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 4: 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(1, 0, 0,
      0.10, 0.90, 0,
      0.05, 0.10, 0.85),
    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]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[2,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[3,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[4,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[5,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[6,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[7,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[8,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[9,1,1]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[10,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[11,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[12,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[13,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[14,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[15,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[16,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[17,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[18,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[19,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[20,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[21,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[22,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[23,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[24,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[25,1,1]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[1,2,1]       0.124   0.050     0.037     0.089     0.122     0.153     0.235 1.02   150
gamma[2,2,1]       0.058   0.037     0.005     0.029     0.052     0.078     0.143 1.01   930
gamma[3,2,1]       0.013   0.013     0.000     0.004     0.009     0.017     0.047 1.01   680
gamma[4,2,1]       0.025   0.021     0.001     0.008     0.019     0.035     0.077 1.01   430
gamma[5,2,1]       0.028   0.022     0.001     0.011     0.022     0.039     0.080 1.01   390
gamma[6,2,1]       0.039   0.028     0.002     0.016     0.034     0.055     0.103 1.01   430
gamma[7,2,1]       0.011   0.010     0.000     0.003     0.008     0.015     0.036 1.00  2200
gamma[8,2,1]       0.103   0.045     0.024     0.070     0.100     0.132     0.199 1.04   150
gamma[9,2,1]       0.118   0.056     0.024     0.078     0.111     0.152     0.242 1.00   640
gamma[10,2,1]      0.154   0.060     0.045     0.111     0.150     0.192     0.284 1.02   170
gamma[11,2,1]      0.266   0.064     0.151     0.223     0.262     0.306     0.402 1.01   270
gamma[12,2,1]      0.304   0.068     0.179     0.256     0.301     0.348     0.450 1.00   520
gamma[13,2,1]      0.217   0.061     0.107     0.176     0.214     0.259     0.346 1.01   230
gamma[14,2,1]      0.008   0.008     0.000     0.002     0.005     0.011     0.030 1.00  4000
gamma[15,2,1]      0.019   0.019     0.001     0.006     0.014     0.026     0.071 1.01   300
gamma[16,2,1]      0.006   0.006     0.000     0.002     0.005     0.009     0.023 1.00  1300
gamma[17,2,1]      0.008   0.009     0.000     0.002     0.006     0.012     0.031 1.01   440
gamma[18,2,1]      0.008   0.008     0.000     0.002     0.006     0.011     0.031 1.00  3800
gamma[19,2,1]      0.179   0.057     0.076     0.139     0.176     0.216     0.295 1.01   290
gamma[20,2,1]      0.183   0.058     0.080     0.141     0.179     0.220     0.305 1.01   180
gamma[21,2,1]      0.217   0.066     0.096     0.170     0.214     0.257     0.359 1.02   170
gamma[22,2,1]      0.234   0.059     0.129     0.193     0.230     0.271     0.362 1.01   390
gamma[23,2,1]      0.362   0.065     0.244     0.316     0.360     0.406     0.499 1.00   690
gamma[24,2,1]      0.235   0.064     0.123     0.190     0.231     0.276     0.373 1.02   150
gamma[25,2,1]      0.402   0.070     0.275     0.351     0.398     0.448     0.544 1.00   680
gamma[1,3,1]       0.007   0.008     0.000     0.001     0.004     0.010     0.028 1.01   270
gamma[2,3,1]       0.003   0.005     0.000     0.000     0.002     0.005     0.017 1.02   240
gamma[3,3,1]       0.004   0.005     0.000     0.000     0.002     0.005     0.017 1.00  2100
gamma[4,3,1]       0.013   0.013     0.000     0.003     0.009     0.020     0.047 1.03    93
gamma[5,3,1]       0.008   0.009     0.000     0.001     0.005     0.011     0.030 1.04   110
gamma[6,3,1]       0.005   0.006     0.000     0.000     0.002     0.007     0.021 1.05   130
gamma[7,3,1]       0.003   0.004     0.000     0.000     0.002     0.005     0.016 1.04   130
gamma[8,3,1]       0.059   0.029     0.004     0.037     0.057     0.077     0.122 1.16    55
gamma[9,3,1]       0.206   0.058     0.097     0.165     0.202     0.245     0.320 1.00   760
gamma[10,3,1]      0.037   0.026     0.000     0.016     0.034     0.054     0.097 1.01   400
gamma[11,3,1]      0.606   0.068     0.473     0.560     0.604     0.652     0.739 1.00  2300
gamma[12,3,1]      0.144   0.045     0.063     0.113     0.141     0.173     0.241 1.00  4000
gamma[13,3,1]      0.119   0.043     0.040     0.089     0.117     0.146     0.208 1.01   260
gamma[14,3,1]      0.003   0.004     0.000     0.000     0.001     0.004     0.015 1.02   340
gamma[15,3,1]      0.037   0.032     0.000     0.011     0.031     0.056     0.113 1.04   150
gamma[16,3,1]      0.002   0.003     0.000     0.000     0.001     0.002     0.009 1.02   170
gamma[17,3,1]      0.003   0.004     0.000     0.000     0.001     0.004     0.015 1.01   950
gamma[18,3,1]      0.006   0.007     0.000     0.001     0.003     0.008     0.026 1.04   110
gamma[19,3,1]      0.023   0.020     0.000     0.007     0.019     0.035     0.071 1.07   140
gamma[20,3,1]      0.005   0.007     0.000     0.001     0.002     0.007     0.026 1.01   260
gamma[21,3,1]      0.052   0.040     0.001     0.020     0.044     0.077     0.148 1.03   250
gamma[22,3,1]      0.083   0.034     0.028     0.059     0.078     0.103     0.159 1.01   440
gamma[23,3,1]      0.640   0.064     0.512     0.595     0.641     0.687     0.760 1.00   740
gamma[24,3,1]      0.078   0.033     0.023     0.055     0.075     0.099     0.151 1.00  2000
gamma[25,3,1]      0.675   0.067     0.541     0.630     0.677     0.721     0.803 1.00   830
gamma[1,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,1,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,1,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,2,2]       0.876   0.050     0.765     0.847     0.878     0.911     0.963 1.01   200
gamma[2,2,2]       0.942   0.037     0.857     0.922     0.948     0.971     0.995 1.00  1000
gamma[3,2,2]       0.987   0.013     0.953     0.983     0.991     0.996     1.000 1.00  4000
gamma[4,2,2]       0.975   0.021     0.923     0.965     0.981     0.992     0.999 1.01   420
gamma[5,2,2]       0.972   0.022     0.920     0.961     0.978     0.989     0.999 1.00   520
gamma[6,2,2]       0.961   0.028     0.897     0.945     0.966     0.984     0.998 1.01   270
gamma[7,2,2]       0.989   0.010     0.964     0.985     0.992     0.997     1.000 1.01  2100
gamma[8,2,2]       0.897   0.045     0.801     0.868     0.900     0.930     0.976 1.02   130
gamma[9,2,2]       0.882   0.056     0.758     0.848     0.889     0.922     0.976 1.01   370
gamma[10,2,2]      0.846   0.060     0.716     0.808     0.850     0.889     0.955 1.02   160
gamma[11,2,2]      0.734   0.064     0.598     0.694     0.738     0.777     0.849 1.01   280
gamma[12,2,2]      0.696   0.068     0.550     0.652     0.699     0.744     0.821 1.00   500
gamma[13,2,2]      0.783   0.061     0.654     0.741     0.786     0.824     0.893 1.01   280
gamma[14,2,2]      0.992   0.008     0.970     0.989     0.995     0.998     1.000 1.01  1600
gamma[15,2,2]      0.981   0.019     0.929     0.974     0.986     0.994     0.999 1.00   590
gamma[16,2,2]      0.994   0.006     0.977     0.991     0.995     0.998     1.000 1.00  4000
gamma[17,2,2]      0.992   0.009     0.969     0.988     0.994     0.998     1.000 1.00  1500
gamma[18,2,2]      0.992   0.008     0.969     0.989     0.994     0.998     1.000 1.00  2500
gamma[19,2,2]      0.821   0.057     0.705     0.784     0.824     0.861     0.924 1.01   320
gamma[20,2,2]      0.817   0.058     0.695     0.780     0.821     0.859     0.920 1.01   190
gamma[21,2,2]      0.783   0.066     0.641     0.743     0.786     0.830     0.904 1.02   160
gamma[22,2,2]      0.766   0.059     0.638     0.729     0.770     0.807     0.871 1.01   330
gamma[23,2,2]      0.638   0.065     0.501     0.594     0.640     0.684     0.756 1.00   640
gamma[24,2,2]      0.765   0.064     0.627     0.724     0.769     0.810     0.877 1.01   170
gamma[25,2,2]      0.598   0.070     0.456     0.552     0.602     0.649     0.725 1.00   640
gamma[1,3,2]       0.035   0.025     0.002     0.015     0.031     0.051     0.092 1.01   790
gamma[2,3,2]       0.022   0.019     0.001     0.007     0.017     0.031     0.071 1.01   430
gamma[3,3,2]       0.019   0.018     0.000     0.006     0.013     0.026     0.067 1.01   800
gamma[4,3,2]       0.047   0.041     0.002     0.016     0.037     0.068     0.152 1.02   180
