]          0.708   0.094     0.536     0.645     0.705     0.768     0.908 1.01   180
lambda[10]         0.588   0.083     0.446     0.533     0.581     0.638     0.763 1.02   160
lambda[11]         0.614   0.083     0.452     0.557     0.613     0.668     0.779 1.01  1000
lambda[12]         0.940   0.141     0.686     0.838     0.933     1.034     1.238 1.03    78
lambda[13]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[14]         1.130   0.268     0.632     0.949     1.124     1.287     1.699 1.07    44
lambda[15]         0.439   0.096     0.298     0.373     0.422     0.486     0.671 1.01   310
lambda[16]         1.275   0.233     0.859     1.105     1.258     1.432     1.769 1.13    25
lambda[17]         1.241   0.243     0.793     1.065     1.228     1.405     1.729 1.08    39
lambda[18]         1.364   0.290     0.887     1.156     1.337     1.527     2.031 1.05   160
lambda[19]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[20]         1.029   0.151     0.757     0.927     1.020     1.120     1.365 1.07    43
lambda[21]         0.870   0.140     0.634     0.765     0.858     0.963     1.162 1.08    42
lambda[22]         1.120   0.142     0.868     1.021     1.110     1.205     1.430 1.02   180
lambda[23]         0.780   0.101     0.591     0.708     0.776     0.843     0.986 1.01   300
lambda[24]         0.867   0.118     0.657     0.787     0.859     0.935     1.131 1.02   140
lambda[25]         0.711   0.096     0.536     0.644     0.708     0.774     0.907 1.01   290
lambda.std[1]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[2]      0.800   0.046     0.707     0.767     0.800     0.836     0.877 1.03    97
lambda.std[3]      0.773   0.052     0.659     0.742     0.777     0.811     0.859 1.02   120
lambda.std[4]      0.745   0.066     0.593     0.707     0.753     0.794     0.850 1.07    47
lambda.std[5]      0.816   0.058     0.683     0.782     0.825     0.856     0.911 1.09    38
lambda.std[6]      0.759   0.062     0.630     0.715     0.760     0.807     0.866 1.08    38
lambda.std[7]      0.815   0.051     0.682     0.790     0.822     0.851     0.890 1.08    39
lambda.std[8]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[9]      0.574   0.051     0.473     0.542     0.576     0.609     0.672 1.01   190
lambda.std[10]     0.504   0.052     0.407     0.470     0.503     0.538     0.607 1.02   160
lambda.std[11]     0.520   0.051     0.412     0.487     0.522     0.556     0.615 1.01   880
lambda.std[12]     0.679   0.055     0.566     0.642     0.682     0.719     0.778 1.03    82
lambda.std[13]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[14]     0.734   0.082     0.534     0.688     0.747     0.790     0.862 1.07    44
lambda.std[15]     0.398   0.070     0.285     0.349     0.389     0.437     0.557 1.01   290
lambda.std[16]     0.778   0.056     0.652     0.741     0.783     0.820     0.870 1.13    26
lambda.std[17]     0.768   0.064     0.621     0.729     0.775     0.815     0.866 1.06    48
lambda.std[18]     0.795   0.060     0.663     0.756     0.801     0.837     0.897 1.03   370
lambda.std[19]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[20]     0.712   0.051     0.604     0.680     0.714     0.746     0.807 1.07    42
lambda.std[21]     0.650   0.059     0.536     0.608     0.651     0.694     0.758 1.07    46
lambda.std[22]     0.742   0.042     0.655     0.714     0.743     0.770     0.820 1.02   180
lambda.std[23]     0.611   0.049     0.509     0.578     0.613     0.645     0.702 1.01   310
lambda.std[24]     0.651   0.050     0.549     0.619     0.652     0.683     0.749 1.02   150
lambda.std[25]     0.576   0.052     0.473     0.542     0.578     0.612     0.672 1.01   290
phi[1,1]           3.603   2.298     1.010     2.176     3.039     4.428     9.327 1.08    49
phi[2,1]           3.059   1.887     0.754     1.859     2.687     3.751     7.649 1.06    58
phi[3,1]           3.117   2.247     0.498     1.740     2.621     3.797     9.606 1.11    52
phi[4,1]           3.399   1.320     1.151     2.559     3.257     4.097     6.377 1.10    49
phi[1,2]           3.059   1.887     0.754     1.859     2.687     3.751     7.649 1.06    58
phi[2,2]           4.064   2.455     1.060     2.296     3.487     5.147    10.603 1.04    67
phi[3,2]           3.074   2.152     0.374     1.607     2.594     4.017     9.025 1.13    35
phi[4,2]           3.673   1.507     1.041     2.686     3.529     4.491     7.169 1.06    50
phi[1,3]           3.117   2.247     0.498     1.740     2.621     3.797     9.606 1.11    52
phi[2,3]           3.074   2.152     0.374     1.607     2.594     4.017     9.025 1.13    35
phi[3,3]           4.037   2.948     0.836     2.032     3.281     4.972    12.539 1.09    39
phi[4,3]           3.327   1.665     0.208     2.156     3.261     4.303     7.106 1.10    37
phi[1,4]           3.399   1.320     1.151     2.559     3.257     4.097     6.377 1.10    49
phi[2,4]           3.673   1.507     1.041     2.686     3.529     4.491     7.169 1.06    50
phi[3,4]           3.327   1.665     0.208     2.156     3.261     4.303     7.106 1.10    37
phi[4,4]           4.476   0.675     3.437     4.023     4.361     4.815     6.150 1.06    87
phi.cor[1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
phi.cor[2,1]       0.815   0.135     0.441     0.759     0.857     0.910     0.964 1.04   140
phi.cor[3,1]       0.821   0.178     0.331     0.782     0.877     0.928     0.975 1.08   110
phi.cor[4,1]       0.864   0.126     0.470     0.842     0.908     0.938     0.970 1.06    84
phi.cor[1,2]       0.815   0.135     0.441     0.759     0.857     0.910     0.964 1.04   140
phi.cor[2,2]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
phi.cor[3,2]       0.769   0.195     0.216     0.715     0.834     0.896     0.967 1.06    94
phi.cor[4,2]       0.873   0.156     0.462     0.862     0.922     0.950     0.976 1.21    45
phi.cor[1,3]       0.821   0.178     0.331     0.782     0.877     0.928     0.975 1.08   110
phi.cor[2,3]       0.769   0.195     0.216     0.715     0.834     0.896     0.967 1.06    94
phi.cor[3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
phi.cor[4,3]       0.795   0.218     0.100     0.751     0.880     0.931     0.968 1.07    73
phi.cor[1,4]       0.864   0.126     0.470     0.842     0.908     0.938     0.970 1.06    84
phi.cor[2,4]       0.873   0.156     0.462     0.862     0.922     0.950     0.976 1.21    45
phi.cor[3,4]       0.795   0.218     0.100     0.751     0.880     0.931     0.968 1.07    73
phi.cor[4,4]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
reli.omega[1]      0.917   0.016     0.882     0.909     0.918     0.927     0.943 1.12    28
reli.omega[2]      0.796   0.018     0.756     0.784     0.797     0.809     0.826 1.04    83
reli.omega[3]      0.872   0.021     0.827     0.857     0.873     0.888     0.906 1.07    47
reli.omega[4]      0.841   0.018     0.799     0.830     0.842     0.853     0.873 1.04    80
tau[1,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[2,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[3,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[4,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[5,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[6,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[7,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[8,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[9,1]           0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[10,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[11,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[12,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[13,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[14,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[15,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[16,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[17,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[18,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[19,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[20,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[21,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[22,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[23,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[24,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[25,1]          0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
tau[1,2]           3.889   0.324     3.329     3.670     3.859     4.087     4.617 1.03   140
tau[2,2]           4.801   0.716     3.673     4.239     4.703     5.325     6.255 1.02   110
tau[3,2]           4.220   0.577     3.253     3.808     4.164     4.589     5.453 1.01   230
tau[4,2]           3.511   0.722     2.253     2.987     3.490     3.979     5.021 1.07    43
tau[5,2]           4.637   0.972     3.082     3.881     4.593     5.259     6.692 1.06    49
tau[6,2]           4.170   0.732     3.031     3.629     4.067     4.608     5.786 1.07    51
tau[7,2]           5.432   0.764     4.023     4.908     5.384     5.927     7.034 1.06    47
tau[8,2]           3.099   0.325     2.532     2.870     3.076     3.304     3.804 1.03   100
tau[9,2]           1.132   0.251     0.643     0.982     1.128     1.280     1.634 1.01   320
tau[10,2]          1.539   0.155     1.287     1.433     1.523     1.626     1.878 1.00  3600
tau[11,2]          0.056   0.046     0.002     0.019     0.045     0.081     0.171 1.00  4000
tau[12,2]          2.690   0.458     1.988     2.366     2.623     2.932     3.807 1.03    90
tau[13,2]          2.758   0.288     2.245     2.554     2.737     2.939     3.371 1.01   230
tau[14,2]          4.573   0.863     3.093     3.968     4.498     5.108     6.466 1.06    49
tau[15,2]          1.722   0.566     1.200     1.400     1.555     1.839     3.081 1.02   820
tau[16,2]          5.510   0.703     4.277     4.993     5.460     5.987     7.001 1.08    35
tau[17,2]          4.676   0.741     3.365     4.152     4.626     5.147     6.250 1.05    62
tau[18,2]          5.255   0.865     3.841     4.684     5.193     5.681     7.469 1.08    68
tau[19,2]          2.694   0.264     2.249     2.509     2.665     2.847     3.308 1.04    78
tau[20,2]          3.450   0.509     2.655     3.077     3.382     3.762     4.636 1.04    62
tau[21,2]          2.429   0.480     1.715     2.062     2.343     2.741     3.488 1.06    48
tau[22,2]          3.267   0.431     2.558     2.958     3.222     3.529     4.234 1.02   120
tau[23,2]          0.042   0.036     0.001     0.014     0.033     0.060     0.135 1.00  4000
tau[24,2]          2.854   0.411     2.184     2.562     2.810     3.087     3.812 1.01   270
tau[25,2]          0.033   0.030     0.001     0.011     0.025     0.048     0.109 1.00  3500
theta[1]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[2]           2.919   0.645     2.001     2.432     2.782     3.323     4.338 1.03   110
theta[3]           2.608   0.543     1.768     2.221     2.528     2.927     3.807 1.02   140
theta[4]           2.378   0.528     1.542     2.000     2.311     2.702     3.600 1.06    54
theta[5]           3.274   0.995     1.874     2.572     3.136     3.746     5.854 1.08    40
theta[6]           2.512   0.626     1.660     2.046     2.370     2.868     3.996 1.10    34
theta[7]           3.168   0.750     1.870     2.665     3.076     3.618     4.827 1.10    30
theta[8]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[9]           1.510   0.136     1.288     1.416     1.497     1.589     1.825 1.01   180
theta[10]          1.353   0.102     1.199     1.284     1.338     1.407     1.583 1.02   160
theta[11]          1.384   0.103     1.205     1.310     1.375     1.447     1.607 1.00  1600
theta[12]          1.903   0.273     1.470     1.702     1.871     2.069     2.533 1.04    74
theta[13]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[14]          2.350   0.641     1.399     1.900     2.264     2.655     3.887 1.06    45
theta[15]          1.202   0.095     1.089     1.139     1.178     1.236     1.451 1.01   410
theta[16]          2.681   0.618     1.738     2.220     2.583     3.051     4.128 1.13    25
theta[17]          2.598   0.619     1.629     2.133     2.507     2.974     3.989 1.09    34
theta[18]          2.944   0.852     1.786     2.336     2.787     3.331     5.127 1.06   110
theta[19]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[20]          2.082   0.321     1.574     1.859     2.039     2.255     2.862 1.06    44
theta[21]          1.776   0.252     1.402     1.585     1.736     1.928     2.350 1.08    39
theta[22]          2.274   0.327     1.753     2.042     2.233     2.452     3.045 1.02   190
theta[23]          1.618   0.160     1.349     1.502     1.602     1.711     1.973 1.01   280
theta[24]          1.765   0.211     1.431     1.620     1.738     1.874     2.278 1.02   130
theta[25]          1.515   0.139     1.288     1.415     1.501     1.599     1.823 1.01   310
deviance       16276.867 121.949 16038.854 16194.304 16276.698 16358.334 16513.894 1.01   500

