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 3: Misclassification in IFA

Model details

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

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

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

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

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

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

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


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


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

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

Model results

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

# data
jags.data <- list(
  y = mydata,
  N = nrow(mydata),
  nit = ncol(mydata),
  map = c(rep(1,7), rep(2,6), rep(3,6), rep(4,6)),
  d = 8,
  M = 4,
  phi.0 = matrix(
    c(1, 0.69, 0.75, 0.78,
      0.69, 1, 0.65, 0.80,
      0.75, 0.65, 1, 0.75,
      0.78, 0.80, 0.75, 1), ncol=4, nrow=4, byrow=T
    ),
  ncat = 3,
  alpha = matrix(
    c(0.85, 0.10, 0.05,
      0, 0.90, 0.10,
      0.0, 0, 1),
    ncol=3, nrow=3, byrow=T
  ),
  xi = 10
)

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

Initializing model
print(model.fit, width=1000)
Inference for Bugs model at "C:/Users/noahp/Documents/GitHub/Padgett-Dissertation/code/pools_study/model_misclass_ifa.txt", fit using jags,
 4 chains, each with 10000 iterations (first 5000 discarded), n.thin = 5
 n.sims = 4000 iterations saved
                 mu.vect sd.vect      2.5%       25%       50%       75%     97.5% Rhat n.eff
gamma[1,1,1]       0.787   0.069     0.641     0.743     0.789     0.836     0.913 1.00  4000
gamma[2,1,1]       0.830   0.058     0.703     0.793     0.835     0.871     0.932 1.01   390
gamma[3,1,1]       0.619   0.092     0.436     0.554     0.623     0.685     0.789 1.01   410
gamma[4,1,1]       0.588   0.097     0.399     0.522     0.588     0.654     0.781 1.01   300
gamma[5,1,1]       0.762   0.080     0.597     0.710     0.768     0.818     0.914 1.00   780
gamma[6,1,1]       0.757   0.085     0.579     0.702     0.760     0.817     0.911 1.00   910
gamma[7,1,1]       0.798   0.070     0.649     0.754     0.800     0.848     0.925 1.01   470
gamma[8,1,1]       0.764   0.090     0.572     0.706     0.773     0.828     0.924 1.00  1400
gamma[9,1,1]       0.862   0.116     0.567     0.815     0.895     0.947     0.991 1.01   370
gamma[10,1,1]      0.777   0.112     0.524     0.703     0.789     0.860     0.956 1.00  1000
gamma[11,1,1]      0.233   0.061     0.122     0.189     0.230     0.273     0.360 1.00  1200
gamma[12,1,1]      0.956   0.033     0.872     0.940     0.965     0.981     0.997 1.00  1500
gamma[13,1,1]      0.962   0.030     0.887     0.948     0.971     0.985     0.997 1.00  3200
gamma[14,1,1]      0.628   0.125     0.383     0.544     0.625     0.716     0.872 1.00   790
gamma[15,1,1]      0.820   0.111     0.584     0.747     0.836     0.911     0.984 1.01   300
gamma[16,1,1]      0.630   0.114     0.387     0.555     0.633     0.710     0.841 1.01   340
gamma[17,1,1]      0.698   0.103     0.480     0.630     0.702     0.772     0.887 1.01   250
gamma[18,1,1]      0.751   0.105     0.529     0.682     0.758     0.827     0.938 1.01   230
gamma[19,1,1]      0.952   0.034     0.867     0.935     0.960     0.977     0.995 1.00  1300
gamma[20,1,1]      0.867   0.060     0.731     0.830     0.874     0.913     0.962 1.01   450
gamma[21,1,1]      0.880   0.064     0.740     0.839     0.888     0.927     0.980 1.00   700
gamma[22,1,1]      0.971   0.023     0.912     0.960     0.977     0.988     0.998 1.01   760
gamma[23,1,1]      0.105   0.039     0.040     0.076     0.101     0.129     0.190 1.00  4000
gamma[24,1,1]      0.956   0.035     0.869     0.937     0.964     0.982     0.997 1.01   560
gamma[25,1,1]      0.133   0.037     0.068     0.107     0.130     0.156     0.213 1.01   460
gamma[1,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,2,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,2,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,3,1]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,3,1]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,1,2]       0.191   0.067     0.066     0.143     0.188     0.235     0.333 1.01  1100
gamma[2,1,2]       0.147   0.054     0.052     0.108     0.144     0.181     0.268 1.00  4000
gamma[3,1,2]       0.346   0.091     0.178     0.280     0.339     0.409     0.536 1.01   280
gamma[4,1,2]       0.337   0.108     0.124     0.262     0.340     0.412     0.540 1.00   750
gamma[5,1,2]       0.218   0.081     0.062     0.163     0.214     0.271     0.381 1.01  1800
gamma[6,1,2]       0.226   0.086     0.071     0.163     0.224     0.282     0.404 1.01   430
gamma[7,1,2]       0.173   0.067     0.053     0.125     0.170     0.214     0.315 1.08    88
gamma[8,1,2]       0.190   0.099     0.012     0.119     0.185     0.254     0.393 1.11    91
gamma[9,1,2]       0.123   0.114     0.003     0.038     0.089     0.172     0.412 1.02   350