gamma[5,3,2]       0.047   0.038     0.002     0.018     0.039     0.067     0.141 1.00  1000
gamma[6,3,2]       0.026   0.023     0.001     0.009     0.020     0.036     0.084 1.00   580
gamma[7,3,2]       0.020   0.017     0.001     0.007     0.015     0.028     0.062 1.00  3700
gamma[8,3,2]       0.093   0.071     0.002     0.036     0.080     0.133     0.256 1.03   110
gamma[9,3,2]       0.172   0.124     0.010     0.071     0.151     0.250     0.453 1.01   620
gamma[10,3,2]      0.077   0.065     0.003     0.028     0.060     0.112     0.243 1.01   660
gamma[11,3,2]      0.048   0.043     0.001     0.015     0.036     0.067     0.159 1.01   290
gamma[12,3,2]      0.169   0.100     0.010     0.094     0.159     0.236     0.378 1.02   310
gamma[13,3,2]      0.156   0.098     0.008     0.078     0.145     0.218     0.373 1.01   540
gamma[14,3,2]      0.018   0.018     0.001     0.006     0.013     0.025     0.067 1.00  4000
gamma[15,3,2]      0.074   0.071     0.001     0.021     0.053     0.105     0.266 1.02   230
gamma[16,3,2]      0.010   0.010     0.000     0.003     0.007     0.014     0.038 1.01   920
gamma[17,3,2]      0.019   0.017     0.001     0.006     0.014     0.026     0.064 1.00  4000
gamma[18,3,2]      0.026   0.023     0.001     0.008     0.020     0.036     0.086 1.02   380
gamma[19,3,2]      0.130   0.081     0.008     0.065     0.123     0.183     0.315 1.00  1900
gamma[20,3,2]      0.075   0.046     0.005     0.040     0.070     0.105     0.172 1.01   940
gamma[21,3,2]      0.251   0.125     0.029     0.156     0.252     0.341     0.497 1.01   320
gamma[22,3,2]      0.209   0.088     0.040     0.149     0.211     0.269     0.384 1.00  3600
gamma[23,3,2]      0.038   0.035     0.001     0.011     0.028     0.053     0.131 1.01   580
gamma[24,3,2]      0.226   0.094     0.045     0.161     0.228     0.292     0.402 1.08   120
gamma[25,3,2]      0.068   0.057     0.004     0.023     0.054     0.095     0.217 1.01   290
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]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,2,3]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,2,3]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,3,3]       0.958   0.024     0.902     0.943     0.961     0.976     0.993 1.00   680
gamma[2,3,3]       0.975   0.019     0.926     0.965     0.979     0.989     0.998 1.00   570
gamma[3,3,3]       0.978   0.018     0.929     0.970     0.982     0.991     0.998 1.00   730
gamma[4,3,3]       0.940   0.040     0.840     0.920     0.949     0.969     0.994 1.00  1500
gamma[5,3,3]       0.945   0.037     0.854     0.925     0.953     0.973     0.993 1.00  1800
gamma[6,3,3]       0.969   0.023     0.912     0.958     0.975     0.986     0.998 1.00   620
gamma[7,3,3]       0.977   0.017     0.934     0.968     0.981     0.990     0.998 1.00  4000
gamma[8,3,3]       0.849   0.061     0.715     0.813     0.857     0.895     0.942 1.01   350
gamma[9,3,3]       0.622   0.111     0.382     0.552     0.634     0.705     0.802 1.01   340
gamma[10,3,3]      0.886   0.064     0.730     0.850     0.898     0.933     0.979 1.01   540
gamma[11,3,3]      0.347   0.069     0.217     0.297     0.346     0.392     0.487 1.01   410
gamma[12,3,3]      0.687   0.085     0.507     0.631     0.691     0.749     0.832 1.00   600
gamma[13,3,3]      0.725   0.084     0.538     0.673     0.732     0.785     0.864 1.00  1100
gamma[14,3,3]      0.979   0.018     0.931     0.971     0.984     0.992     0.998 1.00  2900
gamma[15,3,3]      0.889   0.069     0.711     0.855     0.903     0.936     0.985 1.00  1100
gamma[16,3,3]      0.988   0.011     0.960     0.984     0.991     0.995     0.999 1.00  1600
gamma[17,3,3]      0.978   0.018     0.934     0.970     0.983     0.991     0.998 1.00  1000
gamma[18,3,3]      0.968   0.024     0.910     0.957     0.974     0.986     0.998 1.00  3600
gamma[19,3,3]      0.847   0.075     0.676     0.801     0.857     0.905     0.964 1.00   910
gamma[20,3,3]      0.919   0.046     0.822     0.890     0.924     0.954     0.990 1.00  2300
gamma[21,3,3]      0.696   0.107     0.475     0.626     0.698     0.774     0.895 1.01   440
gamma[22,3,3]      0.709   0.076     0.551     0.657     0.708     0.763     0.853 1.00  2800
gamma[23,3,3]      0.322   0.065     0.206     0.274     0.321     0.367     0.451 1.00  1800
gamma[24,3,3]      0.696   0.083     0.536     0.639     0.697     0.755     0.858 1.01   280
gamma[25,3,3]      0.258   0.061     0.144     0.214     0.257     0.299     0.389 1.01   180
inv.phi[1,1]       3.096   1.618     0.622     1.924     2.813     4.018     7.038 1.02  1000
inv.phi[2,1]      -0.463   1.066    -2.669    -1.101    -0.438     0.216     1.643 1.05    69
inv.phi[3,1]      -1.237   1.065    -3.680    -1.837    -1.094    -0.465     0.463 1.01   280
inv.phi[4,1]      -1.078   1.417    -4.524    -1.782    -0.837    -0.140     1.164 1.06    50
inv.phi[1,2]      -0.463   1.066    -2.669    -1.101    -0.438     0.216     1.643 1.05    69
inv.phi[2,2]       3.030   1.330     1.081     2.072     2.817     3.743     6.273 1.03   180
inv.phi[3,2]       0.079   1.035    -2.001    -0.596     0.095     0.746     2.104 1.05    64
inv.phi[4,2]      -1.995   1.366    -5.116    -2.828    -1.797    -1.008     0.189 1.05    58
inv.phi[1,3]      -1.237   1.065    -3.680    -1.837    -1.094    -0.465     0.463 1.01   280
inv.phi[2,3]       0.079   1.035    -2.001    -0.596     0.095     0.746     2.104 1.05    64
inv.phi[3,3]       2.758   1.340     0.848     1.720     2.550     3.526     5.921 1.05    61
inv.phi[4,3]      -1.143   1.236    -3.667    -1.927    -1.065    -0.279     1.164 1.05    56
inv.phi[1,4]      -1.078   1.417    -4.524    -1.782    -0.837    -0.140     1.164 1.06    50
inv.phi[2,4]      -1.995   1.366    -5.116    -2.828    -1.797    -1.008     0.189 1.05    58
inv.phi[3,4]      -1.143   1.236    -3.667    -1.927    -1.065    -0.279     1.164 1.05    56
inv.phi[4,4]       3.758   1.921     1.006     2.369     3.385     4.801     8.346 1.03   120
lambda[1]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[2]          1.086   0.118     0.881     1.002     1.077     1.164     1.339 1.02   130
lambda[3]          0.744   0.082     0.594     0.687     0.740     0.795     0.918 1.03   130
lambda[4]          0.678   0.076     0.536     0.626     0.675     0.728     0.836 1.01   410
lambda[5]          0.951   0.104     0.761     0.877     0.947     1.019     1.170 1.03    96
lambda[6]          0.860   0.097     0.691     0.791     0.855     0.921     1.070 1.02   500
lambda[7]          0.959   0.102     0.774     0.890     0.954     1.020     1.181 1.02   130
lambda[8]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[9]          0.841   0.103     0.653     0.770     0.837     0.905     1.059 1.01   220
lambda[10]         0.678   0.092     0.505     0.615     0.678     0.740     0.862 1.01   200
lambda[11]         1.233   0.161     0.948     1.123     1.223     1.327     1.601 1.04   110
lambda[12]         1.256   0.158     0.972     1.147     1.242     1.354     1.592 1.02   370
lambda[13]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[14]         0.481   0.059     0.369     0.441     0.478     0.517     0.603 1.01   430
lambda[15]         0.434   0.066     0.312     0.388     0.431     0.478     0.571 1.00  4000
lambda[16]         0.419   0.054     0.314     0.381     0.418     0.454     0.531 1.01   230
lambda[17]         0.669   0.073     0.533     0.619     0.667     0.715     0.814 1.01   280
lambda[18]         0.574   0.067     0.452     0.527     0.570     0.617     0.715 1.03    98
lambda[19]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[20]         1.052   0.126     0.821     0.960     1.047     1.133     1.316 1.03   130
lambda[21]         0.851   0.107     0.661     0.776     0.847     0.917     1.080 1.05    63
lambda[22]         1.475   0.205     1.143     1.332     1.445     1.595     1.948 1.05    61
lambda[23]         2.012   0.226     1.542     1.873     2.017     2.158     2.459 1.02   320
lambda[24]         1.130   0.148     0.862     1.030     1.121     1.220     1.446 1.04    93
lambda[25]         1.848   0.206     1.425     1.710     1.851     1.990     2.237 1.08    43
lambda.std[1]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[2]      0.732   0.036     0.661     0.708     0.733     0.759     0.801 1.02   130
lambda.std[3]      0.595   0.042     0.510     0.566     0.595     0.622     0.676 1.02   140
lambda.std[4]      0.559   0.043     0.472     0.530     0.559     0.589     0.641 1.01   450
lambda.std[5]      0.686   0.040     0.606     0.659     0.688     0.714     0.760 1.03    94
lambda.std[6]      0.649   0.042     0.568     0.621     0.650     0.677     0.731 1.01   620
lambda.std[7]      0.689   0.038     0.612     0.665     0.690     0.714     0.763 1.02   140
lambda.std[8]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[9]      0.640   0.046     0.547     0.610     0.642     0.671     0.727 1.01   210
lambda.std[10]     0.558   0.052     0.450     0.524     0.561     0.595     0.653 1.01   210
lambda.std[11]     0.772   0.040     0.688     0.747     0.774     0.799     0.848 1.03   130