For each parameter, n.eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)
pD = 7397.0 and DIC = 23673.9
DIC is an estimate of expected predictive error (lower deviance is better).
kable(model.fit$BUGSoutput$summary, format="html", digits=3) %>%
  kable_styling(full_width = T) %>%
  scroll_box(width="100%", height="500px")
mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
deviance 16276.867 121.949 16038.854 16194.304 16276.698 16358.334 16513.894 1.01 500
gamma[1,1,1] 0.767 0.061 0.638 0.729 0.770 0.810 0.877 1.00 1500
gamma[2,1,1] 0.841 0.049 0.733 0.809 0.845 0.876 0.929 1.01 390
gamma[3,1,1] 0.612 0.086 0.441 0.554 0.616 0.674 0.771 1.01 310
gamma[4,1,1] 0.522 0.088 0.353 0.461 0.522 0.580 0.693 1.02 140
gamma[5,1,1] 0.699 0.070 0.554 0.654 0.700 0.748 0.828 1.02 110
gamma[6,1,1] 0.721 0.076 0.566 0.671 0.723 0.773 0.866 1.01 210
gamma[7,1,1] 0.769 0.074 0.613 0.721 0.774 0.820 0.899 1.02 110
gamma[8,1,1] 0.698 0.078 0.534 0.647 0.701 0.753 0.838 1.00 4000
gamma[9,1,1] 0.894 0.101 0.607 0.850 0.925 0.970 0.997 1.00 1700
gamma[10,1,1] 0.805 0.123 0.533 0.724 0.823 0.901 0.987 1.00 1500
gamma[11,1,1] 0.263 0.069 0.146 0.214 0.256 0.307 0.413 1.01 190
gamma[12,1,1] 0.959 0.032 0.877 0.941 0.967 0.984 0.998 1.01 380
gamma[13,1,1] 0.962 0.032 0.882 0.945 0.970 0.987 0.999 1.00 770
gamma[14,1,1] 0.575 0.111 0.356 0.497 0.574 0.650 0.789 1.00 890
gamma[15,1,1] 0.820 0.129 0.538 0.732 0.847 0.925 0.993 1.01 460
gamma[16,1,1] 0.634 0.103 0.422 0.570 0.642 0.704 0.823 1.00 820
gamma[17,1,1] 0.692 0.098 0.491 0.626 0.697 0.763 0.870 1.01 320
gamma[18,1,1] 0.593 0.108 0.368 0.521 0.595 0.669 0.794 1.03 150
gamma[19,1,1] 0.953 0.033 0.873 0.933 0.960 0.978 0.998 1.00 2700
gamma[20,1,1] 0.907 0.047 0.808 0.878 0.910 0.940 0.988 1.02 130
gamma[21,1,1] 0.873 0.075 0.710 0.824 0.879 0.930 0.993 1.02 130
gamma[22,1,1] 0.975 0.022 0.920 0.964 0.981 0.991 0.999 1.00 1400
gamma[23,1,1] 0.192 0.053 0.107 0.155 0.185 0.223 0.315 1.01 610
gamma[24,1,1] 0.956 0.036 0.864 0.937 0.964 0.983 0.998 1.00 990
gamma[25,1,1] 0.152 0.042 0.080 0.123 0.149 0.177 0.245 1.01 340
gamma[1,2,1] 0.015 0.018 0.000 0.002 0.009 0.022 0.063 1.00 3700
gamma[2,2,1] 0.008 0.011 0.000 0.001 0.004 0.012 0.039 1.02 290
gamma[3,2,1] 0.005 0.007 0.000 0.001 0.002 0.007 0.023 1.03 240
gamma[4,2,1] 0.005 0.008 0.000 0.001 0.003 0.007 0.028 1.00 670
gamma[5,2,1] 0.015 0.013 0.000 0.005 0.012 0.022 0.049 1.03 400
gamma[6,2,1] 0.023 0.019 0.000 0.008 0.019 0.034 0.072 1.06 89
gamma[7,2,1] 0.007 0.009 0.000 0.001 0.003 0.009 0.031 1.04 130
gamma[8,2,1] 0.020 0.019 0.000 0.004 0.014 0.028 0.070 1.10 52
gamma[9,2,1] 0.018 0.024 0.000 0.002 0.009 0.025 0.089 1.01 960
gamma[10,2,1] 0.020 0.024 0.000 0.003 0.011 0.028 0.087 1.01 650
gamma[11,2,1] 0.035 0.031 0.000 0.013 0.029 0.050 0.114 1.22 44
gamma[12,2,1] 0.077 0.056 0.001 0.031 0.069 0.115 0.200 1.04 120
gamma[13,2,1] 0.051 0.038 0.001 0.022 0.044 0.072 0.140 1.05 110
gamma[14,2,1] 0.008 0.008 0.000 0.002 0.006 0.012 0.030 1.09 48
gamma[15,2,1] 0.007 0.011 0.000 0.001 0.003 0.010 0.039 1.01 480
gamma[16,2,1] 0.002 0.004 0.000 0.000 0.001 0.003 0.013 1.01 310
gamma[17,2,1] 0.005 0.006 0.000 0.000 0.002 0.006 0.023 1.17 36
gamma[18,2,1] 0.004 0.005 0.000 0.000 0.002 0.004 0.017 1.04 87
gamma[19,2,1] 0.014 0.019 0.000 0.002 0.007 0.020 0.069 1.01 390
gamma[20,2,1] 0.019 0.023 0.000 0.002 0.010 0.029 0.085 1.02 950
gamma[21,2,1] 0.022 0.028 0.000 0.003 0.011 0.031 0.102 1.02 280
gamma[22,2,1] 0.039 0.035 0.000 0.010 0.031 0.058 0.123 1.01 630
gamma[23,2,1] 0.075 0.039 0.018 0.047 0.068 0.095 0.169 1.01 240
gamma[24,2,1] 0.034 0.036 0.000 0.006 0.022 0.051 0.129 1.04 110
gamma[25,2,1] 0.038 0.028 0.002 0.018 0.034 0.052 0.108 1.07 70
gamma[1,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,1,2] 0.233 0.061 0.123 0.190 0.230 0.271 0.362 1.00 1300
gamma[2,1,2] 0.159 0.049 0.071 0.124 0.155 0.191 0.267 1.01 380
gamma[3,1,2] 0.388 0.086 0.229 0.326 0.384 0.446 0.559 1.01 300
gamma[4,1,2] 0.478 0.088 0.307 0.420 0.478 0.539 0.647 1.03 110
gamma[5,1,2] 0.301 0.070 0.172 0.252 0.300 0.346 0.446 1.02 110
gamma[6,1,2] 0.279 0.076 0.134 0.227 0.277 0.329 0.434 1.02 180
gamma[7,1,2] 0.231 0.074 0.101 0.180 0.226 0.279 0.387 1.02 110
gamma[8,1,2] 0.302 0.078 0.162 0.247 0.299 0.353 0.466 1.00 4000
gamma[9,1,2] 0.106 0.101 0.003 0.030 0.075 0.150 0.393 1.01 1100
gamma[10,1,2] 0.195 0.123 0.013 0.099 0.177 0.276 0.467 1.01 1100
gamma[11,1,2] 0.737 0.069 0.587 0.693 0.744 0.786 0.854 1.02 160
gamma[12,1,2] 0.041 0.032 0.002 0.016 0.033 0.059 0.123 1.01 260
gamma[13,1,2] 0.038 0.032 0.001 0.013 0.030 0.055 0.118 1.00 800
gamma[14,1,2] 0.425 0.111 0.211 0.350 0.426 0.503 0.644 1.01 460
gamma[15,1,2] 0.180 0.129 0.007 0.075 0.153 0.268 0.462 1.01 290
gamma[16,1,2] 0.366 0.103 0.177 0.296 0.358 0.430 0.578 1.00 700
gamma[17,1,2] 0.308 0.098 0.130 0.237 0.303 0.374 0.509 1.01 490
gamma[18,1,2] 0.407 0.108 0.206 0.331 0.405 0.479 0.632 1.02 200
gamma[19,1,2] 0.047 0.033 0.002 0.022 0.040 0.067 0.127 1.01 1100
gamma[20,1,2] 0.093 0.047 0.012 0.060 0.090 0.122 0.192 1.08 90
gamma[21,1,2] 0.127 0.075 0.007 0.070 0.121 0.176 0.290 1.02 260
gamma[22,1,2] 0.025 0.022 0.001 0.009 0.019 0.036 0.080 1.00 980
gamma[23,1,2] 0.808 0.053 0.685 0.777 0.815 0.845 0.893 1.01 390
gamma[24,1,2] 0.044 0.036 0.002 0.017 0.036 0.063 0.136 1.01 470
gamma[25,1,2] 0.848 0.042 0.755 0.823 0.851 0.877 0.920 1.01 340
gamma[1,2,2] 0.946 0.049 0.817 0.925 0.962 0.982 0.998 1.00 4000
gamma[2,2,2] 0.951 0.049 0.820 0.930 0.967 0.987 0.999 1.00 1300
gamma[3,2,2] 0.696 0.118 0.476 0.608 0.690 0.779 0.935 1.02 170
gamma[4,2,2] 0.952 0.055 0.789 0.937 0.972 0.990 0.999 1.02 150
gamma[5,2,2] 0.916 0.076 0.715 0.880 0.941 0.973 0.995 1.02 180
gamma[6,2,2] 0.828 0.122 0.566 0.748 0.843 0.931 0.992 1.00 3500
gamma[7,2,2] 0.679 0.146 0.422 0.569 0.669 0.787 0.966 1.02 170
gamma[8,2,2] 0.932 0.059 0.780 0.906 0.950 0.976 0.997 1.01 280
gamma[9,2,2] 0.871 0.099 0.612 0.826 0.893 0.942 0.991 1.02 270
gamma[10,2,2] 0.953 0.043 0.837 0.933 0.965 0.985 0.998 1.00 2800
gamma[11,2,2] 0.647 0.050 0.549 0.614 0.645 0.680 0.745 1.01 330
gamma[12,2,2] 0.900 0.064 0.760 0.859 0.910 0.952 0.992 1.00 520
gamma[13,2,2] 0.928 0.046 0.824 0.900 0.935 0.963 0.994 1.01 450
gamma[14,2,2] 0.262 0.054 0.165 0.224 0.259 0.297 0.377 1.00 1100
gamma[15,2,2] 0.623 0.159 0.353 0.503 0.611 0.725 0.959 1.00 1900
gamma[16,2,2] 0.106 0.027 0.060 0.087 0.103 0.122 0.169 1.01 390
gamma[17,2,2] 0.372 0.084 0.222 0.312 0.368 0.425 0.549 1.01 460
gamma[18,2,2] 0.409 0.083 0.267 0.352 0.401 0.463 0.592 1.02 180
gamma[19,2,2] 0.971 0.027 0.900 0.960 0.979 0.991 0.999 1.02 370
gamma[20,2,2] 0.959 0.038 0.866 0.941 0.970 0.987 0.999 1.01 480
gamma[21,2,2] 0.963 0.034 0.869 0.948 0.973 0.988 0.999 1.01 630
gamma[22,2,2] 0.941 0.044 0.832 0.915 0.949 0.975 0.998 1.01 260
gamma[23,2,2] 0.738 0.042 0.650 0.711 0.739 0.766 0.818 1.00 1800
gamma[24,2,2] 0.945 0.046 0.825 0.921 0.957 0.980 0.998 1.01 420
gamma[25,2,2] 0.594 0.052 0.488 0.559 0.595 0.628 0.692 1.00 740
gamma[1,3,2] 0.051 0.023 0.012 0.034 0.048 0.066 0.102 1.00 860
gamma[2,3,2] 0.035 0.019 0.004 0.020 0.032 0.047 0.078 1.01 2900
gamma[3,3,2] 0.033 0.019 0.005 0.018 0.030 0.044 0.079 1.01 410
gamma[4,3,2] 0.171 0.060 0.048 0.132 0.171 0.211 0.291 1.07 57
gamma[5,3,2] 0.118 0.042 0.044 0.088 0.115 0.145 0.207 1.02 140
gamma[6,3,2] 0.041 0.024 0.005 0.024 0.038 0.056 0.095 1.03 240
gamma[7,3,2] 0.024 0.014 0.003 0.014 0.022 0.033 0.057 1.02 260
gamma[8,3,2] 0.230 0.055 0.129 0.192 0.228 0.265 0.345 1.00 1700
gamma[9,3,2] 0.328 0.163 0.028 0.207 0.334 0.451 0.628 1.01 370
gamma[10,3,2] 0.067 0.058 0.001 0.022 0.051 0.099 0.211 1.00 1700
gamma[11,3,2] 0.065 0.059 0.003 0.021 0.049 0.091 0.216 1.01 340
gamma[12,3,2] 0.345 0.079 0.192 0.290 0.344 0.399 0.501 1.00 890
gamma[13,3,2] 0.333 0.069 0.198 0.288 0.332 0.379 0.471 1.00 2300
gamma[14,3,2] 0.055 0.020 0.018 0.041 0.054 0.068 0.098 1.03 160
gamma[15,3,2] 0.105 0.088 0.003 0.033 0.079 0.162 0.308 1.01 590
gamma[16,3,2] 0.006 0.005 0.000 0.003 0.005 0.008 0.018 1.01 350
gamma[17,3,2] 0.032 0.016 0.005 0.020 0.030 0.041 0.066 1.01 810
gamma[18,3,2] 0.048 0.018 0.020 0.036 0.047 0.058 0.090 1.01 180
gamma[19,3,2] 0.127 0.057 0.026 0.084 0.124 0.164 0.242 1.04 110
gamma[20,3,2] 0.064 0.037 0.004 0.035 0.061 0.088 0.146 1.03 150
gamma[21,3,2] 0.294 0.100 0.088 0.226 0.298 0.367 0.476 1.03 110
gamma[22,3,2] 0.262 0.059 0.154 0.220 0.260 0.301 0.380 1.01 490
gamma[23,3,2] 0.057 0.053 0.002 0.018 0.040 0.082 0.197 1.01 850
gamma[24,3,2] 0.272 0.070 0.134 0.225 0.271 0.319 0.406 1.00 680
gamma[25,3,2] 0.069 0.063 0.002 0.022 0.052 0.098 0.229 1.00 780
gamma[1,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,1,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,2,3] 0.038 0.046 0.000 0.005 0.022 0.056 0.156 1.01 570
gamma[2,2,3] 0.040 0.047 0.000 0.005 0.022 0.061 0.171 1.02 660
gamma[3,2,3] 0.299 0.117 0.062 0.216 0.305 0.385 0.519 1.01 290
gamma[4,2,3] 0.043 0.054 0.000 0.005 0.022 0.058 0.200 1.02 150
gamma[5,2,3] 0.069 0.074 0.000 0.012 0.044 0.103 0.262 1.10 63
gamma[6,2,3] 0.149 0.116 0.001 0.050 0.131 0.228 0.405 1.00 4000
gamma[7,2,3] 0.315 0.146 0.025 0.208 0.326 0.425 0.573 1.14 83
gamma[8,2,3] 0.048 0.053 0.000 0.008 0.030 0.069 0.193 1.00 550
gamma[9,2,3] 0.111 0.091 0.001 0.044 0.090 0.153 0.357 1.07 100
gamma[10,2,3] 0.027 0.035 0.000 0.002 0.013 0.039 0.128 1.02 220
gamma[11,2,3] 0.317 0.054 0.215 0.281 0.316 0.354 0.424 1.01 390
gamma[12,2,3] 0.023 0.027 0.000 0.003 0.013 0.035 0.090 1.05 100
gamma[13,2,3] 0.021 0.026 0.000 0.002 0.011 0.030 0.091 1.01 570
gamma[14,2,3] 0.729 0.053 0.616 0.696 0.732 0.766 0.827 1.00 1300
gamma[15,2,3] 0.370 0.159 0.035 0.267 0.383 0.491 0.642 1.04 360
gamma[16,2,3] 0.892 0.027 0.830 0.875 0.895 0.911 0.938 1.01 470
gamma[17,2,3] 0.623 0.083 0.448 0.570 0.628 0.682 0.771 1.01 480
gamma[18,2,3] 0.587 0.083 0.407 0.534 0.595 0.644 0.730 1.02 200
gamma[19,2,3] 0.015 0.019 0.000 0.002 0.008 0.020 0.065 1.01 310
gamma[20,2,3] 0.022 0.029 0.000 0.003 0.011 0.030 0.106 1.08 69
gamma[21,2,3] 0.014 0.020 0.000 0.001 0.007 0.019 0.071 1.01 310
gamma[22,2,3] 0.020 0.024 0.000 0.003 0.011 0.029 0.088 1.05 280
gamma[23,2,3] 0.187 0.046 0.104 0.157 0.186 0.217 0.283 1.01 210
gamma[24,2,3] 0.021 0.027 0.000 0.002 0.010 0.030 0.095 1.03 310
gamma[25,2,3] 0.368 0.058 0.258 0.328 0.366 0.406 0.487 1.00 1500
gamma[1,3,3] 0.949 0.023 0.898 0.934 0.952 0.966 0.988 1.00 1100
gamma[2,3,3] 0.965 0.019 0.922 0.953 0.968 0.980 0.996 1.00 1100
gamma[3,3,3] 0.967 0.019 0.921 0.956 0.970 0.982 0.995 1.00 650
gamma[4,3,3] 0.829 0.060 0.709 0.789 0.829 0.868 0.952 1.04 70
gamma[5,3,3] 0.882 0.042 0.793 0.855 0.885 0.912 0.956 1.02 160
gamma[6,3,3] 0.959 0.024 0.905 0.944 0.962 0.976 0.995 1.01 230
gamma[7,3,3] 0.976 0.014 0.943 0.967 0.978 0.986 0.997 1.01 430
gamma[8,3,3] 0.770 0.055 0.655 0.735 0.772 0.808 0.871 1.00 2300
gamma[9,3,3] 0.672 0.163 0.372 0.549 0.666 0.793 0.972 1.01 200
gamma[10,3,3] 0.933 0.058 0.789 0.901 0.949 0.978 0.999 1.00 1400
gamma[11,3,3] 0.935 0.059 0.784 0.909 0.951 0.979 0.997 1.01 340
gamma[12,3,3] 0.655 0.079 0.499 0.601 0.656 0.710 0.808 1.00 660
gamma[13,3,3] 0.667 0.069 0.529 0.621 0.668 0.712 0.802 1.00 2900
gamma[14,3,3] 0.945 0.020 0.902 0.932 0.946 0.959 0.982 1.01 220
gamma[15,3,3] 0.895 0.088 0.692 0.838 0.921 0.967 0.997 1.00 950