gamma[10,1,2]      0.159   0.113     0.007     0.070     0.136     0.230     0.428 1.02   270
gamma[11,1,2]      0.751   0.060     0.628     0.713     0.753     0.792     0.864 1.00  4000
gamma[12,1,2]      0.026   0.026     0.001     0.008     0.018     0.036     0.099 1.01   450
gamma[13,1,2]      0.026   0.026     0.001     0.008     0.019     0.037     0.097 1.00  3100
gamma[14,1,2]      0.346   0.125     0.096     0.259     0.346     0.434     0.591 1.00   610
gamma[15,1,2]      0.135   0.104     0.003     0.047     0.113     0.200     0.377 1.01   400
gamma[16,1,2]      0.346   0.111     0.150     0.267     0.342     0.418     0.582 1.00   830
gamma[17,1,2]      0.263   0.100     0.087     0.194     0.258     0.330     0.475 1.01   330
gamma[18,1,2]      0.229   0.104     0.046     0.154     0.218     0.295     0.451 1.03   140
gamma[19,1,2]      0.029   0.027     0.001     0.009     0.020     0.040     0.100 1.01   590
gamma[20,1,2]      0.057   0.041     0.003     0.024     0.050     0.082     0.156 1.01   550
gamma[21,1,2]      0.053   0.048     0.002     0.018     0.040     0.072     0.175 1.01  4000
gamma[22,1,2]      0.019   0.019     0.000     0.006     0.014     0.027     0.070 1.00  2300
gamma[23,1,2]      0.890   0.039     0.805     0.865     0.894     0.919     0.955 1.00  1900
gamma[24,1,2]      0.025   0.024     0.001     0.008     0.019     0.035     0.087 1.00  1100
gamma[25,1,2]      0.861   0.037     0.781     0.838     0.864     0.887     0.926 1.00   560
gamma[1,2,2]       0.905   0.078     0.711     0.862     0.926     0.966     0.997 1.00  1400
gamma[2,2,2]       0.883   0.079     0.700     0.836     0.896     0.943     0.993 1.00  2300
gamma[3,2,2]       0.565   0.105     0.371     0.491     0.560     0.630     0.781 1.00   740
gamma[4,2,2]       0.837   0.110     0.582     0.766     0.854     0.925     0.991 1.00   540
gamma[5,2,2]       0.813   0.110     0.572     0.737     0.819     0.899     0.988 1.00  1700
gamma[6,2,2]       0.726   0.123     0.500     0.635     0.725     0.821     0.958 1.01   460
gamma[7,2,2]       0.508   0.113     0.297     0.427     0.503     0.583     0.744 1.02   140
gamma[8,2,2]       0.847   0.093     0.638     0.787     0.857     0.920     0.988 1.00  1000
gamma[9,2,2]       0.786   0.099     0.572     0.725     0.795     0.856     0.958 1.00  3400
gamma[10,2,2]      0.938   0.054     0.808     0.912     0.952     0.979     0.998 1.00   740
gamma[11,2,2]      0.622   0.053     0.518     0.586     0.621     0.658     0.727 1.00  3100
gamma[12,2,2]      0.952   0.038     0.853     0.931     0.961     0.982     0.998 1.00  4000
gamma[13,2,2]      0.948   0.042     0.842     0.926     0.958     0.981     0.998 1.00  4000
gamma[14,2,2]      0.210   0.047     0.128     0.176     0.208     0.240     0.309 1.00  1200
gamma[15,2,2]      0.597   0.153     0.316     0.487     0.588     0.701     0.907 1.00   770
gamma[16,2,2]      0.092   0.025     0.050     0.074     0.090     0.108     0.150 1.00  1300
gamma[17,2,2]      0.295   0.069     0.175     0.245     0.292     0.339     0.445 1.00   590
gamma[18,2,2]      0.285   0.065     0.172     0.238     0.279     0.328     0.425 1.01   290
gamma[19,2,2]      0.970   0.029     0.890     0.958     0.979     0.991     0.999 1.00  1100
gamma[20,2,2]      0.934   0.053     0.802     0.906     0.946     0.975     0.998 1.02   220
gamma[21,2,2]      0.953   0.042     0.840     0.936     0.965     0.985     0.998 1.00  4000
gamma[22,2,2]      0.942   0.045     0.830     0.919     0.951     0.977     0.997 1.00  1100
gamma[23,2,2]      0.750   0.063     0.634     0.705     0.749     0.794     0.876 1.00  2300
gamma[24,2,2]      0.944   0.050     0.811     0.920     0.958     0.982     0.998 1.00  4000
gamma[25,2,2]      0.541   0.053     0.439     0.504     0.542     0.576     0.644 1.00  2200
gamma[1,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[2,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[3,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[4,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[5,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[6,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[7,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[8,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[9,3,2]       0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[10,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[11,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[12,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[13,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[14,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[15,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[16,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[17,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[18,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[19,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[20,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[21,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[22,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[23,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[24,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[25,3,2]      0.000   0.000     0.000     0.000     0.000     0.000     0.000 1.00     1