lambda.std[12]     0.778   0.038     0.697     0.754     0.779     0.804     0.847 1.02   430
lambda.std[13]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[14]     0.432   0.043     0.346     0.404     0.431     0.459     0.517 1.01   460
lambda.std[15]     0.396   0.051     0.298     0.362     0.396     0.431     0.496 1.00  4000
lambda.std[16]     0.385   0.042     0.300     0.356     0.386     0.413     0.469 1.01   240
lambda.std[17]     0.554   0.041     0.470     0.527     0.555     0.581     0.631 1.01   290
lambda.std[18]     0.496   0.043     0.412     0.466     0.496     0.525     0.582 1.03   100
lambda.std[19]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[20]     0.721   0.041     0.635     0.693     0.723     0.750     0.796 1.02   160
lambda.std[21]     0.644   0.047     0.551     0.613     0.646     0.676     0.734 1.05    66
lambda.std[22]     0.823   0.035     0.752     0.800     0.822     0.847     0.890 1.04    64
lambda.std[23]     0.893   0.022     0.839     0.882     0.896     0.907     0.926 1.03   360
lambda.std[24]     0.744   0.043     0.653     0.718     0.746     0.773     0.823 1.03   110
lambda.std[25]     0.876   0.024     0.819     0.863     0.880     0.893     0.913 1.09    41
phi[1,1]           3.531   2.778     0.831     1.970     2.955     4.302     9.084 1.07    56
phi[2,1]           2.257   1.521    -0.299     1.247     2.301     3.193     4.983 1.05    99
phi[3,1]           2.735   1.764     0.282     1.498     2.434     3.687     7.174 1.03   180
phi[4,1]           3.030   1.547    -0.261     2.147     3.075     3.965     6.173 1.10    35
phi[1,2]           2.257   1.521    -0.299     1.247     2.301     3.193     4.983 1.05    99
phi[2,2]           3.030   1.542     0.875     1.952     2.810     3.797     6.639 1.08    41
phi[3,2]           1.918   1.483    -1.921     1.244     2.001     2.760     4.518 1.06    99
phi[4,2]           2.918   1.288    -0.478     2.282     3.023     3.735     5.212 1.14    25
phi[1,3]           2.735   1.764     0.282     1.498     2.434     3.687     7.174 1.03   180
phi[2,3]           1.918   1.483    -1.921     1.244     2.001     2.760     4.518 1.06    99
phi[3,3]           3.845   3.150     0.918     2.080     3.109     4.387    13.616 1.11    32
phi[4,3]           3.239   1.571     0.622     2.274     3.122     3.893     7.151 1.13    39
phi[1,4]           3.030   1.547    -0.261     2.147     3.075     3.965     6.173 1.10    35
phi[2,4]           2.918   1.288    -0.478     2.282     3.023     3.735     5.212 1.14    25
phi[3,4]           3.239   1.571     0.622     2.274     3.122     3.893     7.151 1.13    39
phi[4,4]           4.240   0.654     2.989     3.808     4.213     4.641     5.653 1.08    54
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]       0.719   0.281    -0.151     0.659     0.816     0.891     0.952 1.13    54
phi.cor[3,1]       0.789   0.220     0.151     0.752     0.866     0.920     0.968 1.18    35
phi.cor[4,1]       0.792   0.256    -0.101     0.773     0.889     0.934     0.972 1.15    32
phi.cor[1,2]       0.719   0.281    -0.151     0.659     0.816     0.891     0.952 1.13    54
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]       0.652   0.337    -0.457     0.583     0.777     0.864     0.939 1.10    44
phi.cor[4,2]       0.814   0.263    -0.185     0.827     0.904     0.942     0.971 1.12    42
phi.cor[1,3]       0.789   0.220     0.151     0.752     0.866     0.920     0.968 1.18    35
phi.cor[2,3]       0.652   0.337    -0.457     0.583     0.777     0.864     0.939 1.10    44
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]       0.825   0.181     0.258     0.791     0.883     0.929     0.966 1.13    61
phi.cor[1,4]       0.792   0.256    -0.101     0.773     0.889     0.934     0.972 1.15    32
phi.cor[2,4]       0.814   0.263    -0.185     0.827     0.904     0.942     0.971 1.12    42
phi.cor[3,4]       0.825   0.181     0.258     0.791     0.883     0.929     0.966 1.13    61
phi.cor[4,4]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
reli.omega[1]      0.848   0.015     0.817     0.838     0.848     0.858     0.878 1.05    77
reli.omega[2]      0.857   0.013     0.832     0.847     0.857     0.866     0.883 1.04   110
reli.omega[3]      0.680   0.024     0.634     0.663     0.680     0.696     0.727 1.02   160
reli.omega[4]      0.903   0.011     0.881     0.896     0.904     0.911     0.923 1.05    70
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]           3.123   0.236     2.706     2.955     3.110     3.274     3.626 1.02   140
tau[2,2]           3.155   0.236     2.731     2.992     3.139     3.299     3.672 1.01   460
tau[3,2]           2.354   0.169     2.033     2.238     2.351     2.465     2.687 1.00  4000
tau[4,2]           1.747   0.142     1.487     1.651     1.742     1.842     2.055 1.00  1700
tau[5,2]           2.380   0.198     2.024     2.241     2.372     2.502     2.809 1.00  1500
tau[6,2]           2.624   0.202     2.260     2.480     2.613     2.751     3.060 1.00  1500
tau[7,2]           3.161   0.235     2.740     2.997     3.147     3.304     3.675 1.00  1400
tau[8,2]           2.236   0.205     1.868     2.095     2.223     2.363     2.683 1.00   930
tau[9,2]           1.289   0.155     1.022     1.185     1.280     1.379     1.621 1.00   870
tau[10,2]          1.412   0.142     1.148     1.314     1.404     1.502     1.708 1.00  4000
tau[11,2]          0.999   0.147     0.726     0.897     0.991     1.095     1.302 1.00   550
tau[12,2]          2.558   0.350     1.988     2.314     2.516     2.759     3.374 1.01   640
tau[13,2]          2.116   0.204     1.763     1.974     2.099     2.237     2.569 1.01   360
tau[14,2]          1.697   0.142     1.433     1.599     1.692     1.791     1.993 1.00  2200
tau[15,2]          1.311   0.133     1.080     1.217     1.301     1.392     1.598 1.01   430
tau[16,2]          2.021   0.199     1.632     1.887     2.018     2.151     2.417 1.00  2600
tau[17,2]          2.273   0.172     1.964     2.154     2.267     2.384     2.637 1.00  2500
tau[18,2]          2.220   0.186     1.895     2.094     2.207     2.331     2.617 1.00  1700
tau[19,2]          2.211   0.204     1.872     2.071     2.192     2.328     2.686 1.01   300
tau[20,2]          2.878   0.310     2.351     2.662     2.848     3.062     3.575 1.00  1100
tau[21,2]          1.934   0.252     1.502     1.759     1.915     2.072     2.492 1.00   650
tau[22,2]          3.227   0.485     2.424     2.888     3.163     3.495     4.342 1.02   120
tau[23,2]          1.057   0.191     0.680     0.930     1.051     1.186     1.443 1.00  3300
tau[24,2]          2.878   0.463     2.154     2.550     2.815     3.143     3.946 1.01   340
tau[25,2]          1.555   0.236     1.140     1.388     1.539     1.706     2.056 1.01   170
theta[1]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[2]           2.193   0.262     1.777     2.005     2.160     2.355     2.792 1.02   130
theta[3]           1.560   0.124     1.352     1.472     1.547     1.631     1.842 1.03   120
theta[4]           1.465   0.105     1.287     1.391     1.455     1.530     1.698 1.01   350
theta[5]           1.916   0.202     1.580     1.769     1.898     2.037     2.370 1.03    99
theta[6]           1.748   0.170     1.477     1.626     1.731     1.848     2.146 1.02   370
theta[7]           1.930   0.200     1.598     1.791     1.911     2.040     2.394 1.03   120
theta[8]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[9]           1.718   0.178     1.427     1.592     1.700     1.818     2.122 1.01   230
theta[10]          1.469   0.127     1.255     1.378     1.459     1.547     1.744 1.01   190
theta[11]          2.547   0.412     1.899     2.261     2.496     2.760     3.564 1.04   110
theta[12]          2.602   0.408     1.944     2.317     2.544     2.834     3.534 1.02   320
theta[13]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[14]          1.234   0.057     1.136     1.195     1.229     1.267     1.364 1.01   350
theta[15]          1.193   0.059     1.097     1.150     1.186     1.228     1.326 1.00  4000
theta[16]          1.178   0.046     1.099     1.145     1.175     1.206     1.282 1.01   200
theta[17]          1.453   0.099     1.284     1.384     1.445     1.511     1.663 1.02   250
theta[18]          1.334   0.078     1.204     1.278     1.325     1.381     1.511 1.03    94
theta[19]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[20]          2.122   0.270     1.674     1.923     2.097     2.283     2.732 1.03   120
theta[21]          1.736   0.188     1.436     1.602     1.717     1.841     2.167 1.05    61
theta[22]          3.217   0.636     2.305     2.773     3.087     3.543     4.793 1.05    60
theta[23]          5.101   0.907     3.376     4.507     5.068     5.655     7.045 1.02   300
theta[24]          2.299   0.344     1.742     2.061     2.258     2.489     3.092 1.04    85
theta[25]          4.456   0.761     3.030     3.925     4.427     4.958     6.006 1.07    44
deviance       16470.528 137.244 16192.371 16378.433 16470.004 16563.548 16738.870 1.02   140

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 = 9226.0 and DIC = 25696.5