gamma[16,3,3] 0.994 0.005 0.982 0.992 0.995 0.997 1.000 1.00 630
gamma[17,3,3] 0.968 0.016 0.934 0.959 0.970 0.980 0.995 1.00 1100
gamma[18,3,3] 0.952 0.018 0.910 0.942 0.953 0.964 0.980 1.02 160
gamma[19,3,3] 0.873 0.057 0.758 0.836 0.876 0.916 0.974 1.02 100
gamma[20,3,3] 0.936 0.037 0.854 0.912 0.939 0.965 0.996 1.01 170
gamma[21,3,3] 0.706 0.100 0.524 0.633 0.702 0.774 0.912 1.03 87
gamma[22,3,3] 0.738 0.059 0.620 0.699 0.740 0.780 0.846 1.01 530
gamma[23,3,3] 0.943 0.053 0.803 0.918 0.960 0.982 0.998 1.01 1500
gamma[24,3,3] 0.728 0.070 0.594 0.681 0.729 0.775 0.866 1.00 590
gamma[25,3,3] 0.931 0.063 0.771 0.902 0.948 0.978 0.998 1.01 450
inv.phi[1,1] 3.368 1.621 0.951 2.208 3.123 4.248 7.213 1.09 35
inv.phi[2,1] -0.434 1.046 -2.551 -1.127 -0.389 0.292 1.487 1.02 170
inv.phi[3,1] -1.271 1.144 -3.926 -1.901 -1.155 -0.480 0.566 1.01 220
inv.phi[4,1] -1.270 1.197 -3.901 -1.972 -1.152 -0.480 0.762 1.01 240
inv.phi[1,2] -0.434 1.046 -2.551 -1.127 -0.389 0.292 1.487 1.02 170
inv.phi[2,2] 2.938 1.426 0.879 1.881 2.730 3.737 6.381 1.02 270
inv.phi[3,2] -0.254 1.008 -2.250 -0.892 -0.282 0.371 1.783 1.02 180
inv.phi[4,2] -1.826 1.412 -5.249 -2.569 -1.605 -0.826 0.326 1.02 150
inv.phi[1,3] -1.271 1.144 -3.926 -1.901 -1.155 -0.480 0.566 1.01 220
inv.phi[2,3] -0.254 1.008 -2.250 -0.892 -0.282 0.371 1.783 1.02 180
inv.phi[3,3] 2.641 1.417 0.638 1.597 2.371 3.383 6.162 1.02 260
inv.phi[4,3] -0.757 1.193 -3.407 -1.501 -0.619 0.110 1.213 1.01 320
inv.phi[1,4] -1.270 1.197 -3.901 -1.972 -1.152 -0.480 0.762 1.01 240
inv.phi[2,4] -1.826 1.412 -5.249 -2.569 -1.605 -0.826 0.326 1.02 150
inv.phi[3,4] -0.757 1.193 -3.407 -1.501 -0.619 0.110 1.213 1.01 320
inv.phi[4,4] 3.537 2.014 0.764 2.051 3.114 4.649 8.520 1.03 120
lambda[1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[2] 1.367 0.226 1.000 1.197 1.335 1.524 1.827 1.03 110
lambda[3] 1.251 0.209 0.876 1.105 1.236 1.388 1.675 1.02 130
lambda[4] 1.152 0.224 0.736 1.000 1.145 1.304 1.612 1.06 50
lambda[5] 1.475 0.315 0.935 1.254 1.462 1.657 2.203 1.08 39
lambda[6] 1.205 0.244 0.812 1.023 1.171 1.367 1.731 1.09 35
lambda[7] 1.450 0.255 0.933 1.290 1.441 1.618 1.956 1.09 33
lambda[8] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[9] 0.708 0.094 0.536 0.645 0.705 0.768 0.908 1.01 180
lambda[10] 0.588 0.083 0.446 0.533 0.581 0.638 0.763 1.02 160
lambda[11] 0.614 0.083 0.452 0.557 0.613 0.668 0.779 1.01 1000
lambda[12] 0.940 0.141 0.686 0.838 0.933 1.034 1.238 1.03 78
lambda[13] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[14] 1.130 0.268 0.632 0.949 1.124 1.287 1.699 1.07 44
lambda[15] 0.439 0.096 0.298 0.373 0.422 0.486 0.671 1.01 310
lambda[16] 1.275 0.233 0.859 1.105 1.258 1.432 1.769 1.13 25
lambda[17] 1.241 0.243 0.793 1.065 1.228 1.405 1.729 1.08 39
lambda[18] 1.364 0.290 0.887 1.156 1.337 1.527 2.031 1.05 160
lambda[19] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[20] 1.029 0.151 0.757 0.927 1.020 1.120 1.365 1.07 43
lambda[21] 0.870 0.140 0.634 0.765 0.858 0.963 1.162 1.08 42
lambda[22] 1.120 0.142 0.868 1.021 1.110 1.205 1.430 1.02 180
lambda[23] 0.780 0.101 0.591 0.708 0.776 0.843 0.986 1.01 300
lambda[24] 0.867 0.118 0.657 0.787 0.859 0.935 1.131 1.02 140
lambda[25] 0.711 0.096 0.536 0.644 0.708 0.774 0.907 1.01 290
lambda.std[1] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[2] 0.800 0.046 0.707 0.767 0.800 0.836 0.877 1.03 97
lambda.std[3] 0.773 0.052 0.659 0.742 0.777 0.811 0.859 1.02 120
lambda.std[4] 0.745 0.066 0.593 0.707 0.753 0.794 0.850 1.07 47
lambda.std[5] 0.816 0.058 0.683 0.782 0.825 0.856 0.911 1.09 38
lambda.std[6] 0.759 0.062 0.630 0.715 0.760 0.807 0.866 1.08 38
lambda.std[7] 0.815 0.051 0.682 0.790 0.822 0.851 0.890 1.08 39
lambda.std[8] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[9] 0.574 0.051 0.473 0.542 0.576 0.609 0.672 1.01 190
lambda.std[10] 0.504 0.052 0.407 0.470 0.503 0.538 0.607 1.02 160
lambda.std[11] 0.520 0.051 0.412 0.487 0.522 0.556 0.615 1.01 880
lambda.std[12] 0.679 0.055 0.566 0.642 0.682 0.719 0.778 1.03 82
lambda.std[13] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[14] 0.734 0.082 0.534 0.688 0.747 0.790 0.862 1.07 44
lambda.std[15] 0.398 0.070 0.285 0.349 0.389 0.437 0.557 1.01 290
lambda.std[16] 0.778 0.056 0.652 0.741 0.783 0.820 0.870 1.13 26
lambda.std[17] 0.768 0.064 0.621 0.729 0.775 0.815 0.866 1.06 48
lambda.std[18] 0.795 0.060 0.663 0.756 0.801 0.837 0.897 1.03 370
lambda.std[19] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[20] 0.712 0.051 0.604 0.680 0.714 0.746 0.807 1.07 42
lambda.std[21] 0.650 0.059 0.536 0.608 0.651 0.694 0.758 1.07 46
lambda.std[22] 0.742 0.042 0.655 0.714 0.743 0.770 0.820 1.02 180
lambda.std[23] 0.611 0.049 0.509 0.578 0.613 0.645 0.702 1.01 310
lambda.std[24] 0.651 0.050 0.549 0.619 0.652 0.683 0.749 1.02 150
lambda.std[25] 0.576 0.052 0.473 0.542 0.578 0.612 0.672 1.01 290
phi[1,1] 3.603 2.298 1.010 2.176 3.039 4.428 9.327 1.08 49
phi[2,1] 3.059 1.887 0.754 1.859 2.687 3.751 7.649 1.06 58
phi[3,1] 3.117 2.247 0.498 1.740 2.621 3.797 9.606 1.11 52
phi[4,1] 3.399 1.320 1.151 2.559 3.257 4.097 6.377 1.10 49
phi[1,2] 3.059 1.887 0.754 1.859 2.687 3.751 7.649 1.06 58
phi[2,2] 4.064 2.455 1.060 2.296 3.487 5.147 10.603 1.04 67
phi[3,2] 3.074 2.152 0.374 1.607 2.594 4.017 9.025 1.13 35
phi[4,2] 3.673 1.507 1.041 2.686 3.529 4.491 7.169 1.06 50
phi[1,3] 3.117 2.247 0.498 1.740 2.621 3.797 9.606 1.11 52
phi[2,3] 3.074 2.152 0.374 1.607 2.594 4.017 9.025 1.13 35
phi[3,3] 4.037 2.948 0.836 2.032 3.281 4.972 12.539 1.09 39
phi[4,3] 3.327 1.665 0.208 2.156 3.261 4.303 7.106 1.10 37
phi[1,4] 3.399 1.320 1.151 2.559 3.257 4.097 6.377 1.10 49
phi[2,4] 3.673 1.507 1.041 2.686 3.529 4.491 7.169 1.06 50
phi[3,4] 3.327 1.665 0.208 2.156 3.261 4.303 7.106 1.10 37
phi[4,4] 4.476 0.675 3.437 4.023 4.361 4.815 6.150 1.06 87
phi.cor[1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
phi.cor[2,1] 0.815 0.135 0.441 0.759 0.857 0.910 0.964 1.04 140
phi.cor[3,1] 0.821 0.178 0.331 0.782 0.877 0.928 0.975 1.08 110
phi.cor[4,1] 0.864 0.126 0.470 0.842 0.908 0.938 0.970 1.06 84
phi.cor[1,2] 0.815 0.135 0.441 0.759 0.857 0.910 0.964 1.04 140
phi.cor[2,2] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
phi.cor[3,2] 0.769 0.195 0.216 0.715 0.834 0.896 0.967 1.06 94
phi.cor[4,2] 0.873 0.156 0.462 0.862 0.922 0.950 0.976 1.21 45
phi.cor[1,3] 0.821 0.178 0.331 0.782 0.877 0.928 0.975 1.08 110
phi.cor[2,3] 0.769 0.195 0.216 0.715 0.834 0.896 0.967 1.06 94
phi.cor[3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
phi.cor[4,3] 0.795 0.218 0.100 0.751 0.880 0.931 0.968 1.07 73
phi.cor[1,4] 0.864 0.126 0.470 0.842 0.908 0.938 0.970 1.06 84
phi.cor[2,4] 0.873 0.156 0.462 0.862 0.922 0.950 0.976 1.21 45
phi.cor[3,4] 0.795 0.218 0.100 0.751 0.880 0.931 0.968 1.07 73
phi.cor[4,4] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
reli.omega[1] 0.917 0.016 0.882 0.909 0.918 0.927 0.943 1.12 28
reli.omega[2] 0.796 0.018 0.756 0.784 0.797 0.809 0.826 1.04 83
reli.omega[3] 0.872 0.021 0.827 0.857 0.873 0.888 0.906 1.07 47
reli.omega[4] 0.841 0.018 0.799 0.830 0.842 0.853 0.873 1.04 80
tau[1,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[4,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[5,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[6,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[7,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[8,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[9,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[10,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[11,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[12,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[13,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[14,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[15,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[16,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[17,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[18,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[19,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[20,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[21,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[22,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[23,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[24,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[25,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
tau[1,2] 3.889 0.324 3.329 3.670 3.859 4.087 4.617 1.03 140
tau[2,2] 4.801 0.716 3.673 4.239 4.703 5.325 6.255 1.02 110
tau[3,2] 4.220 0.577 3.253 3.808 4.164 4.589 5.453 1.01 230
tau[4,2] 3.511 0.722 2.253 2.987 3.490 3.979 5.021 1.07 43
tau[5,2] 4.637 0.972 3.082 3.881 4.593 5.259 6.692 1.06 49
tau[6,2] 4.170 0.732 3.031 3.629 4.067 4.608 5.786 1.07 51
tau[7,2] 5.432 0.764 4.023 4.908 5.384 5.927 7.034 1.06 47
tau[8,2] 3.099 0.325 2.532 2.870 3.076 3.304 3.804 1.03 100
tau[9,2] 1.132 0.251 0.643 0.982 1.128 1.280 1.634 1.01 320
tau[10,2] 1.539 0.155 1.287 1.433 1.523 1.626 1.878 1.00 3600
tau[11,2] 0.056 0.046 0.002 0.019 0.045 0.081 0.171 1.00 4000
tau[12,2] 2.690 0.458 1.988 2.366 2.623 2.932 3.807 1.03 90
tau[13,2] 2.758 0.288 2.245 2.554 2.737 2.939 3.371 1.01 230
tau[14,2] 4.573 0.863 3.093 3.968 4.498 5.108 6.466 1.06 49
tau[15,2] 1.722 0.566 1.200 1.400 1.555 1.839 3.081 1.02 820
tau[16,2] 5.510 0.703 4.277 4.993 5.460 5.987 7.001 1.08 35
tau[17,2] 4.676 0.741 3.365 4.152 4.626 5.147 6.250 1.05 62
tau[18,2] 5.255 0.865 3.841 4.684 5.193 5.681 7.469 1.08 68
tau[19,2] 2.694 0.264 2.249 2.509 2.665 2.847 3.308 1.04 78
tau[20,2] 3.450 0.509 2.655 3.077 3.382 3.762 4.636 1.04 62
tau[21,2] 2.429 0.480 1.715 2.062 2.343 2.741 3.488 1.06 48
tau[22,2] 3.267 0.431 2.558 2.958 3.222 3.529 4.234 1.02 120
tau[23,2] 0.042 0.036 0.001 0.014 0.033 0.060 0.135 1.00 4000
tau[24,2] 2.854 0.411 2.184 2.562 2.810 3.087 3.812 1.01 270
tau[25,2] 0.033 0.030 0.001 0.011 0.025 0.048 0.109 1.00 3500
theta[1] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[2] 2.919 0.645 2.001 2.432 2.782 3.323 4.338 1.03 110
theta[3] 2.608 0.543 1.768 2.221 2.528 2.927 3.807 1.02 140
theta[4] 2.378 0.528 1.542 2.000 2.311 2.702 3.600 1.06 54
theta[5] 3.274 0.995 1.874 2.572 3.136 3.746 5.854 1.08 40
theta[6] 2.512 0.626 1.660 2.046 2.370 2.868 3.996 1.10 34
theta[7] 3.168 0.750 1.870 2.665 3.076 3.618 4.827 1.10 30
theta[8] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[9] 1.510 0.136 1.288 1.416 1.497 1.589 1.825 1.01 180
theta[10] 1.353 0.102 1.199 1.284 1.338 1.407 1.583 1.02 160
theta[11] 1.384 0.103 1.205 1.310 1.375 1.447 1.607 1.00 1600
theta[12] 1.903 0.273 1.470 1.702 1.871 2.069 2.533 1.04 74
theta[13] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[14] 2.350 0.641 1.399 1.900 2.264 2.655 3.887 1.06 45
theta[15] 1.202 0.095 1.089 1.139 1.178 1.236 1.451 1.01 410
theta[16] 2.681 0.618 1.738 2.220 2.583 3.051 4.128 1.13 25
theta[17] 2.598 0.619 1.629 2.133 2.507 2.974 3.989 1.09 34
theta[18] 2.944 0.852 1.786 2.336 2.787 3.331 5.127 1.06 110
theta[19] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[20] 2.082 0.321 1.574 1.859 2.039 2.255 2.862 1.06 44
theta[21] 1.776 0.252 1.402 1.585 1.736 1.928 2.350 1.08 39
theta[22] 2.274 0.327 1.753 2.042 2.233 2.452 3.045 1.02 190
theta[23] 1.618 0.160 1.349 1.502 1.602 1.711 1.973 1.01 280
theta[24] 1.765 0.211 1.431 1.620 1.738 1.874 2.278 1.02 130
theta[25] 1.515 0.139 1.288 1.415 1.501 1.599 1.823 1.01 310