gamma[1,1,3]       0.021   0.031     0.000     0.002     0.009     0.028     0.111 1.01   330
gamma[2,1,3]       0.023   0.029     0.000     0.004     0.013     0.032     0.102 1.03   170
gamma[3,1,3]       0.035   0.046     0.000     0.004     0.017     0.047     0.169 1.02   280
gamma[4,1,3]       0.075   0.063     0.001     0.023     0.060     0.114     0.229 1.03   140
gamma[5,1,3]       0.020   0.029     0.000     0.002     0.008     0.025     0.103 1.09    56
gamma[6,1,3]       0.018   0.023     0.000     0.002     0.010     0.025     0.081 1.01   200
gamma[7,1,3]       0.029   0.035     0.000     0.005     0.017     0.040     0.128 1.06    57
gamma[8,1,3]       0.046   0.051     0.000     0.007     0.029     0.068     0.185 1.11    45
gamma[9,1,3]       0.015   0.020     0.000     0.002     0.007     0.022     0.067 1.01   460
gamma[10,1,3]      0.065   0.060     0.000     0.015     0.049     0.098     0.217 1.02   170
gamma[11,1,3]      0.016   0.017     0.000     0.002     0.010     0.024     0.062 1.05   110
gamma[12,1,3]      0.017   0.022     0.000     0.002     0.009     0.024     0.081 1.00  1300
gamma[13,1,3]      0.011   0.015     0.000     0.001     0.005     0.015     0.054 1.03   150
gamma[14,1,3]      0.026   0.033     0.000     0.003     0.013     0.035     0.119 1.02   240
gamma[15,1,3]      0.045   0.055     0.000     0.007     0.024     0.063     0.211 1.01   390
gamma[16,1,3]      0.024   0.031     0.000     0.004     0.012     0.032     0.117 1.03   110
gamma[17,1,3]      0.038   0.044     0.000     0.006     0.021     0.055     0.157 1.03   180
gamma[18,1,3]      0.021   0.030     0.000     0.001     0.008     0.028     0.105 1.11    63
gamma[19,1,3]      0.019   0.022     0.000     0.003     0.011     0.027     0.082 1.03   150
gamma[20,1,3]      0.076   0.060     0.001     0.028     0.063     0.112     0.214 1.01   540
gamma[21,1,3]      0.067   0.052     0.001     0.027     0.058     0.098     0.188 1.02   520
gamma[22,1,3]      0.010   0.014     0.000     0.001     0.004     0.013     0.050 1.12    63
gamma[23,1,3]      0.004   0.006     0.000     0.001     0.002     0.006     0.021 1.06   340
gamma[24,1,3]      0.019   0.026     0.000     0.002     0.009     0.026     0.097 1.01   280
gamma[25,1,3]      0.006   0.008     0.000     0.001     0.003     0.008     0.029 1.02   250
gamma[1,2,3]       0.095   0.078     0.003     0.034     0.074     0.138     0.289 1.00  1600
gamma[2,2,3]       0.117   0.079     0.007     0.057     0.104     0.164     0.300 1.00  4000
gamma[3,2,3]       0.435   0.105     0.219     0.370     0.440     0.509     0.629 1.01   750
gamma[4,2,3]       0.163   0.110     0.009     0.075     0.146     0.234     0.418 1.01   550
gamma[5,2,3]       0.187   0.110     0.012     0.101     0.181     0.263     0.428 1.00   970
gamma[6,2,3]       0.274   0.123     0.042     0.179     0.275     0.365     0.500 1.01   430
gamma[7,2,3]       0.492   0.113     0.256     0.417     0.497     0.573     0.703 1.01   220
gamma[8,2,3]       0.153   0.093     0.012     0.080     0.143     0.213     0.362 1.00  1100
gamma[9,2,3]       0.214   0.099     0.042     0.144     0.205     0.275     0.428 1.01  1200
gamma[10,2,3]      0.062   0.054     0.002     0.021     0.048     0.088     0.192 1.00   830
gamma[11,2,3]      0.378   0.053     0.273     0.342     0.379     0.414     0.482 1.00  3300
gamma[12,2,3]      0.048   0.038     0.002     0.018     0.039     0.069     0.147 1.00   910
gamma[13,2,3]      0.052   0.042     0.002     0.019     0.042     0.074     0.158 1.00  4000
gamma[14,2,3]      0.790   0.047     0.691     0.760     0.792     0.824     0.872 1.00  1100
gamma[15,2,3]      0.403   0.153     0.093     0.299     0.412     0.513     0.684 1.01   770
gamma[16,2,3]      0.908   0.025     0.850     0.892     0.910     0.926     0.950 1.00  1500
gamma[17,2,3]      0.705   0.069     0.555     0.661     0.708     0.755     0.825 1.00   640
gamma[18,2,3]      0.715   0.065     0.575     0.672     0.721     0.762     0.828 1.01   310
gamma[19,2,3]      0.030   0.029     0.001     0.009     0.021     0.042     0.110 1.00   940
gamma[20,2,3]      0.066   0.053     0.002     0.025     0.054     0.094     0.198 1.01   390
gamma[21,2,3]      0.047   0.042     0.002     0.015     0.035     0.064     0.160 1.00  2700
gamma[22,2,3]      0.058   0.045     0.003     0.023     0.049     0.081     0.170 1.01   370
gamma[23,2,3]      0.250   0.063     0.124     0.206     0.251     0.295     0.366 1.00  4000
gamma[24,2,3]      0.056   0.050     0.002     0.018     0.042     0.080     0.189 1.00  2800
gamma[25,2,3]      0.459   0.053     0.356     0.424     0.458     0.496     0.561 1.00  1900