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 16470.528 137.244 16192.371 16378.433 16470.004 16563.548 16738.870 1.02 140
gamma[1,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[2,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[3,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[4,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[5,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[6,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[7,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[8,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[9,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[10,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[11,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[12,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[13,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[14,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[15,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[16,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[17,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[18,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[19,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[20,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[21,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[22,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[23,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[24,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[25,1,1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[1,2,1] 0.124 0.050 0.037 0.089 0.122 0.153 0.235 1.02 150
gamma[2,2,1] 0.058 0.037 0.005 0.029 0.052 0.078 0.143 1.01 930
gamma[3,2,1] 0.013 0.013 0.000 0.004 0.009 0.017 0.047 1.01 680
gamma[4,2,1] 0.025 0.021 0.001 0.008 0.019 0.035 0.077 1.01 430
gamma[5,2,1] 0.028 0.022 0.001 0.011 0.022 0.039 0.080 1.01 390
gamma[6,2,1] 0.039 0.028 0.002 0.016 0.034 0.055 0.103 1.01 430
gamma[7,2,1] 0.011 0.010 0.000 0.003 0.008 0.015 0.036 1.00 2200
gamma[8,2,1] 0.103 0.045 0.024 0.070 0.100 0.132 0.199 1.04 150
gamma[9,2,1] 0.118 0.056 0.024 0.078 0.111 0.152 0.242 1.00 640
gamma[10,2,1] 0.154 0.060 0.045 0.111 0.150 0.192 0.284 1.02 170
gamma[11,2,1] 0.266 0.064 0.151 0.223 0.262 0.306 0.402 1.01 270
gamma[12,2,1] 0.304 0.068 0.179 0.256 0.301 0.348 0.450 1.00 520
gamma[13,2,1] 0.217 0.061 0.107 0.176 0.214 0.259 0.346 1.01 230
gamma[14,2,1] 0.008 0.008 0.000 0.002 0.005 0.011 0.030 1.00 4000
gamma[15,2,1] 0.019 0.019 0.001 0.006 0.014 0.026 0.071 1.01 300
gamma[16,2,1] 0.006 0.006 0.000 0.002 0.005 0.009 0.023 1.00 1300
gamma[17,2,1] 0.008 0.009 0.000 0.002 0.006 0.012 0.031 1.01 440
gamma[18,2,1] 0.008 0.008 0.000 0.002 0.006 0.011 0.031 1.00 3800
gamma[19,2,1] 0.179 0.057 0.076 0.139 0.176 0.216 0.295 1.01 290
gamma[20,2,1] 0.183 0.058 0.080 0.141 0.179 0.220 0.305 1.01 180
gamma[21,2,1] 0.217 0.066 0.096 0.170 0.214 0.257 0.359 1.02 170
gamma[22,2,1] 0.234 0.059 0.129 0.193 0.230 0.271 0.362 1.01 390
gamma[23,2,1] 0.362 0.065 0.244 0.316 0.360 0.406 0.499 1.00 690
gamma[24,2,1] 0.235 0.064 0.123 0.190 0.231 0.276 0.373 1.02 150
gamma[25,2,1] 0.402 0.070 0.275 0.351 0.398 0.448 0.544 1.00 680
gamma[1,3,1] 0.007 0.008 0.000 0.001 0.004 0.010 0.028 1.01 270
gamma[2,3,1] 0.003 0.005 0.000 0.000 0.002 0.005 0.017 1.02 240
gamma[3,3,1] 0.004 0.005 0.000 0.000 0.002 0.005 0.017 1.00 2100
gamma[4,3,1] 0.013 0.013 0.000 0.003 0.009 0.020 0.047 1.03 93
gamma[5,3,1] 0.008 0.009 0.000 0.001 0.005 0.011 0.030 1.04 110
gamma[6,3,1] 0.005 0.006 0.000 0.000 0.002 0.007 0.021 1.05 130
gamma[7,3,1] 0.003 0.004 0.000 0.000 0.002 0.005 0.016 1.04 130
gamma[8,3,1] 0.059 0.029 0.004 0.037 0.057 0.077 0.122 1.16 55
gamma[9,3,1] 0.206 0.058 0.097 0.165 0.202 0.245 0.320 1.00 760
gamma[10,3,1] 0.037 0.026 0.000 0.016 0.034 0.054 0.097 1.01 400
gamma[11,3,1] 0.606 0.068 0.473 0.560 0.604 0.652 0.739 1.00 2300
gamma[12,3,1] 0.144 0.045 0.063 0.113 0.141 0.173 0.241 1.00 4000
gamma[13,3,1] 0.119 0.043 0.040 0.089 0.117 0.146 0.208 1.01 260
gamma[14,3,1] 0.003 0.004 0.000 0.000 0.001 0.004 0.015 1.02 340
gamma[15,3,1] 0.037 0.032 0.000 0.011 0.031 0.056 0.113 1.04 150
gamma[16,3,1] 0.002 0.003 0.000 0.000 0.001 0.002 0.009 1.02 170
gamma[17,3,1] 0.003 0.004 0.000 0.000 0.001 0.004 0.015 1.01 950
gamma[18,3,1] 0.006 0.007 0.000 0.001 0.003 0.008 0.026 1.04 110
gamma[19,3,1] 0.023 0.020 0.000 0.007 0.019 0.035 0.071 1.07 140
gamma[20,3,1] 0.005 0.007 0.000 0.001 0.002 0.007 0.026 1.01 260
gamma[21,3,1] 0.052 0.040 0.001 0.020 0.044 0.077 0.148 1.03 250
gamma[22,3,1] 0.083 0.034 0.028 0.059 0.078 0.103 0.159 1.01 440
gamma[23,3,1] 0.640 0.064 0.512 0.595 0.641 0.687 0.760 1.00 740
gamma[24,3,1] 0.078 0.033 0.023 0.055 0.075 0.099 0.151 1.00 2000
gamma[25,3,1] 0.675 0.067 0.541 0.630 0.677 0.721 0.803 1.00 830
gamma[1,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,1,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,2,2] 0.876 0.050 0.765 0.847 0.878 0.911 0.963 1.01 200
gamma[2,2,2] 0.942 0.037 0.857 0.922 0.948 0.971 0.995 1.00 1000
gamma[3,2,2] 0.987 0.013 0.953 0.983 0.991 0.996 1.000 1.00 4000
gamma[4,2,2] 0.975 0.021 0.923 0.965 0.981 0.992 0.999 1.01 420
gamma[5,2,2] 0.972 0.022 0.920 0.961 0.978 0.989 0.999 1.00 520
gamma[6,2,2] 0.961 0.028 0.897 0.945 0.966 0.984 0.998 1.01 270
gamma[7,2,2] 0.989 0.010 0.964 0.985 0.992 0.997 1.000 1.01 2100
gamma[8,2,2] 0.897 0.045 0.801 0.868 0.900 0.930 0.976 1.02 130
gamma[9,2,2] 0.882 0.056 0.758 0.848 0.889 0.922 0.976 1.01 370
gamma[10,2,2] 0.846 0.060 0.716 0.808 0.850 0.889 0.955 1.02 160
gamma[11,2,2] 0.734 0.064 0.598 0.694 0.738 0.777 0.849 1.01 280
gamma[12,2,2] 0.696 0.068 0.550 0.652 0.699 0.744 0.821 1.00 500
gamma[13,2,2] 0.783 0.061 0.654 0.741 0.786 0.824 0.893 1.01 280
gamma[14,2,2] 0.992 0.008 0.970 0.989 0.995 0.998 1.000 1.01 1600
gamma[15,2,2] 0.981 0.019 0.929 0.974 0.986 0.994 0.999 1.00 590
gamma[16,2,2] 0.994 0.006 0.977 0.991 0.995 0.998 1.000 1.00 4000
gamma[17,2,2] 0.992 0.009 0.969 0.988 0.994 0.998 1.000 1.00 1500
gamma[18,2,2] 0.992 0.008 0.969 0.989 0.994 0.998 1.000 1.00 2500
gamma[19,2,2] 0.821 0.057 0.705 0.784 0.824 0.861 0.924 1.01 320
gamma[20,2,2] 0.817 0.058 0.695 0.780 0.821 0.859 0.920 1.01 190
gamma[21,2,2] 0.783 0.066 0.641 0.743 0.786 0.830 0.904 1.02 160
gamma[22,2,2] 0.766 0.059 0.638 0.729 0.770 0.807 0.871 1.01 330
gamma[23,2,2] 0.638 0.065 0.501 0.594 0.640 0.684 0.756 1.00 640
gamma[24,2,2] 0.765 0.064 0.627 0.724 0.769 0.810 0.877 1.01 170
gamma[25,2,2] 0.598 0.070 0.456 0.552 0.602 0.649 0.725 1.00 640
gamma[1,3,2] 0.035 0.025 0.002 0.015 0.031 0.051 0.092 1.01 790
gamma[2,3,2] 0.022 0.019 0.001 0.007 0.017 0.031 0.071 1.01 430
gamma[3,3,2] 0.019 0.018 0.000 0.006 0.013 0.026 0.067 1.01 800
gamma[4,3,2] 0.047 0.041 0.002 0.016 0.037 0.068 0.152 1.02 180
gamma[5,3,2] 0.047 0.038 0.002 0.018 0.039 0.067 0.141 1.00 1000
gamma[6,3,2] 0.026 0.023 0.001 0.009 0.020 0.036 0.084 1.00 580
gamma[7,3,2] 0.020 0.017 0.001 0.007 0.015 0.028 0.062 1.00 3700
gamma[8,3,2] 0.093 0.071 0.002 0.036 0.080 0.133 0.256 1.03 110
gamma[9,3,2] 0.172 0.124 0.010 0.071 0.151 0.250 0.453 1.01 620
gamma[10,3,2] 0.077 0.065 0.003 0.028 0.060 0.112 0.243 1.01 660
gamma[11,3,2] 0.048 0.043 0.001 0.015 0.036 0.067 0.159 1.01 290
gamma[12,3,2] 0.169 0.100 0.010 0.094 0.159 0.236 0.378 1.02 310
gamma[13,3,2] 0.156 0.098 0.008 0.078 0.145 0.218 0.373 1.01 540
gamma[14,3,2] 0.018 0.018 0.001 0.006 0.013 0.025 0.067 1.00 4000
gamma[15,3,2] 0.074 0.071 0.001 0.021 0.053 0.105 0.266 1.02 230
gamma[16,3,2] 0.010 0.010 0.000 0.003 0.007 0.014 0.038 1.01 920
gamma[17,3,2] 0.019 0.017 0.001 0.006 0.014 0.026 0.064 1.00 4000
gamma[18,3,2] 0.026 0.023 0.001 0.008 0.020 0.036 0.086 1.02 380
gamma[19,3,2] 0.130 0.081 0.008 0.065 0.123 0.183 0.315 1.00 1900
gamma[20,3,2] 0.075 0.046 0.005 0.040 0.070 0.105 0.172 1.01 940
gamma[21,3,2] 0.251 0.125 0.029 0.156 0.252 0.341 0.497 1.01 320
gamma[22,3,2] 0.209 0.088 0.040 0.149 0.211 0.269 0.384 1.00 3600
gamma[23,3,2] 0.038 0.035 0.001 0.011 0.028 0.053 0.131 1.01 580
gamma[24,3,2] 0.226 0.094 0.045 0.161 0.228 0.292 0.402 1.08 120
gamma[25,3,2] 0.068 0.057 0.004 0.023 0.054 0.095 0.217 1.01 290
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] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,2,3] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,3,3] 0.958 0.024 0.902 0.943 0.961 0.976 0.993 1.00 680
gamma[2,3,3] 0.975 0.019 0.926 0.965 0.979 0.989 0.998 1.00 570
gamma[3,3,3] 0.978 0.018 0.929 0.970 0.982 0.991 0.998 1.00 730
gamma[4,3,3] 0.940 0.040 0.840 0.920 0.949 0.969 0.994 1.00 1500
gamma[5,3,3] 0.945 0.037 0.854 0.925 0.953 0.973 0.993 1.00 1800
gamma[6,3,3] 0.969 0.023 0.912 0.958 0.975 0.986 0.998 1.00 620
gamma[7,3,3] 0.977 0.017 0.934 0.968 0.981 0.990 0.998 1.00 4000
gamma[8,3,3] 0.849 0.061 0.715 0.813 0.857 0.895 0.942 1.01 350
gamma[9,3,3] 0.622 0.111 0.382 0.552 0.634 0.705 0.802 1.01 340
gamma[10,3,3] 0.886 0.064 0.730 0.850 0.898 0.933 0.979 1.01 540
gamma[11,3,3] 0.347 0.069 0.217 0.297 0.346 0.392 0.487 1.01 410
gamma[12,3,3] 0.687 0.085 0.507 0.631 0.691 0.749 0.832 1.00 600
gamma[13,3,3] 0.725 0.084 0.538 0.673 0.732 0.785 0.864 1.00 1100