Posterior Distribution Summary

# extract for plotting
jags.mcmc <- as.mcmc(model.fit)
a <- colnames(as.data.frame(jags.mcmc[[1]]))
fit.mcmc <- data.frame(as.matrix(jags.mcmc, chains = T, iters = T))
colnames(fit.mcmc) <- c("chain", "iter", a)
fit.mcmc.ggs <- ggmcmc::ggs(jags.mcmc) # for GRB plot

Factor Loadings (\(\lambda\))

bayesplot::mcmc_areas(fit.mcmc, regex_pars = "lambda.std", prob = 0.8); ggsave("fig/pools_model2_lambda_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/pools_model2_lambda_acf.pdf")
Warning: Removed 336 rows containing missing values (geom_segment).
Warning: Removed 21 row(s) containing missing values (geom_path).

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Warning: Removed 336 rows containing missing values (geom_segment).

Warning: Removed 21 row(s) containing missing values (geom_path).
bayesplot::mcmc_trace(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/pools_model2_lambda_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda.std"); ggsave("fig/pools_model2_lambda_grb.pdf")
Warning: Removed 50 row(s) containing missing values (geom_path).

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Warning: Removed 50 row(s) containing missing values (geom_path).

Factor Correlations

bayesplot::mcmc_areas(
  fit.mcmc,
  pars = c('phi.cor[1,2]', 'phi.cor[1,3]', 'phi.cor[1,4]',
           'phi.cor[2,3]', 'phi.cor[2,4]', 'phi.cor[3,4]'), prob = 0.8)

bayesplot::mcmc_acf(
  fit.mcmc,
  pars = c('phi.cor[1,2]', 'phi.cor[1,3]', 'phi.cor[1,4]',
           'phi.cor[2,3]', 'phi.cor[2,4]', 'phi.cor[3,4]'))

bayesplot::mcmc_trace(
  fit.mcmc,
  pars = c('phi.cor[1,2]', 'phi.cor[1,3]', 'phi.cor[1,4]',
           'phi.cor[2,3]', 'phi.cor[2,4]', 'phi.cor[3,4]'))

ggmcmc::ggs_grb(fit.mcmc.ggs, family = "phi.cor")
Warning: Removed 50 row(s) containing missing values (geom_path).

# save factor correlations
use.vars <- c('phi.cor[1,2]', 'phi.cor[1,3]', 'phi.cor[1,4]',
           'phi.cor[2,3]', 'phi.cor[2,4]', 'phi.cor[3,4]')
extracted_cor <- fit.mcmc[,use.vars]
write.csv(x=extracted_cor, file=paste0(getwd(),"/data/pools/extracted_cor_m2.csv"))

Misclassification

use.vars <- c("gamma[1,1,1]", "gamma[1,1,2]", "gamma[1,1,3]",
             "gamma[1,2,1]", "gamma[1,2,2]", "gamma[1,2,3]",
             "gamma[1,3,1]", "gamma[1,3,2]", "gamma[1,3,3]")
bayesplot::mcmc_areas(fit.mcmc, pars = use.vars, prob = 0.8); ggsave("fig/pools_model3_gamma_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, pars = use.vars); ggsave("fig/pools_model3_gamma_acf.pdf")
Warning: Removed 168 rows containing missing values (geom_segment).

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Warning: Removed 168 rows containing missing values (geom_segment).
bayesplot::mcmc_trace(fit.mcmc, pars = use.vars); ggsave("fig/pools_model3_gamma_trace.pdf")

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Factor Reliability Omega (\(\omega\))

bayesplot::mcmc_areas(fit.mcmc, regex_pars = "reli.omega", prob = 0.8); ggsave("fig/pools_model2_omega_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model2_omega_acf.pdf")

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bayesplot::mcmc_trace(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model2_omega_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "reli.omega"); ggsave("fig/pools_model2_omega_grb.pdf")

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# extract omega posterior for results comparison
extracted_omega <- data.frame(model_2_f1 = fit.mcmc$`reli.omega[1]`,
                              model_2_f2 = fit.mcmc$`reli.omega[2]`,
                              model_2_f3 = fit.mcmc$`reli.omega[3]`,
                              model_2_f4 = fit.mcmc$`reli.omega[4]`)
write.csv(x=extracted_omega, file=paste0(getwd(),"/data/pools/extracted_omega_m2.csv"))

Relationship between factor loading and misclassification

keep.var <- c(
  paste0('lambda.std[',1:25,']'),
  paste0('gamma[',1:25,',1,1]'),
  paste0('gamma[',1:25,',2,2]'),
  paste0('gamma[',1:25,',3,3]')
)
#plot.dat <- fit.mcmc[,keep.var]
plot.dat <- data.frame(
  item = c(paste0("Q4_",c(3:5,9,11,15,18)), 
             paste0("Q5_",c(1:3,5:6,12)), 
             paste0("Q6_",c(2,5:8, 11)), 
             paste0("Q7_",c(2, 4:5, 7:8, 14))),
  factor = c(rep('EfL',7), rep('SC',6), rep('IN',6), rep('EnL',6)),
  lambda.std = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('lambda.std[',1:25,']'),1],
  `gamma[1,1]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',1,1]'),1],
  `gamma[2,2]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',2,2]'),1],
  `gamma[3,3]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',3,3]'),1],
  `gamma[1,2]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',1,2]'),1],
  `gamma[2,1]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',2,1]'),1],
  `gamma[3,1]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',3,1]'),1],
  `gamma[1,3]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',1,3]'),1],
  `gamma[2,3]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',2,3]'),1],
  `gamma[3,2]` = model.fit$BUGSoutput$summary[rownames(model.fit$BUGSoutput$summary)%in% paste0('gamma[',1:25,',3,2]'),1]
) %>%
  pivot_longer(
    cols = contains('gamma'),
    names_to = 'gamma',
    values_to = 'gamma_est'
  )

ggplot(plot.dat, aes(x=gamma_est, y=lambda.std, color=factor))+
  geom_text(aes(label = item)) + 
  facet_wrap(.~gamma, ncol=3)+
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Manuscript Table and Figures