gamma[1,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[2,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[3,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[4,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[5,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[6,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[7,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[8,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[9,3,3]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[10,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[11,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[12,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[13,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[14,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[15,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[16,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[17,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[18,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[19,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[20,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[21,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[22,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[23,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[24,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
gamma[25,3,3]      1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
inv.phi[1,1]       3.199   1.546     0.898     2.039     2.957     4.082     6.881 1.03   110
inv.phi[2,1]      -0.518   1.063    -2.782    -1.166    -0.502     0.173     1.566 1.05    53
inv.phi[3,1]      -1.166   1.121    -3.742    -1.794    -1.040    -0.415     0.718 1.06    54
inv.phi[4,1]      -1.191   1.351    -4.239    -1.975    -1.037    -0.236     0.988 1.04    68
inv.phi[1,2]      -0.518   1.063    -2.782    -1.166    -0.502     0.173     1.566 1.05    53
inv.phi[2,2]       2.927   1.511     0.675     1.831     2.641     3.788     6.543 1.10    34
inv.phi[3,2]      -0.100   0.945    -2.180    -0.634    -0.064     0.502     1.649 1.03    82
inv.phi[4,2]      -1.998   1.420    -5.256    -2.807    -1.752    -0.934     0.068 1.05    62
inv.phi[1,3]      -1.166   1.121    -3.742    -1.794    -1.040    -0.415     0.718 1.06    54
inv.phi[2,3]      -0.100   0.945    -2.180    -0.634    -0.064     0.502     1.649 1.03    82
inv.phi[3,3]       2.600   1.321     0.705     1.600     2.389     3.316     5.707 1.05    59
inv.phi[4,3]      -0.823   1.267    -3.622    -1.597    -0.689     0.099     1.335 1.05    65
inv.phi[1,4]      -1.191   1.351    -4.239    -1.975    -1.037    -0.236     0.988 1.04    68
inv.phi[2,4]      -1.998   1.420    -5.256    -2.807    -1.752    -0.934     0.068 1.05    62
inv.phi[3,4]      -0.823   1.267    -3.622    -1.597    -0.689     0.099     1.335 1.05    65
inv.phi[4,4]       3.886   2.180     0.770     2.237     3.498     5.155     9.043 1.03    95
lambda[1]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[2]          1.459   0.182     1.127     1.330     1.447     1.579     1.842 1.01   620
lambda[3]          1.359   0.178     1.047     1.234     1.344     1.471     1.735 1.01   460
lambda[4]          1.014   0.130     0.764     0.928     1.008     1.097     1.291 1.02   100
lambda[5]          1.127   0.125     0.904     1.040     1.122     1.212     1.384 1.01   500
lambda[6]          1.086   0.135     0.835     0.993     1.084     1.176     1.361 1.01   240
lambda[7]          1.415   0.184     1.098     1.281     1.401     1.537     1.796 1.01   330
lambda[8]          1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[9]          0.864   0.094     0.688     0.799     0.861     0.926     1.052 1.02   140
lambda[10]         0.756   0.095     0.585     0.690     0.749     0.817     0.962 1.01   230
lambda[11]         0.763   0.101     0.578     0.692     0.758     0.828     0.974 1.01   290
lambda[12]         0.923   0.088     0.767     0.861     0.920     0.980     1.108 1.01   290
lambda[13]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[14]         0.827   0.130     0.576     0.740     0.823     0.915     1.086 1.02   110
lambda[15]         0.490   0.074     0.358     0.439     0.485     0.537     0.646 1.02   180
lambda[16]         1.398   0.247     0.963     1.227     1.384     1.559     1.917 1.02   120
lambda[17]         1.295   0.209     0.927     1.136     1.281     1.452     1.697 1.04    71
lambda[18]         0.907   0.139     0.657     0.811     0.900     0.993     1.206 1.02   160
lambda[19]         1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
lambda[20]         1.197   0.129     0.969     1.107     1.190     1.282     1.472 1.01   760
lambda[21]         0.957   0.102     0.769     0.884     0.952     1.024     1.165 1.00   870
lambda[22]         1.111   0.101     0.925     1.041     1.108     1.175     1.319 1.01   240
lambda[23]         0.935   0.112     0.731     0.857     0.928     1.005     1.179 1.01   270
lambda[24]         0.911   0.090     0.754     0.847     0.903     0.965     1.109 1.01   430
lambda[25]         0.840   0.101     0.655     0.770     0.836     0.904     1.055 1.01   250