gamma[14,3,3] 0.979 0.018 0.931 0.971 0.984 0.992 0.998 1.00 2900
gamma[15,3,3] 0.889 0.069 0.711 0.855 0.903 0.936 0.985 1.00 1100
gamma[16,3,3] 0.988 0.011 0.960 0.984 0.991 0.995 0.999 1.00 1600
gamma[17,3,3] 0.978 0.018 0.934 0.970 0.983 0.991 0.998 1.00 1000
gamma[18,3,3] 0.968 0.024 0.910 0.957 0.974 0.986 0.998 1.00 3600
gamma[19,3,3] 0.847 0.075 0.676 0.801 0.857 0.905 0.964 1.00 910
gamma[20,3,3] 0.919 0.046 0.822 0.890 0.924 0.954 0.990 1.00 2300
gamma[21,3,3] 0.696 0.107 0.475 0.626 0.698 0.774 0.895 1.01 440
gamma[22,3,3] 0.709 0.076 0.551 0.657 0.708 0.763 0.853 1.00 2800
gamma[23,3,3] 0.322 0.065 0.206 0.274 0.321 0.367 0.451 1.00 1800
gamma[24,3,3] 0.696 0.083 0.536 0.639 0.697 0.755 0.858 1.01 280
gamma[25,3,3] 0.258 0.061 0.144 0.214 0.257 0.299 0.389 1.01 180
inv.phi[1,1] 3.096 1.618 0.622 1.924 2.813 4.018 7.038 1.02 1000
inv.phi[2,1] -0.463 1.066 -2.669 -1.101 -0.438 0.216 1.643 1.05 69
inv.phi[3,1] -1.237 1.065 -3.680 -1.837 -1.094 -0.465 0.463 1.01 280
inv.phi[4,1] -1.078 1.417 -4.524 -1.782 -0.837 -0.140 1.164 1.06 50
inv.phi[1,2] -0.463 1.066 -2.669 -1.101 -0.438 0.216 1.643 1.05 69
inv.phi[2,2] 3.030 1.330 1.081 2.072 2.817 3.743 6.273 1.03 180
inv.phi[3,2] 0.079 1.035 -2.001 -0.596 0.095 0.746 2.104 1.05 64
inv.phi[4,2] -1.995 1.366 -5.116 -2.828 -1.797 -1.008 0.189 1.05 58
inv.phi[1,3] -1.237 1.065 -3.680 -1.837 -1.094 -0.465 0.463 1.01 280
inv.phi[2,3] 0.079 1.035 -2.001 -0.596 0.095 0.746 2.104 1.05 64
inv.phi[3,3] 2.758 1.340 0.848 1.720 2.550 3.526 5.921 1.05 61
inv.phi[4,3] -1.143 1.236 -3.667 -1.927 -1.065 -0.279 1.164 1.05 56
inv.phi[1,4] -1.078 1.417 -4.524 -1.782 -0.837 -0.140 1.164 1.06 50
inv.phi[2,4] -1.995 1.366 -5.116 -2.828 -1.797 -1.008 0.189 1.05 58
inv.phi[3,4] -1.143 1.236 -3.667 -1.927 -1.065 -0.279 1.164 1.05 56
inv.phi[4,4] 3.758 1.921 1.006 2.369 3.385 4.801 8.346 1.03 120
lambda[1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[2] 1.086 0.118 0.881 1.002 1.077 1.164 1.339 1.02 130
lambda[3] 0.744 0.082 0.594 0.687 0.740 0.795 0.918 1.03 130
lambda[4] 0.678 0.076 0.536 0.626 0.675 0.728 0.836 1.01 410
lambda[5] 0.951 0.104 0.761 0.877 0.947 1.019 1.170 1.03 96
lambda[6] 0.860 0.097 0.691 0.791 0.855 0.921 1.070 1.02 500
lambda[7] 0.959 0.102 0.774 0.890 0.954 1.020 1.181 1.02 130
lambda[8] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[9] 0.841 0.103 0.653 0.770 0.837 0.905 1.059 1.01 220
lambda[10] 0.678 0.092 0.505 0.615 0.678 0.740 0.862 1.01 200
lambda[11] 1.233 0.161 0.948 1.123 1.223 1.327 1.601 1.04 110
lambda[12] 1.256 0.158 0.972 1.147 1.242 1.354 1.592 1.02 370
lambda[13] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[14] 0.481 0.059 0.369 0.441 0.478 0.517 0.603 1.01 430
lambda[15] 0.434 0.066 0.312 0.388 0.431 0.478 0.571 1.00 4000
lambda[16] 0.419 0.054 0.314 0.381 0.418 0.454 0.531 1.01 230
lambda[17] 0.669 0.073 0.533 0.619 0.667 0.715 0.814 1.01 280
lambda[18] 0.574 0.067 0.452 0.527 0.570 0.617 0.715 1.03 98
lambda[19] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[20] 1.052 0.126 0.821 0.960 1.047 1.133 1.316 1.03 130
lambda[21] 0.851 0.107 0.661 0.776 0.847 0.917 1.080 1.05 63
lambda[22] 1.475 0.205 1.143 1.332 1.445 1.595 1.948 1.05 61
lambda[23] 2.012 0.226 1.542 1.873 2.017 2.158 2.459 1.02 320
lambda[24] 1.130 0.148 0.862 1.030 1.121 1.220 1.446 1.04 93
lambda[25] 1.848 0.206 1.425 1.710 1.851 1.990 2.237 1.08 43
lambda.std[1] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[2] 0.732 0.036 0.661 0.708 0.733 0.759 0.801 1.02 130
lambda.std[3] 0.595 0.042 0.510 0.566 0.595 0.622 0.676 1.02 140
lambda.std[4] 0.559 0.043 0.472 0.530 0.559 0.589 0.641 1.01 450
lambda.std[5] 0.686 0.040 0.606 0.659 0.688 0.714 0.760 1.03 94
lambda.std[6] 0.649 0.042 0.568 0.621 0.650 0.677 0.731 1.01 620
lambda.std[7] 0.689 0.038 0.612 0.665 0.690 0.714 0.763 1.02 140
lambda.std[8] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[9] 0.640 0.046 0.547 0.610 0.642 0.671 0.727 1.01 210
lambda.std[10] 0.558 0.052 0.450 0.524 0.561 0.595 0.653 1.01 210
lambda.std[11] 0.772 0.040 0.688 0.747 0.774 0.799 0.848 1.03 130
lambda.std[12] 0.778 0.038 0.697 0.754 0.779 0.804 0.847 1.02 430
lambda.std[13] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[14] 0.432 0.043 0.346 0.404 0.431 0.459 0.517 1.01 460
lambda.std[15] 0.396 0.051 0.298 0.362 0.396 0.431 0.496 1.00 4000
lambda.std[16] 0.385 0.042 0.300 0.356 0.386 0.413 0.469 1.01 240
lambda.std[17] 0.554 0.041 0.470 0.527 0.555 0.581 0.631 1.01 290
lambda.std[18] 0.496 0.043 0.412 0.466 0.496 0.525 0.582 1.03 100
lambda.std[19] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[20] 0.721 0.041 0.635 0.693 0.723 0.750 0.796 1.02 160
lambda.std[21] 0.644 0.047 0.551 0.613 0.646 0.676 0.734 1.05 66
lambda.std[22] 0.823 0.035 0.752 0.800 0.822 0.847 0.890 1.04 64
lambda.std[23] 0.893 0.022 0.839 0.882 0.896 0.907 0.926 1.03 360
lambda.std[24] 0.744 0.043 0.653 0.718 0.746 0.773 0.823 1.03 110
lambda.std[25] 0.876 0.024 0.819 0.863 0.880 0.893 0.913 1.09 41
phi[1,1] 3.531 2.778 0.831 1.970 2.955 4.302 9.084 1.07 56
phi[2,1] 2.257 1.521 -0.299 1.247 2.301 3.193 4.983 1.05 99
phi[3,1] 2.735 1.764 0.282 1.498 2.434 3.687 7.174 1.03 180
phi[4,1] 3.030 1.547 -0.261 2.147 3.075 3.965 6.173 1.10 35
phi[1,2] 2.257 1.521 -0.299 1.247 2.301 3.193 4.983 1.05 99
phi[2,2] 3.030 1.542 0.875 1.952 2.810 3.797 6.639 1.08 41
phi[3,2] 1.918 1.483 -1.921 1.244 2.001 2.760 4.518 1.06 99
phi[4,2] 2.918 1.288 -0.478 2.282 3.023 3.735 5.212 1.14 25
phi[1,3] 2.735 1.764 0.282 1.498 2.434 3.687 7.174 1.03 180
phi[2,3] 1.918 1.483 -1.921 1.244 2.001 2.760 4.518 1.06 99
phi[3,3] 3.845 3.150 0.918 2.080 3.109 4.387 13.616 1.11 32
phi[4,3] 3.239 1.571 0.622 2.274 3.122 3.893 7.151 1.13 39
phi[1,4] 3.030 1.547 -0.261 2.147 3.075 3.965 6.173 1.10 35
phi[2,4] 2.918 1.288 -0.478 2.282 3.023 3.735 5.212 1.14 25
phi[3,4] 3.239 1.571 0.622 2.274 3.122 3.893 7.151 1.13 39
phi[4,4] 4.240 0.654 2.989 3.808 4.213 4.641 5.653 1.08 54
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] 0.719 0.281 -0.151 0.659 0.816 0.891 0.952 1.13 54
phi.cor[3,1] 0.789 0.220 0.151 0.752 0.866 0.920 0.968 1.18 35
phi.cor[4,1] 0.792 0.256 -0.101 0.773 0.889 0.934 0.972 1.15 32
phi.cor[1,2] 0.719 0.281 -0.151 0.659 0.816 0.891 0.952 1.13 54
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] 0.652 0.337 -0.457 0.583 0.777 0.864 0.939 1.10 44
phi.cor[4,2] 0.814 0.263 -0.185 0.827 0.904 0.942 0.971 1.12 42
phi.cor[1,3] 0.789 0.220 0.151 0.752 0.866 0.920 0.968 1.18 35
phi.cor[2,3] 0.652 0.337 -0.457 0.583 0.777 0.864 0.939 1.10 44
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] 0.825 0.181 0.258 0.791 0.883 0.929 0.966 1.13 61
phi.cor[1,4] 0.792 0.256 -0.101 0.773 0.889 0.934 0.972 1.15 32
phi.cor[2,4] 0.814 0.263 -0.185 0.827 0.904 0.942 0.971 1.12 42
phi.cor[3,4] 0.825 0.181 0.258 0.791 0.883 0.929 0.966 1.13 61
phi.cor[4,4] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
reli.omega[1] 0.848 0.015 0.817 0.838 0.848 0.858 0.878 1.05 77
reli.omega[2] 0.857 0.013 0.832 0.847 0.857 0.866 0.883 1.04 110
reli.omega[3] 0.680 0.024 0.634 0.663 0.680 0.696 0.727 1.02 160
reli.omega[4] 0.903 0.011 0.881 0.896 0.904 0.911 0.923 1.05 70
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] 3.123 0.236 2.706 2.955 3.110 3.274 3.626 1.02 140
tau[2,2] 3.155 0.236 2.731 2.992 3.139 3.299 3.672 1.01 460
tau[3,2] 2.354 0.169 2.033 2.238 2.351 2.465 2.687 1.00 4000
tau[4,2] 1.747 0.142 1.487 1.651 1.742 1.842 2.055 1.00 1700
tau[5,2] 2.380 0.198 2.024 2.241 2.372 2.502 2.809 1.00 1500
tau[6,2] 2.624 0.202 2.260 2.480 2.613 2.751 3.060 1.00 1500
tau[7,2] 3.161 0.235 2.740 2.997 3.147 3.304 3.675 1.00 1400
tau[8,2] 2.236 0.205 1.868 2.095 2.223 2.363 2.683 1.00 930
tau[9,2] 1.289 0.155 1.022 1.185 1.280 1.379 1.621 1.00 870
tau[10,2] 1.412 0.142 1.148 1.314 1.404 1.502 1.708 1.00 4000
tau[11,2] 0.999 0.147 0.726 0.897 0.991 1.095 1.302 1.00 550
tau[12,2] 2.558 0.350 1.988 2.314 2.516 2.759 3.374 1.01 640
tau[13,2] 2.116 0.204 1.763 1.974 2.099 2.237 2.569 1.01 360
tau[14,2] 1.697 0.142 1.433 1.599 1.692 1.791 1.993 1.00 2200
tau[15,2] 1.311 0.133 1.080 1.217 1.301 1.392 1.598 1.01 430
tau[16,2] 2.021 0.199 1.632 1.887 2.018 2.151 2.417 1.00 2600
tau[17,2] 2.273 0.172 1.964 2.154 2.267 2.384 2.637 1.00 2500
tau[18,2] 2.220 0.186 1.895 2.094 2.207 2.331 2.617 1.00 1700
tau[19,2] 2.211 0.204 1.872 2.071 2.192 2.328 2.686 1.01 300
tau[20,2] 2.878 0.310 2.351 2.662 2.848 3.062 3.575 1.00 1100
tau[21,2] 1.934 0.252 1.502 1.759 1.915 2.072 2.492 1.00 650
tau[22,2] 3.227 0.485 2.424 2.888 3.163 3.495 4.342 1.02 120
tau[23,2] 1.057 0.191 0.680 0.930 1.051 1.186 1.443 1.00 3300
tau[24,2] 2.878 0.463 2.154 2.550 2.815 3.143 3.946 1.01 340
tau[25,2] 1.555 0.236 1.140 1.388 1.539 1.706 2.056 1.01 170
theta[1] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[2] 2.193 0.262 1.777 2.005 2.160 2.355 2.792 1.02 130
theta[3] 1.560 0.124 1.352 1.472 1.547 1.631 1.842 1.03 120
theta[4] 1.465 0.105 1.287 1.391 1.455 1.530 1.698 1.01 350
theta[5] 1.916 0.202 1.580 1.769 1.898 2.037 2.370 1.03 99
theta[6] 1.748 0.170 1.477 1.626 1.731 1.848 2.146 1.02 370
theta[7] 1.930 0.200 1.598 1.791 1.911 2.040 2.394 1.03 120
theta[8] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[9] 1.718 0.178 1.427 1.592 1.700 1.818 2.122 1.01 230