Table

# print to xtable
print(
  xtable(
    model.fit$BUGSoutput$summary,
    caption = c("pools Model 1 posterior distribution summary")
    ,align = "lrrrrrrrrr"
  ),
  include.rownames=T,
  booktabs=T
)
% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Wed Feb 02 04:15:37 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
  \toprule
 & mean & sd & 2.5\% & 25\% & 50\% & 75\% & 97.5\% & Rhat & n.eff \\ 
  \midrule
deviance & 16276.87 & 121.95 & 16038.85 & 16194.30 & 16276.70 & 16358.33 & 16513.89 & 1.01 & 500.00 \\ 
  gamma[1,1,1] & 0.77 & 0.06 & 0.64 & 0.73 & 0.77 & 0.81 & 0.88 & 1.00 & 1500.00 \\ 
  gamma[2,1,1] & 0.84 & 0.05 & 0.73 & 0.81 & 0.84 & 0.88 & 0.93 & 1.01 & 390.00 \\ 
  gamma[3,1,1] & 0.61 & 0.09 & 0.44 & 0.55 & 0.62 & 0.67 & 0.77 & 1.01 & 310.00 \\ 
  gamma[4,1,1] & 0.52 & 0.09 & 0.35 & 0.46 & 0.52 & 0.58 & 0.69 & 1.02 & 140.00 \\ 
  gamma[5,1,1] & 0.70 & 0.07 & 0.55 & 0.65 & 0.70 & 0.75 & 0.83 & 1.03 & 110.00 \\ 
  gamma[6,1,1] & 0.72 & 0.08 & 0.57 & 0.67 & 0.72 & 0.77 & 0.87 & 1.01 & 210.00 \\ 
  gamma[7,1,1] & 0.77 & 0.07 & 0.61 & 0.72 & 0.77 & 0.82 & 0.90 & 1.02 & 110.00 \\ 
  gamma[8,1,1] & 0.70 & 0.08 & 0.53 & 0.65 & 0.70 & 0.75 & 0.84 & 1.00 & 4000.00 \\ 
  gamma[9,1,1] & 0.89 & 0.10 & 0.61 & 0.85 & 0.93 & 0.97 & 1.00 & 1.00 & 1700.00 \\ 
  gamma[10,1,1] & 0.81 & 0.12 & 0.53 & 0.72 & 0.82 & 0.90 & 0.99 & 1.00 & 1500.00 \\ 
  gamma[11,1,1] & 0.26 & 0.07 & 0.15 & 0.21 & 0.26 & 0.31 & 0.41 & 1.01 & 190.00 \\ 
  gamma[12,1,1] & 0.96 & 0.03 & 0.88 & 0.94 & 0.97 & 0.98 & 1.00 & 1.01 & 380.00 \\ 
  gamma[13,1,1] & 0.96 & 0.03 & 0.88 & 0.95 & 0.97 & 0.99 & 1.00 & 1.00 & 770.00 \\ 
  gamma[14,1,1] & 0.57 & 0.11 & 0.36 & 0.50 & 0.57 & 0.65 & 0.79 & 1.00 & 890.00 \\ 
  gamma[15,1,1] & 0.82 & 0.13 & 0.54 & 0.73 & 0.85 & 0.93 & 0.99 & 1.01 & 460.00 \\ 
  gamma[16,1,1] & 0.63 & 0.10 & 0.42 & 0.57 & 0.64 & 0.70 & 0.82 & 1.00 & 820.00 \\ 
  gamma[17,1,1] & 0.69 & 0.10 & 0.49 & 0.63 & 0.70 & 0.76 & 0.87 & 1.01 & 320.00 \\ 
  gamma[18,1,1] & 0.59 & 0.11 & 0.37 & 0.52 & 0.60 & 0.67 & 0.79 & 1.03 & 150.00 \\ 
  gamma[19,1,1] & 0.95 & 0.03 & 0.87 & 0.93 & 0.96 & 0.98 & 1.00 & 1.00 & 2700.00 \\ 
  gamma[20,1,1] & 0.91 & 0.05 & 0.81 & 0.88 & 0.91 & 0.94 & 0.99 & 1.02 & 130.00 \\ 
  gamma[21,1,1] & 0.87 & 0.07 & 0.71 & 0.82 & 0.88 & 0.93 & 0.99 & 1.02 & 130.00 \\ 
  gamma[22,1,1] & 0.98 & 0.02 & 0.92 & 0.96 & 0.98 & 0.99 & 1.00 & 1.00 & 1400.00 \\ 
  gamma[23,1,1] & 0.19 & 0.05 & 0.11 & 0.15 & 0.18 & 0.22 & 0.31 & 1.01 & 610.00 \\ 
  gamma[24,1,1] & 0.96 & 0.04 & 0.86 & 0.94 & 0.96 & 0.98 & 1.00 & 1.00 & 990.00 \\ 
  gamma[25,1,1] & 0.15 & 0.04 & 0.08 & 0.12 & 0.15 & 0.18 & 0.25 & 1.01 & 340.00 \\ 
  gamma[1,2,1] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.06 & 1.00 & 3700.00 \\ 
  gamma[2,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.04 & 1.02 & 290.00 \\ 
  gamma[3,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.03 & 240.00 \\ 
  gamma[4,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.00 & 670.00 \\ 
  gamma[5,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.02 & 0.05 & 1.03 & 400.00 \\ 
  gamma[6,2,1] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.03 & 0.07 & 1.06 & 89.00 \\ 
  gamma[7,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.04 & 130.00 \\ 
  gamma[8,2,1] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.07 & 1.10 & 52.00 \\ 
  gamma[9,2,1] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.09 & 1.01 & 960.00 \\ 
  gamma[10,2,1] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.09 & 1.01 & 650.00 \\ 
  gamma[11,2,1] & 0.04 & 0.03 & 0.00 & 0.01 & 0.03 & 0.05 & 0.11 & 1.22 & 44.00 \\ 
  gamma[12,2,1] & 0.08 & 0.06 & 0.00 & 0.03 & 0.07 & 0.12 & 0.20 & 1.04 & 120.00 \\ 
  gamma[13,2,1] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.14 & 1.05 & 110.00 \\ 
  gamma[14,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.03 & 1.09 & 48.00 \\ 
  gamma[15,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.04 & 1.01 & 480.00 \\ 
  gamma[16,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 1.01 & 310.00 \\ 
  gamma[17,2,1] & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.17 & 36.00 \\ 
  gamma[18,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 1.04 & 87.00 \\ 
  gamma[19,2,1] & 0.01 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.07 & 1.01 & 390.00 \\ 
  gamma[20,2,1] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.08 & 1.02 & 950.00 \\ 
  gamma[21,2,1] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.02 & 280.00 \\ 
  gamma[22,2,1] & 0.04 & 0.04 & 0.00 & 0.01 & 0.03 & 0.06 & 0.12 & 1.01 & 630.00 \\ 
  gamma[23,2,1] & 0.07 & 0.04 & 0.02 & 0.05 & 0.07 & 0.10 & 0.17 & 1.01 & 240.00 \\ 
  gamma[24,2,1] & 0.03 & 0.04 & 0.00 & 0.01 & 0.02 & 0.05 & 0.13 & 1.04 & 110.00 \\ 
  gamma[25,2,1] & 0.04 & 0.03 & 0.00 & 0.02 & 0.03 & 0.05 & 0.11 & 1.08 & 70.00 \\ 
  gamma[1,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,1,2] & 0.23 & 0.06 & 0.12 & 0.19 & 0.23 & 0.27 & 0.36 & 1.00 & 1300.00 \\ 
  gamma[2,1,2] & 0.16 & 0.05 & 0.07 & 0.12 & 0.16 & 0.19 & 0.27 & 1.01 & 380.00 \\ 
  gamma[3,1,2] & 0.39 & 0.09 & 0.23 & 0.33 & 0.38 & 0.45 & 0.56 & 1.01 & 300.00 \\ 
  gamma[4,1,2] & 0.48 & 0.09 & 0.31 & 0.42 & 0.48 & 0.54 & 0.65 & 1.03 & 110.00 \\ 
  gamma[5,1,2] & 0.30 & 0.07 & 0.17 & 0.25 & 0.30 & 0.35 & 0.45 & 1.02 & 110.00 \\ 
  gamma[6,1,2] & 0.28 & 0.08 & 0.13 & 0.23 & 0.28 & 0.33 & 0.43 & 1.02 & 180.00 \\ 
  gamma[7,1,2] & 0.23 & 0.07 & 0.10 & 0.18 & 0.23 & 0.28 & 0.39 & 1.02 & 110.00 \\ 
  gamma[8,1,2] & 0.30 & 0.08 & 0.16 & 0.25 & 0.30 & 0.35 & 0.47 & 1.00 & 4000.00 \\ 
  gamma[9,1,2] & 0.11 & 0.10 & 0.00 & 0.03 & 0.07 & 0.15 & 0.39 & 1.01 & 1100.00 \\ 
  gamma[10,1,2] & 0.19 & 0.12 & 0.01 & 0.10 & 0.18 & 0.28 & 0.47 & 1.01 & 1100.00 \\ 
  gamma[11,1,2] & 0.74 & 0.07 & 0.59 & 0.69 & 0.74 & 0.79 & 0.85 & 1.02 & 160.00 \\ 
  gamma[12,1,2] & 0.04 & 0.03 & 0.00 & 0.02 & 0.03 & 0.06 & 0.12 & 1.01 & 260.00 \\ 
  gamma[13,1,2] & 0.04 & 0.03 & 0.00 & 0.01 & 0.03 & 0.05 & 0.12 & 1.00 & 800.00 \\ 
  gamma[14,1,2] & 0.43 & 0.11 & 0.21 & 0.35 & 0.43 & 0.50 & 0.64 & 1.01 & 460.00 \\ 
  gamma[15,1,2] & 0.18 & 0.13 & 0.01 & 0.07 & 0.15 & 0.27 & 0.46 & 1.01 & 290.00 \\ 
  gamma[16,1,2] & 0.37 & 0.10 & 0.18 & 0.30 & 0.36 & 0.43 & 0.58 & 1.00 & 700.00 \\ 
  gamma[17,1,2] & 0.31 & 0.10 & 0.13 & 0.24 & 0.30 & 0.37 & 0.51 & 1.01 & 490.00 \\ 
  gamma[18,1,2] & 0.41 & 0.11 & 0.21 & 0.33 & 0.40 & 0.48 & 0.63 & 1.02 & 200.00 \\ 
  gamma[19,1,2] & 0.05 & 0.03 & 0.00 & 0.02 & 0.04 & 0.07 & 0.13 & 1.01 & 1100.00 \\ 
  gamma[20,1,2] & 0.09 & 0.05 & 0.01 & 0.06 & 0.09 & 0.12 & 0.19 & 1.08 & 90.00 \\ 
  gamma[21,1,2] & 0.13 & 0.07 & 0.01 & 0.07 & 0.12 & 0.18 & 0.29 & 1.02 & 260.00 \\ 
  gamma[22,1,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.08 & 1.00 & 980.00 \\ 
  gamma[23,1,2] & 0.81 & 0.05 & 0.69 & 0.78 & 0.82 & 0.85 & 0.89 & 1.01 & 390.00 \\ 
  gamma[24,1,2] & 0.04 & 0.04 & 0.00 & 0.02 & 0.04 & 0.06 & 0.14 & 1.01 & 470.00 \\ 
  gamma[25,1,2] & 0.85 & 0.04 & 0.75 & 0.82 & 0.85 & 0.88 & 0.92 & 1.01 & 340.00 \\ 
  gamma[1,2,2] & 0.95 & 0.05 & 0.82 & 0.92 & 0.96 & 0.98 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[2,2,2] & 0.95 & 0.05 & 0.82 & 0.93 & 0.97 & 0.99 & 1.00 & 1.01 & 1300.00 \\ 
  gamma[3,2,2] & 0.70 & 0.12 & 0.48 & 0.61 & 0.69 & 0.78 & 0.93 & 1.02 & 170.00 \\ 
  gamma[4,2,2] & 0.95 & 0.06 & 0.79 & 0.94 & 0.97 & 0.99 & 1.00 & 1.02 & 150.00 \\ 
  gamma[5,2,2] & 0.92 & 0.08 & 0.71 & 0.88 & 0.94 & 0.97 & 1.00 & 1.02 & 180.00 \\ 
  gamma[6,2,2] & 0.83 & 0.12 & 0.57 & 0.75 & 0.84 & 0.93 & 0.99 & 1.00 & 3500.00 \\ 
  gamma[7,2,2] & 0.68 & 0.15 & 0.42 & 0.57 & 0.67 & 0.79 & 0.97 & 1.02 & 170.00 \\ 
  gamma[8,2,2] & 0.93 & 0.06 & 0.78 & 0.91 & 0.95 & 0.98 & 1.00 & 1.01 & 280.00 \\ 
  gamma[9,2,2] & 0.87 & 0.10 & 0.61 & 0.83 & 0.89 & 0.94 & 0.99 & 1.02 & 270.00 \\ 
  gamma[10,2,2] & 0.95 & 0.04 & 0.84 & 0.93 & 0.96 & 0.98 & 1.00 & 1.00 & 2800.00 \\ 
  gamma[11,2,2] & 0.65 & 0.05 & 0.55 & 0.61 & 0.65 & 0.68 & 0.75 & 1.01 & 330.00 \\ 
  gamma[12,2,2] & 0.90 & 0.06 & 0.76 & 0.86 & 0.91 & 0.95 & 0.99 & 1.01 & 520.00 \\ 
  gamma[13,2,2] & 0.93 & 0.05 & 0.82 & 0.90 & 0.94 & 0.96 & 0.99 & 1.01 & 450.00 \\ 
  gamma[14,2,2] & 0.26 & 0.05 & 0.16 & 0.22 & 0.26 & 0.30 & 0.38 & 1.00 & 1100.00 \\ 
  gamma[15,2,2] & 0.62 & 0.16 & 0.35 & 0.50 & 0.61 & 0.73 & 0.96 & 1.00 & 1900.00 \\ 
  gamma[16,2,2] & 0.11 & 0.03 & 0.06 & 0.09 & 0.10 & 0.12 & 0.17 & 1.01 & 390.00 \\ 
  gamma[17,2,2] & 0.37 & 0.08 & 0.22 & 0.31 & 0.37 & 0.43 & 0.55 & 1.01 & 460.00 \\ 
  gamma[18,2,2] & 0.41 & 0.08 & 0.27 & 0.35 & 0.40 & 0.46 & 0.59 & 1.02 & 180.00 \\ 
  gamma[19,2,2] & 0.97 & 0.03 & 0.90 & 0.96 & 0.98 & 0.99 & 1.00 & 1.02 & 370.00 \\ 
  gamma[20,2,2] & 0.96 & 0.04 & 0.87 & 0.94 & 0.97 & 0.99 & 1.00 & 1.01 & 480.00 \\ 
  gamma[21,2,2] & 0.96 & 0.03 & 0.87 & 0.95 & 0.97 & 0.99 & 1.00 & 1.01 & 630.00 \\ 
  gamma[22,2,2] & 0.94 & 0.04 & 0.83 & 0.92 & 0.95 & 0.98 & 1.00 & 1.02 & 260.00 \\ 
  gamma[23,2,2] & 0.74 & 0.04 & 0.65 & 0.71 & 0.74 & 0.77 & 0.82 & 1.00 & 1800.00 \\ 
  gamma[24,2,2] & 0.95 & 0.05 & 0.82 & 0.92 & 0.96 & 0.98 & 1.00 & 1.01 & 420.00 \\ 
  gamma[25,2,2] & 0.59 & 0.05 & 0.49 & 0.56 & 0.60 & 0.63 & 0.69 & 1.00 & 740.00 \\ 
  gamma[1,3,2] & 0.05 & 0.02 & 0.01 & 0.03 & 0.05 & 0.07 & 0.10 & 1.00 & 860.00 \\ 
  gamma[2,3,2] & 0.03 & 0.02 & 0.00 & 0.02 & 0.03 & 0.05 & 0.08 & 1.01 & 2900.00 \\ 
  gamma[3,3,2] & 0.03 & 0.02 & 0.00 & 0.02 & 0.03 & 0.04 & 0.08 & 1.01 & 410.00 \\ 
  gamma[4,3,2] & 0.17 & 0.06 & 0.05 & 0.13 & 0.17 & 0.21 & 0.29 & 1.08 & 57.00 \\ 
  gamma[5,3,2] & 0.12 & 0.04 & 0.04 & 0.09 & 0.12 & 0.15 & 0.21 & 1.02 & 140.00 \\ 
  gamma[6,3,2] & 0.04 & 0.02 & 0.00 & 0.02 & 0.04 & 0.06 & 0.10 & 1.03 & 240.00 \\ 
  gamma[7,3,2] & 0.02 & 0.01 & 0.00 & 0.01 & 0.02 & 0.03 & 0.06 & 1.02 & 260.00 \\ 