lambda.std[1]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[2]      0.821   0.033     0.748     0.799     0.823     0.845     0.879 1.01   840
lambda.std[3]      0.801   0.037     0.723     0.777     0.802     0.827     0.866 1.01   390
lambda.std[4]      0.708   0.045     0.607     0.680     0.710     0.739     0.791 1.02   110
lambda.std[5]      0.745   0.037     0.671     0.721     0.747     0.771     0.810 1.01   420
lambda.std[6]      0.731   0.042     0.641     0.705     0.735     0.762     0.806 1.01   270
lambda.std[7]      0.812   0.036     0.739     0.788     0.814     0.838     0.874 1.01   290
lambda.std[8]      0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[9]      0.651   0.041     0.567     0.624     0.652     0.680     0.725 1.02   140
lambda.std[10]     0.600   0.048     0.505     0.568     0.599     0.633     0.693 1.02   210
lambda.std[11]     0.603   0.050     0.500     0.569     0.604     0.638     0.698 1.01   290
lambda.std[12]     0.676   0.035     0.609     0.652     0.677     0.700     0.742 1.01   290
lambda.std[13]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[14]     0.632   0.060     0.499     0.595     0.635     0.675     0.736 1.03   110
lambda.std[15]     0.438   0.053     0.337     0.402     0.436     0.473     0.542 1.02   180
lambda.std[16]     0.805   0.050     0.694     0.775     0.811     0.842     0.887 1.02   140
lambda.std[17]     0.784   0.049     0.680     0.751     0.788     0.824     0.862 1.04    79
lambda.std[18]     0.666   0.056     0.549     0.630     0.669     0.705     0.770 1.03   140
lambda.std[19]     0.707   0.000     0.707     0.707     0.707     0.707     0.707 1.00     1
lambda.std[20]     0.764   0.034     0.696     0.742     0.765     0.789     0.827 1.01   820
lambda.std[21]     0.688   0.038     0.610     0.662     0.690     0.715     0.759 1.00   830
lambda.std[22]     0.741   0.030     0.679     0.721     0.742     0.762     0.797 1.01   220
lambda.std[23]     0.679   0.043     0.590     0.651     0.680     0.709     0.763 1.01   270
lambda.std[24]     0.671   0.036     0.602     0.646     0.670     0.694     0.743 1.01   420
lambda.std[25]     0.640   0.045     0.548     0.610     0.641     0.671     0.726 1.01   240
phi[1,1]           2.590   1.414     0.715     1.511     2.328     3.377     6.130 1.01   580
phi[2,1]           2.025   1.217     0.210     1.174     1.873     2.761     4.778 1.04   110
phi[3,1]           1.865   1.277     0.004     1.029     1.679     2.467     4.959 1.03   210
phi[4,1]           2.155   0.963     0.249     1.511     2.171     2.824     4.002 1.01   400
phi[1,2]           2.025   1.217     0.210     1.174     1.873     2.761     4.778 1.04   110
phi[2,2]           3.217   2.517     0.965     1.891     2.635     3.774     9.479 1.13    32
phi[3,2]           1.776   1.279    -0.596     1.029     1.731     2.471     4.346 1.04   180
phi[4,2]           2.525   0.954     0.730     1.921     2.469     3.092     4.438 1.09    46
phi[1,3]           1.865   1.277     0.004     1.029     1.679     2.467     4.959 1.03   210
phi[2,3]           1.776   1.279    -0.596     1.029     1.731     2.471     4.346 1.04   180
phi[3,3]           2.586   1.680     0.702     1.541     2.233     3.137     6.440 1.04   120
phi[4,3]           1.914   1.134    -0.748     1.340     2.061     2.620     3.852 1.03   370
phi[1,4]           2.155   0.963     0.249     1.511     2.171     2.824     4.002 1.01   400
phi[2,4]           2.525   0.954     0.730     1.921     2.469     3.092     4.438 1.09    46
phi[3,4]           1.914   1.134    -0.748     1.340     2.061     2.620     3.852 1.03   370
phi[4,4]           2.958   0.307     2.408     2.740     2.942     3.166     3.592 1.01   220
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]       0.732   0.223     0.133     0.656     0.804     0.883     0.951 1.07   100
phi.cor[3,1]       0.721   0.241     0.003     0.646     0.793     0.884     0.955 1.02   170
phi.cor[4,1]       0.779   0.214     0.121     0.735     0.855     0.912     0.960 1.07   120
phi.cor[1,2]       0.732   0.223     0.133     0.656     0.804     0.883     0.951 1.07   100
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]       0.651   0.299    -0.245     0.566     0.757     0.848     0.930 1.05   170
phi.cor[4,2]       0.843   0.153     0.397     0.816     0.893     0.933     0.968 1.04   160
phi.cor[1,3]       0.721   0.241     0.003     0.646     0.793     0.884     0.955 1.02   170
phi.cor[2,3]       0.651   0.299    -0.245     0.566     0.757     0.848     0.930 1.05   170
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]       0.698   0.321    -0.348     0.655     0.818     0.892     0.947 1.06    97
phi.cor[1,4]       0.779   0.214     0.121     0.735     0.855     0.912     0.960 1.07   120
phi.cor[2,4]       0.843   0.153     0.397     0.816     0.893     0.933     0.968 1.04   160
phi.cor[3,4]       0.698   0.321    -0.348     0.655     0.818     0.892     0.947 1.06    97
phi.cor[4,4]       1.000   0.000     1.000     1.000     1.000     1.000     1.000 1.00     1