theta[10] 1.469 0.127 1.255 1.378 1.459 1.547 1.744 1.01 190
theta[11] 2.547 0.412 1.899 2.261 2.496 2.760 3.564 1.04 110
theta[12] 2.602 0.408 1.944 2.317 2.544 2.834 3.534 1.02 320
theta[13] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[14] 1.234 0.057 1.136 1.195 1.229 1.267 1.364 1.01 350
theta[15] 1.193 0.059 1.097 1.150 1.186 1.228 1.326 1.00 4000
theta[16] 1.178 0.046 1.099 1.145 1.175 1.206 1.282 1.01 200
theta[17] 1.453 0.099 1.284 1.384 1.445 1.511 1.663 1.02 250
theta[18] 1.334 0.078 1.204 1.278 1.325 1.381 1.511 1.03 94
theta[19] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[20] 2.122 0.270 1.674 1.923 2.097 2.283 2.732 1.03 120
theta[21] 1.736 0.188 1.436 1.602 1.717 1.841 2.167 1.05 61
theta[22] 3.217 0.636 2.305 2.773 3.087 3.543 4.793 1.05 60
theta[23] 5.101 0.907 3.376 4.507 5.068 5.655 7.045 1.02 300
theta[24] 2.299 0.344 1.742 2.061 2.258 2.489 3.092 1.04 85
theta[25] 4.456 0.761 3.030 3.925 4.427 4.958 6.006 1.07 44

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_model4_lambda_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/pools_model4_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_model4_lambda_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda.std"); ggsave("fig/pools_model4_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_m4.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 336 rows containing missing values (geom_segment).
Warning: Removed 63 row(s) containing missing values (geom_path).

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

Warning: Removed 63 row(s) containing missing values (geom_path).
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_model4_omega_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model4_omega_acf.pdf")

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bayesplot::mcmc_trace(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model4_omega_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "reli.omega"); ggsave("fig/pools_model4_omega_grb.pdf")

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# extract omega posterior for results comparison
extracted_omega <- data.frame(model_4_f1 = fit.mcmc$`reli.omega[1]`,
                              model_4_f2 = fit.mcmc$`reli.omega[2]`,
                              model_4_f3 = fit.mcmc$`reli.omega[3]`,
                              model_4_f4 = fit.mcmc$`reli.omega[4]`)
write.csv(x=extracted_omega, file=paste0(getwd(),"/data/pools/extracted_omega_m4.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 4 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 04:19:46 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
  \toprule
 & mean & sd & 2.5\% & 25\% & 50\% & 75\% & 97.5\% & Rhat & n.eff \\ 
  \midrule
deviance & 16470.53 & 137.24 & 16192.37 & 16378.43 & 16470.00 & 16563.55 & 16738.87 & 1.02 & 140.00 \\ 
  gamma[1,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[2,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[3,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[4,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[5,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[6,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[7,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[8,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[9,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[10,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[11,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[12,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[13,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[14,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[15,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[16,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[17,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[18,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[19,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[20,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[21,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[22,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[23,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[24,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[25,1,1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[1,2,1] & 0.12 & 0.05 & 0.04 & 0.09 & 0.12 & 0.15 & 0.24 & 1.02 & 150.00 \\ 
  gamma[2,2,1] & 0.06 & 0.04 & 0.00 & 0.03 & 0.05 & 0.08 & 0.14 & 1.01 & 930.00 \\ 
  gamma[3,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.02 & 0.05 & 1.01 & 680.00 \\ 
  gamma[4,2,1] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.08 & 1.01 & 430.00 \\ 
  gamma[5,2,1] & 0.03 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.08 & 1.01 & 390.00 \\ 
  gamma[6,2,1] & 0.04 & 0.03 & 0.00 & 0.02 & 0.03 & 0.05 & 0.10 & 1.01 & 430.00 \\ 
  gamma[7,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.02 & 0.04 & 1.00 & 2200.00 \\ 
  gamma[8,2,1] & 0.10 & 0.04 & 0.02 & 0.07 & 0.10 & 0.13 & 0.20 & 1.04 & 150.00 \\ 
  gamma[9,2,1] & 0.12 & 0.06 & 0.02 & 0.08 & 0.11 & 0.15 & 0.24 & 1.00 & 640.00 \\ 
  gamma[10,2,1] & 0.15 & 0.06 & 0.05 & 0.11 & 0.15 & 0.19 & 0.28 & 1.02 & 170.00 \\ 
  gamma[11,2,1] & 0.27 & 0.06 & 0.15 & 0.22 & 0.26 & 0.31 & 0.40 & 1.01 & 270.00 \\ 
  gamma[12,2,1] & 0.30 & 0.07 & 0.18 & 0.26 & 0.30 & 0.35 & 0.45 & 1.01 & 520.00 \\ 
  gamma[13,2,1] & 0.22 & 0.06 & 0.11 & 0.18 & 0.21 & 0.26 & 0.35 & 1.01 & 230.00 \\ 
  gamma[14,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.03 & 1.00 & 4000.00 \\ 
  gamma[15,2,1] & 0.02 & 0.02 & 0.00 & 0.01 & 0.01 & 0.03 & 0.07 & 1.02 & 300.00 \\ 
  gamma[16,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.00 & 1300.00 \\ 
  gamma[17,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.03 & 1.01 & 440.00 \\ 
  gamma[18,2,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.03 & 1.00 & 3800.00 \\ 
  gamma[19,2,1] & 0.18 & 0.06 & 0.08 & 0.14 & 0.18 & 0.22 & 0.30 & 1.01 & 290.00 \\ 
  gamma[20,2,1] & 0.18 & 0.06 & 0.08 & 0.14 & 0.18 & 0.22 & 0.31 & 1.01 & 180.00 \\ 
  gamma[21,2,1] & 0.22 & 0.07 & 0.10 & 0.17 & 0.21 & 0.26 & 0.36 & 1.02 & 170.00 \\ 
  gamma[22,2,1] & 0.23 & 0.06 & 0.13 & 0.19 & 0.23 & 0.27 & 0.36 & 1.01 & 390.00 \\ 
  gamma[23,2,1] & 0.36 & 0.07 & 0.24 & 0.32 & 0.36 & 0.41 & 0.50 & 1.00 & 690.00 \\ 
  gamma[24,2,1] & 0.24 & 0.06 & 0.12 & 0.19 & 0.23 & 0.28 & 0.37 & 1.02 & 150.00 \\ 
  gamma[25,2,1] & 0.40 & 0.07 & 0.27 & 0.35 & 0.40 & 0.45 & 0.54 & 1.00 & 680.00 \\ 
  gamma[1,3,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.01 & 270.00 \\ 
  gamma[2,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 1.02 & 240.00 \\ 
  gamma[3,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.00 & 2100.00 \\ 
  gamma[4,3,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.02 & 0.05 & 1.03 & 93.00 \\ 
  gamma[5,3,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.03 & 1.05 & 110.00 \\ 
  gamma[6,3,1] & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.05 & 130.00 \\ 
  gamma[7,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 1.04 & 130.00 \\ 
  gamma[8,3,1] & 0.06 & 0.03 & 0.00 & 0.04 & 0.06 & 0.08 & 0.12 & 1.16 & 55.00 \\ 
  gamma[9,3,1] & 0.21 & 0.06 & 0.10 & 0.16 & 0.20 & 0.24 & 0.32 & 1.00 & 760.00 \\ 
  gamma[10,3,1] & 0.04 & 0.03 & 0.00 & 0.02 & 0.03 & 0.05 & 0.10 & 1.01 & 400.00 \\ 
  gamma[11,3,1] & 0.61 & 0.07 & 0.47 & 0.56 & 0.60 & 0.65 & 0.74 & 1.00 & 2300.00 \\ 
  gamma[12,3,1] & 0.14 & 0.05 & 0.06 & 0.11 & 0.14 & 0.17 & 0.24 & 1.00 & 4000.00 \\ 
  gamma[13,3,1] & 0.12 & 0.04 & 0.04 & 0.09 & 0.12 & 0.15 & 0.21 & 1.01 & 260.00 \\ 
  gamma[14,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 1.02 & 340.00 \\ 
  gamma[15,3,1] & 0.04 & 0.03 & 0.00 & 0.01 & 0.03 & 0.06 & 0.11 & 1.04 & 150.00 \\ 
  gamma[16,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 1.02 & 170.00 \\ 
  gamma[17,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 1.01 & 950.00 \\ 
  gamma[18,3,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.04 & 110.00 \\ 
  gamma[19,3,1] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.03 & 0.07 & 1.07 & 140.00 \\ 
  gamma[20,3,1] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.01 & 260.00 \\ 
  gamma[21,3,1] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.08 & 0.15 & 1.03 & 250.00 \\ 
  gamma[22,3,1] & 0.08 & 0.03 & 0.03 & 0.06 & 0.08 & 0.10 & 0.16 & 1.01 & 440.00 \\ 
  gamma[23,3,1] & 0.64 & 0.06 & 0.51 & 0.59 & 0.64 & 0.69 & 0.76 & 1.00 & 740.00 \\ 
  gamma[24,3,1] & 0.08 & 0.03 & 0.02 & 0.05 & 0.07 & 0.10 & 0.15 & 1.00 & 2000.00 \\ 
  gamma[25,3,1] & 0.67 & 0.07 & 0.54 & 0.63 & 0.68 & 0.72 & 0.80 & 1.00 & 830.00 \\ 
  gamma[1,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,1,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,2,2] & 0.88 & 0.05 & 0.76 & 0.85 & 0.88 & 0.91 & 0.96 & 1.01 & 200.00 \\ 
  gamma[2,2,2] & 0.94 & 0.04 & 0.86 & 0.92 & 0.95 & 0.97 & 1.00 & 1.00 & 1000.00 \\ 
  gamma[3,2,2] & 0.99 & 0.01 & 0.95 & 0.98 & 0.99 & 1.00 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[4,2,2] & 0.98 & 0.02 & 0.92 & 0.96 & 0.98 & 0.99 & 1.00 & 1.01 & 420.00 \\ 
  gamma[5,2,2] & 0.97 & 0.02 & 0.92 & 0.96 & 0.98 & 0.99 & 1.00 & 1.01 & 520.00 \\ 
  gamma[6,2,2] & 0.96 & 0.03 & 0.90 & 0.95 & 0.97 & 0.98 & 1.00 & 1.01 & 270.00 \\ 