  gamma[8,3,2] & 0.23 & 0.06 & 0.13 & 0.19 & 0.23 & 0.27 & 0.34 & 1.00 & 1700.00 \\ 
  gamma[9,3,2] & 0.33 & 0.16 & 0.03 & 0.21 & 0.33 & 0.45 & 0.63 & 1.01 & 370.00 \\ 
  gamma[10,3,2] & 0.07 & 0.06 & 0.00 & 0.02 & 0.05 & 0.10 & 0.21 & 1.00 & 1700.00 \\ 
  gamma[11,3,2] & 0.07 & 0.06 & 0.00 & 0.02 & 0.05 & 0.09 & 0.22 & 1.01 & 340.00 \\ 
  gamma[12,3,2] & 0.35 & 0.08 & 0.19 & 0.29 & 0.34 & 0.40 & 0.50 & 1.00 & 890.00 \\ 
  gamma[13,3,2] & 0.33 & 0.07 & 0.20 & 0.29 & 0.33 & 0.38 & 0.47 & 1.00 & 2300.00 \\ 
  gamma[14,3,2] & 0.06 & 0.02 & 0.02 & 0.04 & 0.05 & 0.07 & 0.10 & 1.03 & 160.00 \\ 
  gamma[15,3,2] & 0.10 & 0.09 & 0.00 & 0.03 & 0.08 & 0.16 & 0.31 & 1.01 & 590.00 \\ 
  gamma[16,3,2] & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.01 & 350.00 \\ 
  gamma[17,3,2] & 0.03 & 0.02 & 0.01 & 0.02 & 0.03 & 0.04 & 0.07 & 1.01 & 810.00 \\ 
  gamma[18,3,2] & 0.05 & 0.02 & 0.02 & 0.04 & 0.05 & 0.06 & 0.09 & 1.01 & 180.00 \\ 
  gamma[19,3,2] & 0.13 & 0.06 & 0.03 & 0.08 & 0.12 & 0.16 & 0.24 & 1.04 & 110.00 \\ 
  gamma[20,3,2] & 0.06 & 0.04 & 0.00 & 0.03 & 0.06 & 0.09 & 0.15 & 1.03 & 150.00 \\ 
  gamma[21,3,2] & 0.29 & 0.10 & 0.09 & 0.23 & 0.30 & 0.37 & 0.48 & 1.03 & 110.00 \\ 
  gamma[22,3,2] & 0.26 & 0.06 & 0.15 & 0.22 & 0.26 & 0.30 & 0.38 & 1.01 & 490.00 \\ 
  gamma[23,3,2] & 0.06 & 0.05 & 0.00 & 0.02 & 0.04 & 0.08 & 0.20 & 1.01 & 850.00 \\ 
  gamma[24,3,2] & 0.27 & 0.07 & 0.13 & 0.23 & 0.27 & 0.32 & 0.41 & 1.00 & 680.00 \\ 
  gamma[25,3,2] & 0.07 & 0.06 & 0.00 & 0.02 & 0.05 & 0.10 & 0.23 & 1.00 & 780.00 \\ 
  gamma[1,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,1,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,2,3] & 0.04 & 0.05 & 0.00 & 0.01 & 0.02 & 0.06 & 0.16 & 1.01 & 570.00 \\ 
  gamma[2,2,3] & 0.04 & 0.05 & 0.00 & 0.00 & 0.02 & 0.06 & 0.17 & 1.02 & 660.00 \\ 
  gamma[3,2,3] & 0.30 & 0.12 & 0.06 & 0.22 & 0.31 & 0.38 & 0.52 & 1.01 & 290.00 \\ 
  gamma[4,2,3] & 0.04 & 0.05 & 0.00 & 0.01 & 0.02 & 0.06 & 0.20 & 1.02 & 150.00 \\ 
  gamma[5,2,3] & 0.07 & 0.07 & 0.00 & 0.01 & 0.04 & 0.10 & 0.26 & 1.10 & 63.00 \\ 
  gamma[6,2,3] & 0.15 & 0.12 & 0.00 & 0.05 & 0.13 & 0.23 & 0.40 & 1.00 & 4000.00 \\ 
  gamma[7,2,3] & 0.31 & 0.15 & 0.02 & 0.21 & 0.33 & 0.43 & 0.57 & 1.14 & 83.00 \\ 
  gamma[8,2,3] & 0.05 & 0.05 & 0.00 & 0.01 & 0.03 & 0.07 & 0.19 & 1.01 & 550.00 \\ 
  gamma[9,2,3] & 0.11 & 0.09 & 0.00 & 0.04 & 0.09 & 0.15 & 0.36 & 1.07 & 100.00 \\ 
  gamma[10,2,3] & 0.03 & 0.04 & 0.00 & 0.00 & 0.01 & 0.04 & 0.13 & 1.02 & 220.00 \\ 
  gamma[11,2,3] & 0.32 & 0.05 & 0.22 & 0.28 & 0.32 & 0.35 & 0.42 & 1.01 & 390.00 \\ 
  gamma[12,2,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.09 & 1.05 & 100.00 \\ 
  gamma[13,2,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.09 & 1.01 & 570.00 \\ 
  gamma[14,2,3] & 0.73 & 0.05 & 0.62 & 0.70 & 0.73 & 0.77 & 0.83 & 1.00 & 1300.00 \\ 
  gamma[15,2,3] & 0.37 & 0.16 & 0.03 & 0.27 & 0.38 & 0.49 & 0.64 & 1.04 & 360.00 \\ 
  gamma[16,2,3] & 0.89 & 0.03 & 0.83 & 0.88 & 0.89 & 0.91 & 0.94 & 1.01 & 470.00 \\ 
  gamma[17,2,3] & 0.62 & 0.08 & 0.45 & 0.57 & 0.63 & 0.68 & 0.77 & 1.01 & 480.00 \\ 
  gamma[18,2,3] & 0.59 & 0.08 & 0.41 & 0.53 & 0.59 & 0.64 & 0.73 & 1.02 & 200.00 \\ 
  gamma[19,2,3] & 0.01 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.06 & 1.01 & 310.00 \\ 
  gamma[20,2,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.11 & 1.08 & 69.00 \\ 
  gamma[21,2,3] & 0.01 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.07 & 1.01 & 310.00 \\ 
  gamma[22,2,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.09 & 1.05 & 280.00 \\ 
  gamma[23,2,3] & 0.19 & 0.05 & 0.10 & 0.16 & 0.19 & 0.22 & 0.28 & 1.01 & 210.00 \\ 
  gamma[24,2,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.03 & 310.00 \\ 
  gamma[25,2,3] & 0.37 & 0.06 & 0.26 & 0.33 & 0.37 & 0.41 & 0.49 & 1.00 & 1500.00 \\ 
  gamma[1,3,3] & 0.95 & 0.02 & 0.90 & 0.93 & 0.95 & 0.97 & 0.99 & 1.00 & 1100.00 \\ 
  gamma[2,3,3] & 0.97 & 0.02 & 0.92 & 0.95 & 0.97 & 0.98 & 1.00 & 1.00 & 1100.00 \\ 
  gamma[3,3,3] & 0.97 & 0.02 & 0.92 & 0.96 & 0.97 & 0.98 & 1.00 & 1.00 & 650.00 \\ 
  gamma[4,3,3] & 0.83 & 0.06 & 0.71 & 0.79 & 0.83 & 0.87 & 0.95 & 1.04 & 70.00 \\ 
  gamma[5,3,3] & 0.88 & 0.04 & 0.79 & 0.85 & 0.88 & 0.91 & 0.96 & 1.02 & 160.00 \\ 
  gamma[6,3,3] & 0.96 & 0.02 & 0.90 & 0.94 & 0.96 & 0.98 & 1.00 & 1.02 & 230.00 \\ 
  gamma[7,3,3] & 0.98 & 0.01 & 0.94 & 0.97 & 0.98 & 0.99 & 1.00 & 1.01 & 430.00 \\ 
  gamma[8,3,3] & 0.77 & 0.06 & 0.66 & 0.73 & 0.77 & 0.81 & 0.87 & 1.00 & 2300.00 \\ 
  gamma[9,3,3] & 0.67 & 0.16 & 0.37 & 0.55 & 0.67 & 0.79 & 0.97 & 1.01 & 200.00 \\ 
  gamma[10,3,3] & 0.93 & 0.06 & 0.79 & 0.90 & 0.95 & 0.98 & 1.00 & 1.00 & 1400.00 \\ 
  gamma[11,3,3] & 0.93 & 0.06 & 0.78 & 0.91 & 0.95 & 0.98 & 1.00 & 1.01 & 340.00 \\ 
  gamma[12,3,3] & 0.65 & 0.08 & 0.50 & 0.60 & 0.66 & 0.71 & 0.81 & 1.00 & 660.00 \\ 
  gamma[13,3,3] & 0.67 & 0.07 & 0.53 & 0.62 & 0.67 & 0.71 & 0.80 & 1.00 & 2900.00 \\ 
  gamma[14,3,3] & 0.94 & 0.02 & 0.90 & 0.93 & 0.95 & 0.96 & 0.98 & 1.01 & 220.00 \\ 
  gamma[15,3,3] & 0.90 & 0.09 & 0.69 & 0.84 & 0.92 & 0.97 & 1.00 & 1.00 & 950.00 \\ 
  gamma[16,3,3] & 0.99 & 0.00 & 0.98 & 0.99 & 1.00 & 1.00 & 1.00 & 1.01 & 630.00 \\ 
  gamma[17,3,3] & 0.97 & 0.02 & 0.93 & 0.96 & 0.97 & 0.98 & 0.99 & 1.00 & 1100.00 \\ 
  gamma[18,3,3] & 0.95 & 0.02 & 0.91 & 0.94 & 0.95 & 0.96 & 0.98 & 1.02 & 160.00 \\ 
  gamma[19,3,3] & 0.87 & 0.06 & 0.76 & 0.84 & 0.88 & 0.92 & 0.97 & 1.03 & 100.00 \\ 
  gamma[20,3,3] & 0.94 & 0.04 & 0.85 & 0.91 & 0.94 & 0.97 & 1.00 & 1.02 & 170.00 \\ 
  gamma[21,3,3] & 0.71 & 0.10 & 0.52 & 0.63 & 0.70 & 0.77 & 0.91 & 1.03 & 87.00 \\ 
  gamma[22,3,3] & 0.74 & 0.06 & 0.62 & 0.70 & 0.74 & 0.78 & 0.85 & 1.01 & 530.00 \\ 
  gamma[23,3,3] & 0.94 & 0.05 & 0.80 & 0.92 & 0.96 & 0.98 & 1.00 & 1.01 & 1500.00 \\ 
  gamma[24,3,3] & 0.73 & 0.07 & 0.59 & 0.68 & 0.73 & 0.77 & 0.87 & 1.00 & 590.00 \\ 
  gamma[25,3,3] & 0.93 & 0.06 & 0.77 & 0.90 & 0.95 & 0.98 & 1.00 & 1.01 & 450.00 \\ 
  inv.phi[1,1] & 3.37 & 1.62 & 0.95 & 2.21 & 3.12 & 4.25 & 7.21 & 1.10 & 35.00 \\ 
  inv.phi[2,1] & -0.43 & 1.05 & -2.55 & -1.13 & -0.39 & 0.29 & 1.49 & 1.02 & 170.00 \\ 
  inv.phi[3,1] & -1.27 & 1.14 & -3.93 & -1.90 & -1.15 & -0.48 & 0.57 & 1.01 & 220.00 \\ 
  inv.phi[4,1] & -1.27 & 1.20 & -3.90 & -1.97 & -1.15 & -0.48 & 0.76 & 1.02 & 240.00 \\ 
  inv.phi[1,2] & -0.43 & 1.05 & -2.55 & -1.13 & -0.39 & 0.29 & 1.49 & 1.02 & 170.00 \\ 
  inv.phi[2,2] & 2.94 & 1.43 & 0.88 & 1.88 & 2.73 & 3.74 & 6.38 & 1.02 & 270.00 \\ 
  inv.phi[3,2] & -0.25 & 1.01 & -2.25 & -0.89 & -0.28 & 0.37 & 1.78 & 1.02 & 180.00 \\ 
  inv.phi[4,2] & -1.83 & 1.41 & -5.25 & -2.57 & -1.60 & -0.83 & 0.33 & 1.02 & 150.00 \\ 
  inv.phi[1,3] & -1.27 & 1.14 & -3.93 & -1.90 & -1.15 & -0.48 & 0.57 & 1.01 & 220.00 \\ 
  inv.phi[2,3] & -0.25 & 1.01 & -2.25 & -0.89 & -0.28 & 0.37 & 1.78 & 1.02 & 180.00 \\ 
  inv.phi[3,3] & 2.64 & 1.42 & 0.64 & 1.60 & 2.37 & 3.38 & 6.16 & 1.02 & 260.00 \\ 
  inv.phi[4,3] & -0.76 & 1.19 & -3.41 & -1.50 & -0.62 & 0.11 & 1.21 & 1.01 & 320.00 \\ 
  inv.phi[1,4] & -1.27 & 1.20 & -3.90 & -1.97 & -1.15 & -0.48 & 0.76 & 1.02 & 240.00 \\ 
  inv.phi[2,4] & -1.83 & 1.41 & -5.25 & -2.57 & -1.60 & -0.83 & 0.33 & 1.02 & 150.00 \\ 
  inv.phi[3,4] & -0.76 & 1.19 & -3.41 & -1.50 & -0.62 & 0.11 & 1.21 & 1.01 & 320.00 \\ 
  inv.phi[4,4] & 3.54 & 2.01 & 0.76 & 2.05 & 3.11 & 4.65 & 8.52 & 1.03 & 120.00 \\ 
  lambda[1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[2] & 1.37 & 0.23 & 1.00 & 1.20 & 1.34 & 1.52 & 1.83 & 1.03 & 110.00 \\ 
  lambda[3] & 1.25 & 0.21 & 0.88 & 1.11 & 1.24 & 1.39 & 1.68 & 1.02 & 130.00 \\ 
  lambda[4] & 1.15 & 0.22 & 0.74 & 1.00 & 1.14 & 1.30 & 1.61 & 1.06 & 50.00 \\ 
  lambda[5] & 1.47 & 0.32 & 0.93 & 1.25 & 1.46 & 1.66 & 2.20 & 1.08 & 39.00 \\ 
  lambda[6] & 1.21 & 0.24 & 0.81 & 1.02 & 1.17 & 1.37 & 1.73 & 1.09 & 35.00 \\ 
  lambda[7] & 1.45 & 0.26 & 0.93 & 1.29 & 1.44 & 1.62 & 1.96 & 1.09 & 33.00 \\ 
  lambda[8] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[9] & 0.71 & 0.09 & 0.54 & 0.64 & 0.71 & 0.77 & 0.91 & 1.01 & 180.00 \\ 
  lambda[10] & 0.59 & 0.08 & 0.45 & 0.53 & 0.58 & 0.64 & 0.76 & 1.02 & 160.00 \\ 
  lambda[11] & 0.61 & 0.08 & 0.45 & 0.56 & 0.61 & 0.67 & 0.78 & 1.01 & 1000.00 \\ 
  lambda[12] & 0.94 & 0.14 & 0.69 & 0.84 & 0.93 & 1.03 & 1.24 & 1.03 & 78.00 \\ 
  lambda[13] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[14] & 1.13 & 0.27 & 0.63 & 0.95 & 1.12 & 1.29 & 1.70 & 1.07 & 44.00 \\ 
  lambda[15] & 0.44 & 0.10 & 0.30 & 0.37 & 0.42 & 0.49 & 0.67 & 1.01 & 310.00 \\ 
  lambda[16] & 1.28 & 0.23 & 0.86 & 1.10 & 1.26 & 1.43 & 1.77 & 1.13 & 25.00 \\ 
  lambda[17] & 1.24 & 0.24 & 0.79 & 1.06 & 1.23 & 1.40 & 1.73 & 1.08 & 39.00 \\ 
  lambda[18] & 1.36 & 0.29 & 0.89 & 1.16 & 1.34 & 1.53 & 2.03 & 1.05 & 160.00 \\ 
  lambda[19] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[20] & 1.03 & 0.15 & 0.76 & 0.93 & 1.02 & 1.12 & 1.36 & 1.07 & 43.00 \\ 
  lambda[21] & 0.87 & 0.14 & 0.63 & 0.76 & 0.86 & 0.96 & 1.16 & 1.08 & 42.00 \\ 
  lambda[22] & 1.12 & 0.14 & 0.87 & 1.02 & 1.11 & 1.21 & 1.43 & 1.02 & 180.00 \\ 
  lambda[23] & 0.78 & 0.10 & 0.59 & 0.71 & 0.78 & 0.84 & 0.99 & 1.01 & 300.00 \\ 
  lambda[24] & 0.87 & 0.12 & 0.66 & 0.79 & 0.86 & 0.93 & 1.13 & 1.02 & 140.00 \\ 
  lambda[25] & 0.71 & 0.10 & 0.54 & 0.64 & 0.71 & 0.77 & 0.91 & 1.01 & 290.00 \\ 
  lambda.std[1] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[2] & 0.80 & 0.05 & 0.71 & 0.77 & 0.80 & 0.84 & 0.88 & 1.03 & 97.00 \\ 
  lambda.std[3] & 0.77 & 0.05 & 0.66 & 0.74 & 0.78 & 0.81 & 0.86 & 1.03 & 120.00 \\ 
  lambda.std[4] & 0.74 & 0.07 & 0.59 & 0.71 & 0.75 & 0.79 & 0.85 & 1.07 & 47.00 \\ 
  lambda.std[5] & 0.82 & 0.06 & 0.68 & 0.78 & 0.83 & 0.86 & 0.91 & 1.09 & 38.00 \\ 
  lambda.std[6] & 0.76 & 0.06 & 0.63 & 0.72 & 0.76 & 0.81 & 0.87 & 1.08 & 38.00 \\ 