reli.omega[1]      0.910   0.009     0.891     0.904     0.911     0.917     0.927 1.01   660
reli.omega[2]      0.824   0.012     0.799     0.815     0.824     0.833     0.846 1.03    95
reli.omega[3]      0.852   0.020     0.812     0.838     0.853     0.866     0.888 1.02   230
reli.omega[4]      0.861   0.012     0.837     0.853     0.861     0.869     0.884 1.02   190
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]           3.126   0.166     2.802     3.013     3.125     3.242     3.455 1.00   890
tau[2,2]           4.009   0.364     3.375     3.754     3.987     4.244     4.812 1.01   230
tau[3,2]           3.623   0.317     3.038     3.399     3.610     3.831     4.283 1.00  2500
tau[4,2]           2.206   0.181     1.865     2.085     2.204     2.316     2.583 1.02   150
tau[5,2]           2.736   0.210     2.348     2.591     2.726     2.871     3.163 1.01   540
tau[6,2]           3.155   0.253     2.685     2.981     3.145     3.317     3.694 1.01   420
tau[7,2]           4.327   0.388     3.642     4.053     4.297     4.565     5.171 1.01   240
tau[8,2]           2.049   0.130     1.796     1.961     2.049     2.137     2.308 1.00  1300
tau[9,2]           0.955   0.141     0.656     0.869     0.965     1.054     1.198 1.00  4000
tau[10,2]          1.510   0.115     1.289     1.430     1.508     1.587     1.744 1.00   890
tau[11,2]          0.079   0.062     0.003     0.029     0.065     0.119     0.226 1.00  4000
tau[12,2]          1.746   0.110     1.534     1.671     1.744     1.819     1.966 1.00   680
tau[13,2]          1.813   0.104     1.611     1.741     1.814     1.883     2.014 1.00  4000
tau[14,2]          2.922   0.222     2.520     2.762     2.918     3.069     3.380 1.01   230
tau[15,2]          1.424   0.137     1.167     1.330     1.423     1.516     1.701 1.00  1100
tau[16,2]          4.979   0.535     4.054     4.596     4.942     5.324     6.106 1.03   100
tau[17,2]          3.798   0.341     3.181     3.554     3.783     4.024     4.520 1.04    81
tau[18,2]          3.220   0.253     2.742     3.047     3.207     3.382     3.733 1.01   340
tau[19,2]          2.147   0.115     1.926     2.069     2.146     2.227     2.371 1.00  1600
tau[20,2]          2.988   0.208     2.608     2.844     2.972     3.119     3.424 1.00   560
tau[21,2]          1.770   0.122     1.537     1.687     1.768     1.853     2.014 1.00  2200
tau[22,2]          2.152   0.137     1.904     2.057     2.147     2.243     2.431 1.00  1000
tau[23,2]          0.138   0.079     0.009     0.074     0.135     0.193     0.299 1.00  4000
tau[24,2]          1.979   0.124     1.748     1.893     1.976     2.060     2.232 1.00  2100
tau[25,2]          0.046   0.040     0.001     0.016     0.035     0.066     0.145 1.00  1100
theta[1]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[2]           3.161   0.542     2.269     2.770     3.094     3.492     4.392 1.01   540
theta[3]           2.878   0.496     2.096     2.523     2.807     3.164     4.009 1.00   510
theta[4]           2.045   0.269     1.584     1.860     2.017     2.203     2.666 1.03   100
theta[5]           2.287   0.286     1.818     2.081     2.259     2.468     2.915 1.01   570
theta[6]           2.198   0.298     1.697     1.986     2.175     2.383     2.851 1.01   220
theta[7]           3.035   0.534     2.206     2.641     2.963     3.364     4.227 1.01   350
theta[8]           2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[9]           1.756   0.166     1.473     1.638     1.741     1.858     2.107 1.02   140
theta[10]          1.581   0.148     1.342     1.476     1.561     1.667     1.926 1.01   270
theta[11]          1.592   0.158     1.334     1.479     1.574     1.686     1.949 1.01   290
theta[12]          1.860   0.164     1.588     1.741     1.846     1.961     2.227 1.01   280
theta[13]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[14]          1.702   0.219     1.332     1.547     1.677     1.838     2.179 1.02   120
theta[15]          1.246   0.075     1.128     1.192     1.235     1.289     1.417 1.02   180
theta[16]          3.016   0.714     1.928     2.504     2.915     3.431     4.677 1.03   110
theta[17]          2.720   0.553     1.860     2.291     2.640     3.109     3.881 1.04    68
theta[18]          1.842   0.263     1.432     1.657     1.810     1.987     2.455 1.02   200
theta[19]          2.000   0.000     2.000     2.000     2.000     2.000     2.000 1.00     1
theta[20]          2.451   0.314     1.939     2.226     2.415     2.644     3.168 1.01   710
theta[21]          1.926   0.197     1.591     1.781     1.907     2.049     2.357 1.00   920
theta[22]          2.244   0.228     1.855     2.083     2.228     2.381     2.740 1.01   250
theta[23]          1.886   0.214     1.534     1.735     1.861     2.011     2.390 1.01   270
theta[24]          1.837   0.169     1.568     1.718     1.816     1.931     2.231 1.01   450
theta[25]          1.716   0.174     1.430     1.594     1.699     1.818     2.113 1.01   280
deviance       15491.432 122.187 15248.149 15413.528 15490.959 15574.984 15725.502 1.00   780