  gamma[7,2,2] & 0.99 & 0.01 & 0.96 & 0.98 & 0.99 & 1.00 & 1.00 & 1.01 & 2100.00 \\ 
  gamma[8,2,2] & 0.90 & 0.04 & 0.80 & 0.87 & 0.90 & 0.93 & 0.98 & 1.02 & 130.00 \\ 
  gamma[9,2,2] & 0.88 & 0.06 & 0.76 & 0.85 & 0.89 & 0.92 & 0.98 & 1.01 & 370.00 \\ 
  gamma[10,2,2] & 0.85 & 0.06 & 0.72 & 0.81 & 0.85 & 0.89 & 0.95 & 1.02 & 160.00 \\ 
  gamma[11,2,2] & 0.73 & 0.06 & 0.60 & 0.69 & 0.74 & 0.78 & 0.85 & 1.01 & 280.00 \\ 
  gamma[12,2,2] & 0.70 & 0.07 & 0.55 & 0.65 & 0.70 & 0.74 & 0.82 & 1.01 & 500.00 \\ 
  gamma[13,2,2] & 0.78 & 0.06 & 0.65 & 0.74 & 0.79 & 0.82 & 0.89 & 1.01 & 280.00 \\ 
  gamma[14,2,2] & 0.99 & 0.01 & 0.97 & 0.99 & 0.99 & 1.00 & 1.00 & 1.01 & 1600.00 \\ 
  gamma[15,2,2] & 0.98 & 0.02 & 0.93 & 0.97 & 0.99 & 0.99 & 1.00 & 1.01 & 590.00 \\ 
  gamma[16,2,2] & 0.99 & 0.01 & 0.98 & 0.99 & 1.00 & 1.00 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[17,2,2] & 0.99 & 0.01 & 0.97 & 0.99 & 0.99 & 1.00 & 1.00 & 1.00 & 1500.00 \\ 
  gamma[18,2,2] & 0.99 & 0.01 & 0.97 & 0.99 & 0.99 & 1.00 & 1.00 & 1.00 & 2500.00 \\ 
  gamma[19,2,2] & 0.82 & 0.06 & 0.70 & 0.78 & 0.82 & 0.86 & 0.92 & 1.01 & 320.00 \\ 
  gamma[20,2,2] & 0.82 & 0.06 & 0.69 & 0.78 & 0.82 & 0.86 & 0.92 & 1.01 & 190.00 \\ 
  gamma[21,2,2] & 0.78 & 0.07 & 0.64 & 0.74 & 0.79 & 0.83 & 0.90 & 1.02 & 160.00 \\ 
  gamma[22,2,2] & 0.77 & 0.06 & 0.64 & 0.73 & 0.77 & 0.81 & 0.87 & 1.01 & 330.00 \\ 
  gamma[23,2,2] & 0.64 & 0.07 & 0.50 & 0.59 & 0.64 & 0.68 & 0.76 & 1.00 & 640.00 \\ 
  gamma[24,2,2] & 0.76 & 0.06 & 0.63 & 0.72 & 0.77 & 0.81 & 0.88 & 1.02 & 170.00 \\ 
  gamma[25,2,2] & 0.60 & 0.07 & 0.46 & 0.55 & 0.60 & 0.65 & 0.73 & 1.00 & 640.00 \\ 
  gamma[1,3,2] & 0.04 & 0.02 & 0.00 & 0.02 & 0.03 & 0.05 & 0.09 & 1.01 & 790.00 \\ 
  gamma[2,3,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.03 & 0.07 & 1.01 & 430.00 \\ 
  gamma[3,3,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.01 & 0.03 & 0.07 & 1.01 & 800.00 \\ 
  gamma[4,3,2] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.15 & 1.02 & 180.00 \\ 
  gamma[5,3,2] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.14 & 1.00 & 1000.00 \\ 
  gamma[6,3,2] & 0.03 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.08 & 1.00 & 580.00 \\ 
  gamma[7,3,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.02 & 0.03 & 0.06 & 1.00 & 3700.00 \\ 
  gamma[8,3,2] & 0.09 & 0.07 & 0.00 & 0.04 & 0.08 & 0.13 & 0.26 & 1.03 & 110.00 \\ 
  gamma[9,3,2] & 0.17 & 0.12 & 0.01 & 0.07 & 0.15 & 0.25 & 0.45 & 1.01 & 620.00 \\ 
  gamma[10,3,2] & 0.08 & 0.07 & 0.00 & 0.03 & 0.06 & 0.11 & 0.24 & 1.01 & 660.00 \\ 
  gamma[11,3,2] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.16 & 1.01 & 290.00 \\ 
  gamma[12,3,2] & 0.17 & 0.10 & 0.01 & 0.09 & 0.16 & 0.24 & 0.38 & 1.02 & 310.00 \\ 
  gamma[13,3,2] & 0.16 & 0.10 & 0.01 & 0.08 & 0.14 & 0.22 & 0.37 & 1.02 & 540.00 \\ 
  gamma[14,3,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.01 & 0.03 & 0.07 & 1.00 & 4000.00 \\ 
  gamma[15,3,2] & 0.07 & 0.07 & 0.00 & 0.02 & 0.05 & 0.11 & 0.27 & 1.02 & 230.00 \\ 
  gamma[16,3,2] & 0.01 & 0.01 & 0.00 & 0.00 & 0.01 & 0.01 & 0.04 & 1.01 & 920.00 \\ 
  gamma[17,3,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.01 & 0.03 & 0.06 & 1.00 & 4000.00 \\ 
  gamma[18,3,2] & 0.03 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.09 & 1.02 & 380.00 \\ 
  gamma[19,3,2] & 0.13 & 0.08 & 0.01 & 0.07 & 0.12 & 0.18 & 0.31 & 1.00 & 1900.00 \\ 
  gamma[20,3,2] & 0.08 & 0.05 & 0.00 & 0.04 & 0.07 & 0.11 & 0.17 & 1.01 & 940.00 \\ 
  gamma[21,3,2] & 0.25 & 0.13 & 0.03 & 0.16 & 0.25 & 0.34 & 0.50 & 1.01 & 320.00 \\ 
  gamma[22,3,2] & 0.21 & 0.09 & 0.04 & 0.15 & 0.21 & 0.27 & 0.38 & 1.00 & 3600.00 \\ 
  gamma[23,3,2] & 0.04 & 0.04 & 0.00 & 0.01 & 0.03 & 0.05 & 0.13 & 1.02 & 580.00 \\ 
  gamma[24,3,2] & 0.23 & 0.09 & 0.05 & 0.16 & 0.23 & 0.29 & 0.40 & 1.08 & 120.00 \\ 
  gamma[25,3,2] & 0.07 & 0.06 & 0.00 & 0.02 & 0.05 & 0.10 & 0.22 & 1.01 & 290.00 \\ 
  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] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,2,3] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,3,3] & 0.96 & 0.02 & 0.90 & 0.94 & 0.96 & 0.98 & 0.99 & 1.00 & 680.00 \\ 
  gamma[2,3,3] & 0.97 & 0.02 & 0.93 & 0.96 & 0.98 & 0.99 & 1.00 & 1.01 & 570.00 \\ 
  gamma[3,3,3] & 0.98 & 0.02 & 0.93 & 0.97 & 0.98 & 0.99 & 1.00 & 1.00 & 730.00 \\ 
  gamma[4,3,3] & 0.94 & 0.04 & 0.84 & 0.92 & 0.95 & 0.97 & 0.99 & 1.00 & 1500.00 \\ 
  gamma[5,3,3] & 0.94 & 0.04 & 0.85 & 0.92 & 0.95 & 0.97 & 0.99 & 1.00 & 1800.00 \\ 
  gamma[6,3,3] & 0.97 & 0.02 & 0.91 & 0.96 & 0.97 & 0.99 & 1.00 & 1.00 & 620.00 \\ 
  gamma[7,3,3] & 0.98 & 0.02 & 0.93 & 0.97 & 0.98 & 0.99 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[8,3,3] & 0.85 & 0.06 & 0.71 & 0.81 & 0.86 & 0.89 & 0.94 & 1.01 & 350.00 \\ 
  gamma[9,3,3] & 0.62 & 0.11 & 0.38 & 0.55 & 0.63 & 0.70 & 0.80 & 1.01 & 340.00 \\ 
  gamma[10,3,3] & 0.89 & 0.06 & 0.73 & 0.85 & 0.90 & 0.93 & 0.98 & 1.01 & 540.00 \\ 
  gamma[11,3,3] & 0.35 & 0.07 & 0.22 & 0.30 & 0.35 & 0.39 & 0.49 & 1.01 & 410.00 \\ 
  gamma[12,3,3] & 0.69 & 0.08 & 0.51 & 0.63 & 0.69 & 0.75 & 0.83 & 1.00 & 600.00 \\ 
  gamma[13,3,3] & 0.73 & 0.08 & 0.54 & 0.67 & 0.73 & 0.79 & 0.86 & 1.00 & 1100.00 \\ 
  gamma[14,3,3] & 0.98 & 0.02 & 0.93 & 0.97 & 0.98 & 0.99 & 1.00 & 1.00 & 2900.00 \\ 
  gamma[15,3,3] & 0.89 & 0.07 & 0.71 & 0.86 & 0.90 & 0.94 & 0.98 & 1.00 & 1100.00 \\ 
  gamma[16,3,3] & 0.99 & 0.01 & 0.96 & 0.98 & 0.99 & 1.00 & 1.00 & 1.00 & 1600.00 \\ 
  gamma[17,3,3] & 0.98 & 0.02 & 0.93 & 0.97 & 0.98 & 0.99 & 1.00 & 1.00 & 1000.00 \\ 
  gamma[18,3,3] & 0.97 & 0.02 & 0.91 & 0.96 & 0.97 & 0.99 & 1.00 & 1.00 & 3600.00 \\ 
  gamma[19,3,3] & 0.85 & 0.08 & 0.68 & 0.80 & 0.86 & 0.90 & 0.96 & 1.00 & 910.00 \\ 
  gamma[20,3,3] & 0.92 & 0.05 & 0.82 & 0.89 & 0.92 & 0.95 & 0.99 & 1.00 & 2300.00 \\ 
  gamma[21,3,3] & 0.70 & 0.11 & 0.47 & 0.63 & 0.70 & 0.77 & 0.90 & 1.01 & 440.00 \\ 
  gamma[22,3,3] & 0.71 & 0.08 & 0.55 & 0.66 & 0.71 & 0.76 & 0.85 & 1.00 & 2800.00 \\ 
  gamma[23,3,3] & 0.32 & 0.06 & 0.21 & 0.27 & 0.32 & 0.37 & 0.45 & 1.00 & 1800.00 \\ 
  gamma[24,3,3] & 0.70 & 0.08 & 0.54 & 0.64 & 0.70 & 0.75 & 0.86 & 1.01 & 280.00 \\ 
  gamma[25,3,3] & 0.26 & 0.06 & 0.14 & 0.21 & 0.26 & 0.30 & 0.39 & 1.01 & 180.00 \\ 
  inv.phi[1,1] & 3.10 & 1.62 & 0.62 & 1.92 & 2.81 & 4.02 & 7.04 & 1.02 & 1000.00 \\ 
  inv.phi[2,1] & -0.46 & 1.07 & -2.67 & -1.10 & -0.44 & 0.22 & 1.64 & 1.05 & 69.00 \\ 
  inv.phi[3,1] & -1.24 & 1.07 & -3.68 & -1.84 & -1.09 & -0.46 & 0.46 & 1.01 & 280.00 \\ 
  inv.phi[4,1] & -1.08 & 1.42 & -4.52 & -1.78 & -0.84 & -0.14 & 1.16 & 1.06 & 50.00 \\ 
  inv.phi[1,2] & -0.46 & 1.07 & -2.67 & -1.10 & -0.44 & 0.22 & 1.64 & 1.05 & 69.00 \\ 
  inv.phi[2,2] & 3.03 & 1.33 & 1.08 & 2.07 & 2.82 & 3.74 & 6.27 & 1.03 & 180.00 \\ 
  inv.phi[3,2] & 0.08 & 1.03 & -2.00 & -0.60 & 0.09 & 0.75 & 2.10 & 1.05 & 64.00 \\ 
  inv.phi[4,2] & -1.99 & 1.37 & -5.12 & -2.83 & -1.80 & -1.01 & 0.19 & 1.05 & 58.00 \\ 
  inv.phi[1,3] & -1.24 & 1.07 & -3.68 & -1.84 & -1.09 & -0.46 & 0.46 & 1.01 & 280.00 \\ 
  inv.phi[2,3] & 0.08 & 1.03 & -2.00 & -0.60 & 0.09 & 0.75 & 2.10 & 1.05 & 64.00 \\ 
  inv.phi[3,3] & 2.76 & 1.34 & 0.85 & 1.72 & 2.55 & 3.53 & 5.92 & 1.05 & 61.00 \\ 
  inv.phi[4,3] & -1.14 & 1.24 & -3.67 & -1.93 & -1.07 & -0.28 & 1.16 & 1.05 & 56.00 \\ 
  inv.phi[1,4] & -1.08 & 1.42 & -4.52 & -1.78 & -0.84 & -0.14 & 1.16 & 1.06 & 50.00 \\ 
  inv.phi[2,4] & -1.99 & 1.37 & -5.12 & -2.83 & -1.80 & -1.01 & 0.19 & 1.05 & 58.00 \\ 
  inv.phi[3,4] & -1.14 & 1.24 & -3.67 & -1.93 & -1.07 & -0.28 & 1.16 & 1.05 & 56.00 \\ 
  inv.phi[4,4] & 3.76 & 1.92 & 1.01 & 2.37 & 3.38 & 4.80 & 8.35 & 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] & 1.09 & 0.12 & 0.88 & 1.00 & 1.08 & 1.16 & 1.34 & 1.02 & 130.00 \\ 
  lambda[3] & 0.74 & 0.08 & 0.59 & 0.69 & 0.74 & 0.79 & 0.92 & 1.03 & 130.00 \\ 
  lambda[4] & 0.68 & 0.08 & 0.54 & 0.63 & 0.67 & 0.73 & 0.84 & 1.01 & 410.00 \\ 
  lambda[5] & 0.95 & 0.10 & 0.76 & 0.88 & 0.95 & 1.02 & 1.17 & 1.03 & 96.00 \\ 
  lambda[6] & 0.86 & 0.10 & 0.69 & 0.79 & 0.86 & 0.92 & 1.07 & 1.02 & 500.00 \\ 
  lambda[7] & 0.96 & 0.10 & 0.77 & 0.89 & 0.95 & 1.02 & 1.18 & 1.02 & 130.00 \\ 
  lambda[8] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[9] & 0.84 & 0.10 & 0.65 & 0.77 & 0.84 & 0.90 & 1.06 & 1.01 & 220.00 \\ 
  lambda[10] & 0.68 & 0.09 & 0.50 & 0.61 & 0.68 & 0.74 & 0.86 & 1.01 & 200.00 \\ 
  lambda[11] & 1.23 & 0.16 & 0.95 & 1.12 & 1.22 & 1.33 & 1.60 & 1.04 & 110.00 \\ 
  lambda[12] & 1.26 & 0.16 & 0.97 & 1.15 & 1.24 & 1.35 & 1.59 & 1.02 & 370.00 \\ 
  lambda[13] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[14] & 0.48 & 0.06 & 0.37 & 0.44 & 0.48 & 0.52 & 0.60 & 1.01 & 430.00 \\ 
  lambda[15] & 0.43 & 0.07 & 0.31 & 0.39 & 0.43 & 0.48 & 0.57 & 1.00 & 4000.00 \\ 
  lambda[16] & 0.42 & 0.05 & 0.31 & 0.38 & 0.42 & 0.45 & 0.53 & 1.01 & 230.00 \\ 
  lambda[17] & 0.67 & 0.07 & 0.53 & 0.62 & 0.67 & 0.71 & 0.81 & 1.01 & 280.00 \\ 
  lambda[18] & 0.57 & 0.07 & 0.45 & 0.53 & 0.57 & 0.62 & 0.71 & 1.03 & 98.00 \\ 
  lambda[19] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[20] & 1.05 & 0.13 & 0.82 & 0.96 & 1.05 & 1.13 & 1.32 & 1.03 & 130.00 \\ 
  lambda[21] & 0.85 & 0.11 & 0.66 & 0.78 & 0.85 & 0.92 & 1.08 & 1.05 & 63.00 \\ 