  lambda.std[7] & 0.81 & 0.05 & 0.68 & 0.79 & 0.82 & 0.85 & 0.89 & 1.08 & 39.00 \\ 
  lambda.std[8] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[9] & 0.57 & 0.05 & 0.47 & 0.54 & 0.58 & 0.61 & 0.67 & 1.01 & 190.00 \\ 
  lambda.std[10] & 0.50 & 0.05 & 0.41 & 0.47 & 0.50 & 0.54 & 0.61 & 1.02 & 160.00 \\ 
  lambda.std[11] & 0.52 & 0.05 & 0.41 & 0.49 & 0.52 & 0.56 & 0.61 & 1.01 & 880.00 \\ 
  lambda.std[12] & 0.68 & 0.05 & 0.57 & 0.64 & 0.68 & 0.72 & 0.78 & 1.03 & 82.00 \\ 
  lambda.std[13] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[14] & 0.73 & 0.08 & 0.53 & 0.69 & 0.75 & 0.79 & 0.86 & 1.07 & 44.00 \\ 
  lambda.std[15] & 0.40 & 0.07 & 0.29 & 0.35 & 0.39 & 0.44 & 0.56 & 1.01 & 290.00 \\ 
  lambda.std[16] & 0.78 & 0.06 & 0.65 & 0.74 & 0.78 & 0.82 & 0.87 & 1.13 & 26.00 \\ 
  lambda.std[17] & 0.77 & 0.06 & 0.62 & 0.73 & 0.78 & 0.81 & 0.87 & 1.06 & 48.00 \\ 
  lambda.std[18] & 0.79 & 0.06 & 0.66 & 0.76 & 0.80 & 0.84 & 0.90 & 1.03 & 370.00 \\ 
  lambda.std[19] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[20] & 0.71 & 0.05 & 0.60 & 0.68 & 0.71 & 0.75 & 0.81 & 1.07 & 42.00 \\ 
  lambda.std[21] & 0.65 & 0.06 & 0.54 & 0.61 & 0.65 & 0.69 & 0.76 & 1.07 & 46.00 \\ 
  lambda.std[22] & 0.74 & 0.04 & 0.66 & 0.71 & 0.74 & 0.77 & 0.82 & 1.02 & 180.00 \\ 
  lambda.std[23] & 0.61 & 0.05 & 0.51 & 0.58 & 0.61 & 0.64 & 0.70 & 1.01 & 310.00 \\ 
  lambda.std[24] & 0.65 & 0.05 & 0.55 & 0.62 & 0.65 & 0.68 & 0.75 & 1.02 & 150.00 \\ 
  lambda.std[25] & 0.58 & 0.05 & 0.47 & 0.54 & 0.58 & 0.61 & 0.67 & 1.01 & 290.00 \\ 
  phi[1,1] & 3.60 & 2.30 & 1.01 & 2.18 & 3.04 & 4.43 & 9.33 & 1.08 & 49.00 \\ 
  phi[2,1] & 3.06 & 1.89 & 0.75 & 1.86 & 2.69 & 3.75 & 7.65 & 1.06 & 58.00 \\ 
  phi[3,1] & 3.12 & 2.25 & 0.50 & 1.74 & 2.62 & 3.80 & 9.61 & 1.11 & 52.00 \\ 
  phi[4,1] & 3.40 & 1.32 & 1.15 & 2.56 & 3.26 & 4.10 & 6.38 & 1.10 & 49.00 \\ 
  phi[1,2] & 3.06 & 1.89 & 0.75 & 1.86 & 2.69 & 3.75 & 7.65 & 1.06 & 58.00 \\ 
  phi[2,2] & 4.06 & 2.46 & 1.06 & 2.30 & 3.49 & 5.15 & 10.60 & 1.04 & 67.00 \\ 
  phi[3,2] & 3.07 & 2.15 & 0.37 & 1.61 & 2.59 & 4.02 & 9.02 & 1.13 & 35.00 \\ 
  phi[4,2] & 3.67 & 1.51 & 1.04 & 2.69 & 3.53 & 4.49 & 7.17 & 1.06 & 50.00 \\ 
  phi[1,3] & 3.12 & 2.25 & 0.50 & 1.74 & 2.62 & 3.80 & 9.61 & 1.11 & 52.00 \\ 
  phi[2,3] & 3.07 & 2.15 & 0.37 & 1.61 & 2.59 & 4.02 & 9.02 & 1.13 & 35.00 \\ 
  phi[3,3] & 4.04 & 2.95 & 0.84 & 2.03 & 3.28 & 4.97 & 12.54 & 1.09 & 39.00 \\ 
  phi[4,3] & 3.33 & 1.66 & 0.21 & 2.16 & 3.26 & 4.30 & 7.11 & 1.10 & 37.00 \\ 
  phi[1,4] & 3.40 & 1.32 & 1.15 & 2.56 & 3.26 & 4.10 & 6.38 & 1.10 & 49.00 \\ 
  phi[2,4] & 3.67 & 1.51 & 1.04 & 2.69 & 3.53 & 4.49 & 7.17 & 1.06 & 50.00 \\ 
  phi[3,4] & 3.33 & 1.66 & 0.21 & 2.16 & 3.26 & 4.30 & 7.11 & 1.10 & 37.00 \\ 
  phi[4,4] & 4.48 & 0.67 & 3.44 & 4.02 & 4.36 & 4.81 & 6.15 & 1.06 & 87.00 \\ 
  phi.cor[1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  phi.cor[2,1] & 0.82 & 0.13 & 0.44 & 0.76 & 0.86 & 0.91 & 0.96 & 1.04 & 140.00 \\ 
  phi.cor[3,1] & 0.82 & 0.18 & 0.33 & 0.78 & 0.88 & 0.93 & 0.97 & 1.08 & 110.00 \\ 
  phi.cor[4,1] & 0.86 & 0.13 & 0.47 & 0.84 & 0.91 & 0.94 & 0.97 & 1.06 & 84.00 \\ 
  phi.cor[1,2] & 0.82 & 0.13 & 0.44 & 0.76 & 0.86 & 0.91 & 0.96 & 1.04 & 140.00 \\ 
  phi.cor[2,2] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  phi.cor[3,2] & 0.77 & 0.20 & 0.22 & 0.71 & 0.83 & 0.90 & 0.97 & 1.06 & 94.00 \\ 
  phi.cor[4,2] & 0.87 & 0.16 & 0.46 & 0.86 & 0.92 & 0.95 & 0.98 & 1.21 & 45.00 \\ 
  phi.cor[1,3] & 0.82 & 0.18 & 0.33 & 0.78 & 0.88 & 0.93 & 0.97 & 1.08 & 110.00 \\ 
  phi.cor[2,3] & 0.77 & 0.20 & 0.22 & 0.71 & 0.83 & 0.90 & 0.97 & 1.06 & 94.00 \\ 
  phi.cor[3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  phi.cor[4,3] & 0.80 & 0.22 & 0.10 & 0.75 & 0.88 & 0.93 & 0.97 & 1.07 & 73.00 \\ 
  phi.cor[1,4] & 0.86 & 0.13 & 0.47 & 0.84 & 0.91 & 0.94 & 0.97 & 1.06 & 84.00 \\ 
  phi.cor[2,4] & 0.87 & 0.16 & 0.46 & 0.86 & 0.92 & 0.95 & 0.98 & 1.21 & 45.00 \\ 
  phi.cor[3,4] & 0.80 & 0.22 & 0.10 & 0.75 & 0.88 & 0.93 & 0.97 & 1.07 & 73.00 \\ 
  phi.cor[4,4] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  reli.omega[1] & 0.92 & 0.02 & 0.88 & 0.91 & 0.92 & 0.93 & 0.94 & 1.12 & 28.00 \\ 
  reli.omega[2] & 0.80 & 0.02 & 0.76 & 0.78 & 0.80 & 0.81 & 0.83 & 1.04 & 83.00 \\ 
  reli.omega[3] & 0.87 & 0.02 & 0.83 & 0.86 & 0.87 & 0.89 & 0.91 & 1.07 & 47.00 \\ 
  reli.omega[4] & 0.84 & 0.02 & 0.80 & 0.83 & 0.84 & 0.85 & 0.87 & 1.04 & 80.00 \\ 
  tau[1,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[4,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[5,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[6,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[7,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[8,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[9,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[10,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[11,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[12,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[13,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[14,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[15,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[16,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[17,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[18,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[19,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[20,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[21,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[22,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[23,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[24,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[25,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  tau[1,2] & 3.89 & 0.32 & 3.33 & 3.67 & 3.86 & 4.09 & 4.62 & 1.03 & 140.00 \\ 
  tau[2,2] & 4.80 & 0.72 & 3.67 & 4.24 & 4.70 & 5.32 & 6.25 & 1.02 & 110.00 \\ 
  tau[3,2] & 4.22 & 0.58 & 3.25 & 3.81 & 4.16 & 4.59 & 5.45 & 1.02 & 230.00 \\ 
  tau[4,2] & 3.51 & 0.72 & 2.25 & 2.99 & 3.49 & 3.98 & 5.02 & 1.07 & 43.00 \\ 
  tau[5,2] & 4.64 & 0.97 & 3.08 & 3.88 & 4.59 & 5.26 & 6.69 & 1.06 & 49.00 \\ 
  tau[6,2] & 4.17 & 0.73 & 3.03 & 3.63 & 4.07 & 4.61 & 5.79 & 1.07 & 51.00 \\ 
  tau[7,2] & 5.43 & 0.76 & 4.02 & 4.91 & 5.38 & 5.93 & 7.03 & 1.06 & 47.00 \\ 
  tau[8,2] & 3.10 & 0.33 & 2.53 & 2.87 & 3.08 & 3.30 & 3.80 & 1.03 & 100.00 \\ 
  tau[9,2] & 1.13 & 0.25 & 0.64 & 0.98 & 1.13 & 1.28 & 1.63 & 1.01 & 320.00 \\ 
  tau[10,2] & 1.54 & 0.15 & 1.29 & 1.43 & 1.52 & 1.63 & 1.88 & 1.00 & 3600.00 \\ 
  tau[11,2] & 0.06 & 0.05 & 0.00 & 0.02 & 0.04 & 0.08 & 0.17 & 1.00 & 4000.00 \\ 
  tau[12,2] & 2.69 & 0.46 & 1.99 & 2.37 & 2.62 & 2.93 & 3.81 & 1.03 & 90.00 \\ 
  tau[13,2] & 2.76 & 0.29 & 2.25 & 2.55 & 2.74 & 2.94 & 3.37 & 1.01 & 230.00 \\ 
  tau[14,2] & 4.57 & 0.86 & 3.09 & 3.97 & 4.50 & 5.11 & 6.47 & 1.06 & 49.00 \\ 
  tau[15,2] & 1.72 & 0.57 & 1.20 & 1.40 & 1.56 & 1.84 & 3.08 & 1.02 & 820.00 \\ 
  tau[16,2] & 5.51 & 0.70 & 4.28 & 4.99 & 5.46 & 5.99 & 7.00 & 1.08 & 35.00 \\ 
  tau[17,2] & 4.68 & 0.74 & 3.36 & 4.15 & 4.63 & 5.15 & 6.25 & 1.05 & 62.00 \\ 
  tau[18,2] & 5.25 & 0.86 & 3.84 & 4.68 & 5.19 & 5.68 & 7.47 & 1.08 & 68.00 \\ 
  tau[19,2] & 2.69 & 0.26 & 2.25 & 2.51 & 2.66 & 2.85 & 3.31 & 1.04 & 78.00 \\ 
  tau[20,2] & 3.45 & 0.51 & 2.66 & 3.08 & 3.38 & 3.76 & 4.64 & 1.04 & 62.00 \\ 
  tau[21,2] & 2.43 & 0.48 & 1.72 & 2.06 & 2.34 & 2.74 & 3.49 & 1.06 & 48.00 \\ 
  tau[22,2] & 3.27 & 0.43 & 2.56 & 2.96 & 3.22 & 3.53 & 4.23 & 1.02 & 120.00 \\ 
  tau[23,2] & 0.04 & 0.04 & 0.00 & 0.01 & 0.03 & 0.06 & 0.13 & 1.00 & 4000.00 \\ 
  tau[24,2] & 2.85 & 0.41 & 2.18 & 2.56 & 2.81 & 3.09 & 3.81 & 1.01 & 270.00 \\ 
  tau[25,2] & 0.03 & 0.03 & 0.00 & 0.01 & 0.02 & 0.05 & 0.11 & 1.00 & 3500.00 \\ 
  theta[1] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[2] & 2.92 & 0.64 & 2.00 & 2.43 & 2.78 & 3.32 & 4.34 & 1.03 & 110.00 \\ 
  theta[3] & 2.61 & 0.54 & 1.77 & 2.22 & 2.53 & 2.93 & 3.81 & 1.02 & 140.00 \\ 
  theta[4] & 2.38 & 0.53 & 1.54 & 2.00 & 2.31 & 2.70 & 3.60 & 1.06 & 54.00 \\ 
  theta[5] & 3.27 & 1.00 & 1.87 & 2.57 & 3.14 & 3.75 & 5.85 & 1.08 & 40.00 \\ 
  theta[6] & 2.51 & 0.63 & 1.66 & 2.05 & 2.37 & 2.87 & 4.00 & 1.10 & 34.00 \\ 
  theta[7] & 3.17 & 0.75 & 1.87 & 2.66 & 3.08 & 3.62 & 4.83 & 1.10 & 30.00 \\ 
  theta[8] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[9] & 1.51 & 0.14 & 1.29 & 1.42 & 1.50 & 1.59 & 1.82 & 1.01 & 180.00 \\ 
  theta[10] & 1.35 & 0.10 & 1.20 & 1.28 & 1.34 & 1.41 & 1.58 & 1.02 & 160.00 \\ 
  theta[11] & 1.38 & 0.10 & 1.20 & 1.31 & 1.38 & 1.45 & 1.61 & 1.00 & 1600.00 \\ 
  theta[12] & 1.90 & 0.27 & 1.47 & 1.70 & 1.87 & 2.07 & 2.53 & 1.04 & 74.00 \\ 
  theta[13] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[14] & 2.35 & 0.64 & 1.40 & 1.90 & 2.26 & 2.66 & 3.89 & 1.06 & 45.00 \\ 
  theta[15] & 1.20 & 0.09 & 1.09 & 1.14 & 1.18 & 1.24 & 1.45 & 1.01 & 410.00 \\ 
  theta[16] & 2.68 & 0.62 & 1.74 & 2.22 & 2.58 & 3.05 & 4.13 & 1.13 & 25.00 \\ 
  theta[17] & 2.60 & 0.62 & 1.63 & 2.13 & 2.51 & 2.97 & 3.99 & 1.09 & 34.00 \\ 
  theta[18] & 2.94 & 0.85 & 1.79 & 2.34 & 2.79 & 3.33 & 5.13 & 1.06 & 110.00 \\ 
  theta[19] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[20] & 2.08 & 0.32 & 1.57 & 1.86 & 2.04 & 2.26 & 2.86 & 1.06 & 44.00 \\ 
  theta[21] & 1.78 & 0.25 & 1.40 & 1.59 & 1.74 & 1.93 & 2.35 & 1.08 & 39.00 \\ 
  theta[22] & 2.27 & 0.33 & 1.75 & 2.04 & 2.23 & 2.45 & 3.04 & 1.02 & 190.00 \\ 
  theta[23] & 1.62 & 0.16 & 1.35 & 1.50 & 1.60 & 1.71 & 1.97 & 1.01 & 280.00 \\ 
  theta[24] & 1.76 & 0.21 & 1.43 & 1.62 & 1.74 & 1.87 & 2.28 & 1.02 & 130.00 \\ 
  theta[25] & 1.52 & 0.14 & 1.29 & 1.42 & 1.50 & 1.60 & 1.82 & 1.01 & 310.00 \\ 
   \bottomrule
\end{tabular}
\caption{pools Model 1 posterior distribution summary} 
\end{table}