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 = 7441.5 and DIC = 22932.9
DIC is an estimate of expected predictive error (lower deviance is better).
kable(model.fit$BUGSoutput$summary, format="html", digits=3) %>%
  kable_styling(full_width = T) %>%
  scroll_box(width="100%", height="500px")
mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
deviance 15491.432 122.187 15248.149 15413.528 15490.959 15574.984 15725.502 1.00 780
gamma[1,1,1] 0.787 0.069 0.641 0.743 0.789 0.836 0.913 1.00 4000
gamma[2,1,1] 0.830 0.058 0.703 0.793 0.835 0.871 0.932 1.01 390
gamma[3,1,1] 0.619 0.092 0.436 0.554 0.623 0.685 0.789 1.01 410
gamma[4,1,1] 0.588 0.097 0.399 0.522 0.588 0.654 0.781 1.01 300
gamma[5,1,1] 0.762 0.080 0.597 0.710 0.768 0.818 0.914 1.00 780
gamma[6,1,1] 0.757 0.085 0.579 0.702 0.760 0.817 0.911 1.00 910
gamma[7,1,1] 0.798 0.070 0.649 0.754 0.800 0.848 0.925 1.01 470
gamma[8,1,1] 0.764 0.090 0.572 0.706 0.773 0.828 0.924 1.00 1400
gamma[9,1,1] 0.862 0.116 0.567 0.815 0.895 0.947 0.991 1.01 370
gamma[10,1,1] 0.777 0.112 0.524 0.703 0.789 0.860 0.956 1.00 1000
gamma[11,1,1] 0.233 0.061 0.122 0.189 0.230 0.273 0.360 1.00 1200
gamma[12,1,1] 0.956 0.033 0.872 0.940 0.965 0.981 0.997 1.00 1500
gamma[13,1,1] 0.962 0.030 0.887 0.948 0.971 0.985 0.997 1.00 3200
gamma[14,1,1] 0.628 0.125 0.383 0.544 0.625 0.716 0.872 1.00 790
gamma[15,1,1] 0.820 0.111 0.584 0.747 0.836 0.911 0.984 1.01 300
gamma[16,1,1] 0.630 0.114 0.387 0.555 0.633 0.710 0.841 1.01 340
gamma[17,1,1] 0.698 0.103 0.480 0.630 0.702 0.772 0.887 1.01 250
gamma[18,1,1] 0.751 0.105 0.529 0.682 0.758 0.827 0.938 1.01 230
gamma[19,1,1] 0.952 0.034 0.867 0.935 0.960 0.977 0.995 1.00 1300
gamma[20,1,1] 0.867 0.060 0.731 0.830 0.874 0.913 0.962 1.01 450
gamma[21,1,1] 0.880 0.064 0.740 0.839 0.888 0.927 0.980 1.00 700
gamma[22,1,1] 0.971 0.023 0.912 0.960 0.977 0.988 0.998 1.01 760
gamma[23,1,1] 0.105 0.039 0.040 0.076 0.101 0.129 0.190 1.00 4000
gamma[24,1,1] 0.956 0.035 0.869 0.937 0.964 0.982 0.997 1.01 560
gamma[25,1,1] 0.133 0.037 0.068 0.107 0.130 0.156 0.213 1.01 460
gamma[1,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,2,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,3,1] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,1,2] 0.191 0.067 0.066 0.143 0.188 0.235 0.333 1.01 1100
gamma[2,1,2] 0.147 0.054 0.052 0.108 0.144 0.181 0.268 1.00 4000
gamma[3,1,2] 0.346 0.091 0.178 0.280 0.339 0.409 0.536 1.01 280
gamma[4,1,2] 0.337 0.108 0.124 0.262 0.340 0.412 0.540 1.00 750
gamma[5,1,2] 0.218 0.081 0.062 0.163 0.214 0.271 0.381 1.01 1800
gamma[6,1,2] 0.226 0.086 0.071 0.163 0.224 0.282 0.404 1.01 430
gamma[7,1,2] 0.173 0.067 0.053 0.125 0.170 0.214 0.315 1.08 88
gamma[8,1,2] 0.190 0.099 0.012 0.119 0.185 0.254 0.393 1.11 91
gamma[9,1,2] 0.123 0.114 0.003 0.038 0.089 0.172 0.412 1.02 350
gamma[10,1,2] 0.159 0.113 0.007 0.070 0.136 0.230 0.428 1.02 270
gamma[11,1,2] 0.751 0.060 0.628 0.713 0.753 0.792 0.864 1.00 4000
gamma[12,1,2] 0.026 0.026 0.001 0.008 0.018 0.036 0.099 1.01 450
gamma[13,1,2] 0.026 0.026 0.001 0.008 0.019 0.037 0.097 1.00 3100
gamma[14,1,2] 0.346 0.125 0.096 0.259 0.346 0.434 0.591 1.00 610
gamma[15,1,2] 0.135 0.104 0.003 0.047 0.113 0.200 0.377 1.01 400
gamma[16,1,2] 0.346 0.111 0.150 0.267 0.342 0.418 0.582 1.00 830
gamma[17,1,2] 0.263 0.100 0.087 0.194 0.258 0.330 0.475 1.01 330
gamma[18,1,2] 0.229 0.104 0.046 0.154 0.218 0.295 0.451 1.03 140
gamma[19,1,2] 0.029 0.027 0.001 0.009 0.020 0.040 0.100 1.01 590
gamma[20,1,2] 0.057 0.041 0.003 0.024 0.050 0.082 0.156 1.01 550
gamma[21,1,2] 0.053 0.048 0.002 0.018 0.040 0.072 0.175 1.01 4000
gamma[22,1,2] 0.019 0.019 0.000 0.006 0.014 0.027 0.070 1.00 2300
gamma[23,1,2] 0.890 0.039 0.805 0.865 0.894 0.919 0.955 1.00 1900
gamma[24,1,2] 0.025 0.024 0.001 0.008 0.019 0.035 0.087 1.00 1100
gamma[25,1,2] 0.861 0.037 0.781 0.838 0.864 0.887 0.926 1.00 560
gamma[1,2,2] 0.905 0.078 0.711 0.862 0.926 0.966 0.997 1.00 1400
gamma[2,2,2] 0.883 0.079 0.700 0.836 0.896 0.943 0.993 1.00 2300
gamma[3,2,2] 0.565 0.105 0.371 0.491 0.560 0.630 0.781 1.00 740
gamma[4,2,2] 0.837 0.110 0.582 0.766 0.854 0.925 0.991 1.00 540
gamma[5,2,2] 0.813 0.110 0.572 0.737 0.819 0.899 0.988 1.00 1700
gamma[6,2,2] 0.726 0.123 0.500 0.635 0.725 0.821 0.958 1.01 460
gamma[7,2,2] 0.508 0.113 0.297 0.427 0.503 0.583 0.744 1.02 140