  lambda[22] & 1.47 & 0.21 & 1.14 & 1.33 & 1.44 & 1.59 & 1.95 & 1.05 & 61.00 \\ 
  lambda[23] & 2.01 & 0.23 & 1.54 & 1.87 & 2.02 & 2.16 & 2.46 & 1.02 & 320.00 \\ 
  lambda[24] & 1.13 & 0.15 & 0.86 & 1.03 & 1.12 & 1.22 & 1.45 & 1.04 & 93.00 \\ 
  lambda[25] & 1.85 & 0.21 & 1.42 & 1.71 & 1.85 & 1.99 & 2.24 & 1.08 & 43.00 \\ 
  lambda.std[1] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[2] & 0.73 & 0.04 & 0.66 & 0.71 & 0.73 & 0.76 & 0.80 & 1.02 & 130.00 \\ 
  lambda.std[3] & 0.59 & 0.04 & 0.51 & 0.57 & 0.59 & 0.62 & 0.68 & 1.02 & 140.00 \\ 
  lambda.std[4] & 0.56 & 0.04 & 0.47 & 0.53 & 0.56 & 0.59 & 0.64 & 1.01 & 450.00 \\ 
  lambda.std[5] & 0.69 & 0.04 & 0.61 & 0.66 & 0.69 & 0.71 & 0.76 & 1.03 & 94.00 \\ 
  lambda.std[6] & 0.65 & 0.04 & 0.57 & 0.62 & 0.65 & 0.68 & 0.73 & 1.01 & 620.00 \\ 
  lambda.std[7] & 0.69 & 0.04 & 0.61 & 0.66 & 0.69 & 0.71 & 0.76 & 1.02 & 140.00 \\ 
  lambda.std[8] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[9] & 0.64 & 0.05 & 0.55 & 0.61 & 0.64 & 0.67 & 0.73 & 1.02 & 210.00 \\ 
  lambda.std[10] & 0.56 & 0.05 & 0.45 & 0.52 & 0.56 & 0.59 & 0.65 & 1.01 & 210.00 \\ 
  lambda.std[11] & 0.77 & 0.04 & 0.69 & 0.75 & 0.77 & 0.80 & 0.85 & 1.03 & 130.00 \\ 
  lambda.std[12] & 0.78 & 0.04 & 0.70 & 0.75 & 0.78 & 0.80 & 0.85 & 1.02 & 430.00 \\ 
  lambda.std[13] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[14] & 0.43 & 0.04 & 0.35 & 0.40 & 0.43 & 0.46 & 0.52 & 1.01 & 460.00 \\ 
  lambda.std[15] & 0.40 & 0.05 & 0.30 & 0.36 & 0.40 & 0.43 & 0.50 & 1.00 & 4000.00 \\ 
  lambda.std[16] & 0.39 & 0.04 & 0.30 & 0.36 & 0.39 & 0.41 & 0.47 & 1.01 & 240.00 \\ 
  lambda.std[17] & 0.55 & 0.04 & 0.47 & 0.53 & 0.56 & 0.58 & 0.63 & 1.01 & 290.00 \\ 
  lambda.std[18] & 0.50 & 0.04 & 0.41 & 0.47 & 0.50 & 0.53 & 0.58 & 1.03 & 100.00 \\ 
  lambda.std[19] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[20] & 0.72 & 0.04 & 0.63 & 0.69 & 0.72 & 0.75 & 0.80 & 1.02 & 160.00 \\ 
  lambda.std[21] & 0.64 & 0.05 & 0.55 & 0.61 & 0.65 & 0.68 & 0.73 & 1.05 & 66.00 \\ 
  lambda.std[22] & 0.82 & 0.04 & 0.75 & 0.80 & 0.82 & 0.85 & 0.89 & 1.04 & 64.00 \\ 
  lambda.std[23] & 0.89 & 0.02 & 0.84 & 0.88 & 0.90 & 0.91 & 0.93 & 1.03 & 360.00 \\ 
  lambda.std[24] & 0.74 & 0.04 & 0.65 & 0.72 & 0.75 & 0.77 & 0.82 & 1.03 & 110.00 \\ 
  lambda.std[25] & 0.88 & 0.02 & 0.82 & 0.86 & 0.88 & 0.89 & 0.91 & 1.09 & 41.00 \\ 
  phi[1,1] & 3.53 & 2.78 & 0.83 & 1.97 & 2.96 & 4.30 & 9.08 & 1.07 & 56.00 \\ 
  phi[2,1] & 2.26 & 1.52 & -0.30 & 1.25 & 2.30 & 3.19 & 4.98 & 1.05 & 99.00 \\ 
  phi[3,1] & 2.73 & 1.76 & 0.28 & 1.50 & 2.43 & 3.69 & 7.17 & 1.03 & 180.00 \\ 
  phi[4,1] & 3.03 & 1.55 & -0.26 & 2.15 & 3.07 & 3.97 & 6.17 & 1.10 & 35.00 \\ 
  phi[1,2] & 2.26 & 1.52 & -0.30 & 1.25 & 2.30 & 3.19 & 4.98 & 1.05 & 99.00 \\ 
  phi[2,2] & 3.03 & 1.54 & 0.88 & 1.95 & 2.81 & 3.80 & 6.64 & 1.08 & 41.00 \\ 
  phi[3,2] & 1.92 & 1.48 & -1.92 & 1.24 & 2.00 & 2.76 & 4.52 & 1.07 & 99.00 \\ 
  phi[4,2] & 2.92 & 1.29 & -0.48 & 2.28 & 3.02 & 3.73 & 5.21 & 1.14 & 25.00 \\ 
  phi[1,3] & 2.73 & 1.76 & 0.28 & 1.50 & 2.43 & 3.69 & 7.17 & 1.03 & 180.00 \\ 
  phi[2,3] & 1.92 & 1.48 & -1.92 & 1.24 & 2.00 & 2.76 & 4.52 & 1.07 & 99.00 \\ 
  phi[3,3] & 3.84 & 3.15 & 0.92 & 2.08 & 3.11 & 4.39 & 13.62 & 1.11 & 32.00 \\ 
  phi[4,3] & 3.24 & 1.57 & 0.62 & 2.27 & 3.12 & 3.89 & 7.15 & 1.13 & 39.00 \\ 
  phi[1,4] & 3.03 & 1.55 & -0.26 & 2.15 & 3.07 & 3.97 & 6.17 & 1.10 & 35.00 \\ 
  phi[2,4] & 2.92 & 1.29 & -0.48 & 2.28 & 3.02 & 3.73 & 5.21 & 1.14 & 25.00 \\ 
  phi[3,4] & 3.24 & 1.57 & 0.62 & 2.27 & 3.12 & 3.89 & 7.15 & 1.13 & 39.00 \\ 
  phi[4,4] & 4.24 & 0.65 & 2.99 & 3.81 & 4.21 & 4.64 & 5.65 & 1.08 & 54.00 \\ 
  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] & 0.72 & 0.28 & -0.15 & 0.66 & 0.82 & 0.89 & 0.95 & 1.13 & 54.00 \\ 
  phi.cor[3,1] & 0.79 & 0.22 & 0.15 & 0.75 & 0.87 & 0.92 & 0.97 & 1.18 & 35.00 \\ 
  phi.cor[4,1] & 0.79 & 0.26 & -0.10 & 0.77 & 0.89 & 0.93 & 0.97 & 1.15 & 32.00 \\ 
  phi.cor[1,2] & 0.72 & 0.28 & -0.15 & 0.66 & 0.82 & 0.89 & 0.95 & 1.13 & 54.00 \\ 
  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] & 0.65 & 0.34 & -0.46 & 0.58 & 0.78 & 0.86 & 0.94 & 1.10 & 44.00 \\ 
  phi.cor[4,2] & 0.81 & 0.26 & -0.18 & 0.83 & 0.90 & 0.94 & 0.97 & 1.12 & 42.00 \\ 
  phi.cor[1,3] & 0.79 & 0.22 & 0.15 & 0.75 & 0.87 & 0.92 & 0.97 & 1.18 & 35.00 \\ 
  phi.cor[2,3] & 0.65 & 0.34 & -0.46 & 0.58 & 0.78 & 0.86 & 0.94 & 1.10 & 44.00 \\ 
  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] & 0.82 & 0.18 & 0.26 & 0.79 & 0.88 & 0.93 & 0.97 & 1.13 & 61.00 \\ 
  phi.cor[1,4] & 0.79 & 0.26 & -0.10 & 0.77 & 0.89 & 0.93 & 0.97 & 1.15 & 32.00 \\ 
  phi.cor[2,4] & 0.81 & 0.26 & -0.18 & 0.83 & 0.90 & 0.94 & 0.97 & 1.12 & 42.00 \\ 
  phi.cor[3,4] & 0.82 & 0.18 & 0.26 & 0.79 & 0.88 & 0.93 & 0.97 & 1.13 & 61.00 \\ 
  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] & 0.85 & 0.02 & 0.82 & 0.84 & 0.85 & 0.86 & 0.88 & 1.05 & 77.00 \\ 
  reli.omega[2] & 0.86 & 0.01 & 0.83 & 0.85 & 0.86 & 0.87 & 0.88 & 1.04 & 110.00 \\ 
  reli.omega[3] & 0.68 & 0.02 & 0.63 & 0.66 & 0.68 & 0.70 & 0.73 & 1.02 & 160.00 \\ 
  reli.omega[4] & 0.90 & 0.01 & 0.88 & 0.90 & 0.90 & 0.91 & 0.92 & 1.05 & 70.00 \\ 
  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] & 3.12 & 0.24 & 2.71 & 2.95 & 3.11 & 3.27 & 3.63 & 1.02 & 140.00 \\ 
  tau[2,2] & 3.15 & 0.24 & 2.73 & 2.99 & 3.14 & 3.30 & 3.67 & 1.01 & 460.00 \\ 
  tau[3,2] & 2.35 & 0.17 & 2.03 & 2.24 & 2.35 & 2.47 & 2.69 & 1.00 & 4000.00 \\ 
  tau[4,2] & 1.75 & 0.14 & 1.49 & 1.65 & 1.74 & 1.84 & 2.06 & 1.00 & 1700.00 \\ 
  tau[5,2] & 2.38 & 0.20 & 2.02 & 2.24 & 2.37 & 2.50 & 2.81 & 1.00 & 1500.00 \\ 
  tau[6,2] & 2.62 & 0.20 & 2.26 & 2.48 & 2.61 & 2.75 & 3.06 & 1.00 & 1500.00 \\ 
  tau[7,2] & 3.16 & 0.23 & 2.74 & 3.00 & 3.15 & 3.30 & 3.68 & 1.00 & 1400.00 \\ 
  tau[8,2] & 2.24 & 0.20 & 1.87 & 2.10 & 2.22 & 2.36 & 2.68 & 1.00 & 930.00 \\ 
  tau[9,2] & 1.29 & 0.15 & 1.02 & 1.18 & 1.28 & 1.38 & 1.62 & 1.00 & 870.00 \\ 
  tau[10,2] & 1.41 & 0.14 & 1.15 & 1.31 & 1.40 & 1.50 & 1.71 & 1.00 & 4000.00 \\ 
  tau[11,2] & 1.00 & 0.15 & 0.73 & 0.90 & 0.99 & 1.10 & 1.30 & 1.01 & 550.00 \\ 
  tau[12,2] & 2.56 & 0.35 & 1.99 & 2.31 & 2.52 & 2.76 & 3.37 & 1.01 & 640.00 \\ 
  tau[13,2] & 2.12 & 0.20 & 1.76 & 1.97 & 2.10 & 2.24 & 2.57 & 1.01 & 360.00 \\ 
  tau[14,2] & 1.70 & 0.14 & 1.43 & 1.60 & 1.69 & 1.79 & 1.99 & 1.00 & 2200.00 \\ 
  tau[15,2] & 1.31 & 0.13 & 1.08 & 1.22 & 1.30 & 1.39 & 1.60 & 1.01 & 430.00 \\ 
  tau[16,2] & 2.02 & 0.20 & 1.63 & 1.89 & 2.02 & 2.15 & 2.42 & 1.00 & 2600.00 \\ 
  tau[17,2] & 2.27 & 0.17 & 1.96 & 2.15 & 2.27 & 2.38 & 2.64 & 1.00 & 2500.00 \\ 
  tau[18,2] & 2.22 & 0.19 & 1.90 & 2.09 & 2.21 & 2.33 & 2.62 & 1.00 & 1700.00 \\ 
  tau[19,2] & 2.21 & 0.20 & 1.87 & 2.07 & 2.19 & 2.33 & 2.69 & 1.01 & 300.00 \\ 
  tau[20,2] & 2.88 & 0.31 & 2.35 & 2.66 & 2.85 & 3.06 & 3.57 & 1.00 & 1100.00 \\ 
  tau[21,2] & 1.93 & 0.25 & 1.50 & 1.76 & 1.91 & 2.07 & 2.49 & 1.00 & 650.00 \\ 
  tau[22,2] & 3.23 & 0.48 & 2.42 & 2.89 & 3.16 & 3.49 & 4.34 & 1.02 & 120.00 \\ 
  tau[23,2] & 1.06 & 0.19 & 0.68 & 0.93 & 1.05 & 1.19 & 1.44 & 1.00 & 3300.00 \\ 
  tau[24,2] & 2.88 & 0.46 & 2.15 & 2.55 & 2.81 & 3.14 & 3.95 & 1.01 & 340.00 \\ 
  tau[25,2] & 1.55 & 0.24 & 1.14 & 1.39 & 1.54 & 1.71 & 2.06 & 1.02 & 170.00 \\ 
  theta[1] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[2] & 2.19 & 0.26 & 1.78 & 2.00 & 2.16 & 2.36 & 2.79 & 1.02 & 130.00 \\ 
  theta[3] & 1.56 & 0.12 & 1.35 & 1.47 & 1.55 & 1.63 & 1.84 & 1.03 & 120.00 \\ 
  theta[4] & 1.47 & 0.10 & 1.29 & 1.39 & 1.45 & 1.53 & 1.70 & 1.01 & 350.00 \\ 
  theta[5] & 1.92 & 0.20 & 1.58 & 1.77 & 1.90 & 2.04 & 2.37 & 1.03 & 99.00 \\ 
  theta[6] & 1.75 & 0.17 & 1.48 & 1.63 & 1.73 & 1.85 & 2.15 & 1.02 & 370.00 \\ 
  theta[7] & 1.93 & 0.20 & 1.60 & 1.79 & 1.91 & 2.04 & 2.39 & 1.03 & 120.00 \\ 
  theta[8] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[9] & 1.72 & 0.18 & 1.43 & 1.59 & 1.70 & 1.82 & 2.12 & 1.01 & 230.00 \\ 
  theta[10] & 1.47 & 0.13 & 1.25 & 1.38 & 1.46 & 1.55 & 1.74 & 1.02 & 190.00 \\ 
  theta[11] & 2.55 & 0.41 & 1.90 & 2.26 & 2.50 & 2.76 & 3.56 & 1.05 & 110.00 \\ 
  theta[12] & 2.60 & 0.41 & 1.94 & 2.32 & 2.54 & 2.83 & 3.53 & 1.02 & 320.00 \\ 
  theta[13] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[14] & 1.23 & 0.06 & 1.14 & 1.19 & 1.23 & 1.27 & 1.36 & 1.01 & 350.00 \\ 
  theta[15] & 1.19 & 0.06 & 1.10 & 1.15 & 1.19 & 1.23 & 1.33 & 1.00 & 4000.00 \\ 
  theta[16] & 1.18 & 0.05 & 1.10 & 1.15 & 1.17 & 1.21 & 1.28 & 1.02 & 200.00 \\ 
  theta[17] & 1.45 & 0.10 & 1.28 & 1.38 & 1.45 & 1.51 & 1.66 & 1.02 & 250.00 \\ 
  theta[18] & 1.33 & 0.08 & 1.20 & 1.28 & 1.33 & 1.38 & 1.51 & 1.03 & 94.00 \\ 
  theta[19] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[20] & 2.12 & 0.27 & 1.67 & 1.92 & 2.10 & 2.28 & 2.73 & 1.03 & 120.00 \\ 
  theta[21] & 1.74 & 0.19 & 1.44 & 1.60 & 1.72 & 1.84 & 2.17 & 1.05 & 61.00 \\ 
  theta[22] & 3.22 & 0.64 & 2.31 & 2.77 & 3.09 & 3.54 & 4.79 & 1.05 & 60.00 \\ 
  theta[23] & 5.10 & 0.91 & 3.38 & 4.51 & 5.07 & 5.66 & 7.04 & 1.02 & 300.00 \\ 
  theta[24] & 2.30 & 0.34 & 1.74 & 2.06 & 2.26 & 2.49 & 3.09 & 1.04 & 85.00 \\ 
  theta[25] & 4.46 & 0.76 & 3.03 & 3.93 & 4.43 & 4.96 & 6.01 & 1.07 & 44.00 \\ 
   \bottomrule
\end{tabular}
\caption{pools Model 4 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