sessionInfo()
R version 4.0.5 (2021-03-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] readxl_1.3.1         car_3.0-10           carData_3.0-4       
 [4] mvtnorm_1.1-1        LaplacesDemon_16.1.4 runjags_2.2.0-2     
 [7] lme4_1.1-26          Matrix_1.3-2         sirt_3.9-4          
[10] R2jags_0.6-1         rjags_4-12           eRm_1.0-2           
[13] diffIRT_1.5          statmod_1.4.35       xtable_1.8-4        
[16] kableExtra_1.3.4     lavaan_0.6-7         polycor_0.7-10      
[19] bayesplot_1.8.0      ggmcmc_1.5.1.1       coda_0.19-4         
[22] data.table_1.14.0    patchwork_1.1.1      forcats_0.5.1       
[25] stringr_1.4.0        dplyr_1.0.5          purrr_0.3.4         
[28] readr_1.4.0          tidyr_1.1.3          tibble_3.1.0        
[31] ggplot2_3.3.5        tidyverse_1.3.0      workflowr_1.6.2     

loaded via a namespace (and not attached):
 [1] minqa_1.2.4        TAM_3.5-19         colorspace_2.0-0   rio_0.5.26        
 [5] ellipsis_0.3.1     ggridges_0.5.3     rprojroot_2.0.2    fs_1.5.0          
 [9] rstudioapi_0.13    farver_2.1.0       fansi_0.4.2        lubridate_1.7.10  
[13] xml2_1.3.2         splines_4.0.5      mnormt_2.0.2       knitr_1.31        
[17] jsonlite_1.7.2     nloptr_1.2.2.2     broom_0.7.5        dbplyr_2.1.0      
[21] compiler_4.0.5     httr_1.4.2         backports_1.2.1    assertthat_0.2.1  
[25] cli_2.3.1          later_1.1.0.1      htmltools_0.5.1.1  tools_4.0.5       
[29] gtable_0.3.0       glue_1.4.2         reshape2_1.4.4     Rcpp_1.0.7        
[33] cellranger_1.1.0   jquerylib_0.1.3    vctrs_0.3.6        svglite_2.0.0     
[37] nlme_3.1-152       psych_2.0.12       xfun_0.21          ps_1.6.0          
[41] openxlsx_4.2.3     rvest_1.0.0        lifecycle_1.0.0    MASS_7.3-53.1     
[45] scales_1.1.1       ragg_1.1.1         hms_1.0.0          promises_1.2.0.1  
[49] parallel_4.0.5     RColorBrewer_1.1-2 curl_4.3           yaml_2.2.1        
[53] sass_0.3.1         reshape_0.8.8      stringi_1.5.3      highr_0.8         
[57] zip_2.1.1          boot_1.3-27        rlang_0.4.10       pkgconfig_2.0.3   
[61] systemfonts_1.0.1  evaluate_0.14      lattice_0.20-41    labeling_0.4.2    
[65] tidyselect_1.1.0   GGally_2.1.1       plyr_1.8.6         magrittr_2.0.1    
[69] R6_2.5.0           generics_0.1.0     DBI_1.1.1          foreign_0.8-81    
[73] pillar_1.5.1       haven_2.3.1        withr_2.4.1        abind_1.4-5       
[77] modelr_0.1.8       crayon_1.4.1       utf8_1.1.4         tmvnsim_1.0-2     
[81] rmarkdown_2.7      grid_4.0.5         CDM_7.5-15         pbivnorm_0.6.0    
[85] git2r_0.28.0       reprex_1.0.0       digest_0.6.27      webshot_0.5.2     
[89] httpuv_1.5.5       textshaping_0.3.1  stats4_4.0.5       munsell_0.5.0     
[93] viridisLite_0.3.0  bslib_0.2.4        R2WinBUGS_2.1-21