gamma[8,2,2] 0.847 0.093 0.638 0.787 0.857 0.920 0.988 1.00 1000
gamma[9,2,2] 0.786 0.099 0.572 0.725 0.795 0.856 0.958 1.00 3400
gamma[10,2,2] 0.938 0.054 0.808 0.912 0.952 0.979 0.998 1.00 740
gamma[11,2,2] 0.622 0.053 0.518 0.586 0.621 0.658 0.727 1.00 3100
gamma[12,2,2] 0.952 0.038 0.853 0.931 0.961 0.982 0.998 1.00 4000
gamma[13,2,2] 0.948 0.042 0.842 0.926 0.958 0.981 0.998 1.00 4000
gamma[14,2,2] 0.210 0.047 0.128 0.176 0.208 0.240 0.309 1.00 1200
gamma[15,2,2] 0.597 0.153 0.316 0.487 0.588 0.701 0.907 1.00 770
gamma[16,2,2] 0.092 0.025 0.050 0.074 0.090 0.108 0.150 1.00 1300
gamma[17,2,2] 0.295 0.069 0.175 0.245 0.292 0.339 0.445 1.00 590
gamma[18,2,2] 0.285 0.065 0.172 0.238 0.279 0.328 0.425 1.01 290
gamma[19,2,2] 0.970 0.029 0.890 0.958 0.979 0.991 0.999 1.00 1100
gamma[20,2,2] 0.934 0.053 0.802 0.906 0.946 0.975 0.998 1.02 220
gamma[21,2,2] 0.953 0.042 0.840 0.936 0.965 0.985 0.998 1.00 4000
gamma[22,2,2] 0.942 0.045 0.830 0.919 0.951 0.977 0.997 1.00 1100
gamma[23,2,2] 0.750 0.063 0.634 0.705 0.749 0.794 0.876 1.00 2300
gamma[24,2,2] 0.944 0.050 0.811 0.920 0.958 0.982 0.998 1.00 4000
gamma[25,2,2] 0.541 0.053 0.439 0.504 0.542 0.576 0.644 1.00 2200
gamma[1,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[2,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[3,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[4,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[5,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[6,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[7,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[8,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[9,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[10,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[11,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[12,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[13,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[14,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[15,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[16,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[17,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[18,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[19,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[20,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[21,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[22,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[23,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[24,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[25,3,2] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00 1
gamma[1,1,3] 0.021 0.031 0.000 0.002 0.009 0.028 0.111 1.01 330
gamma[2,1,3] 0.023 0.029 0.000 0.004 0.013 0.032 0.102 1.03 170
gamma[3,1,3] 0.035 0.046 0.000 0.004 0.017 0.047 0.169 1.02 280
gamma[4,1,3] 0.075 0.063 0.001 0.023 0.060 0.114 0.229 1.03 140
gamma[5,1,3] 0.020 0.029 0.000 0.002 0.008 0.025 0.103 1.09 56
gamma[6,1,3] 0.018 0.023 0.000 0.002 0.010 0.025 0.081 1.01 200
gamma[7,1,3] 0.029 0.035 0.000 0.005 0.017 0.040 0.128 1.06 57
gamma[8,1,3] 0.046 0.051 0.000 0.007 0.029 0.068 0.185 1.11 45
gamma[9,1,3] 0.015 0.020 0.000 0.002 0.007 0.022 0.067 1.01 460
gamma[10,1,3] 0.065 0.060 0.000 0.015 0.049 0.098 0.217 1.02 170
gamma[11,1,3] 0.016 0.017 0.000 0.002 0.010 0.024 0.062 1.05 110
gamma[12,1,3] 0.017 0.022 0.000 0.002 0.009 0.024 0.081 1.00 1300
gamma[13,1,3] 0.011 0.015 0.000 0.001 0.005 0.015 0.054 1.03 150
gamma[14,1,3] 0.026 0.033 0.000 0.003 0.013 0.035 0.119 1.02 240
gamma[15,1,3] 0.045 0.055 0.000 0.007 0.024 0.063 0.211 1.01 390
gamma[16,1,3] 0.024 0.031 0.000 0.004 0.012 0.032 0.117 1.03 110
gamma[17,1,3] 0.038 0.044 0.000 0.006 0.021 0.055 0.157 1.03 180
gamma[18,1,3] 0.021 0.030 0.000 0.001 0.008 0.028 0.105 1.11 63
gamma[19,1,3] 0.019 0.022 0.000 0.003 0.011 0.027 0.082 1.03 150
gamma[20,1,3] 0.076 0.060 0.001 0.028 0.063 0.112 0.214 1.01 540
gamma[21,1,3] 0.067 0.052 0.001 0.027 0.058 0.098 0.188 1.02 520
gamma[22,1,3] 0.010 0.014 0.000 0.001 0.004 0.013 0.050 1.12 63
gamma[23,1,3] 0.004 0.006 0.000 0.001 0.002 0.006 0.021 1.06 340
gamma[24,1,3] 0.019 0.026 0.000 0.002 0.009 0.026 0.097 1.01 280
gamma[25,1,3] 0.006 0.008 0.000 0.001 0.003 0.008 0.029 1.02 250
gamma[1,2,3] 0.095 0.078 0.003 0.034 0.074 0.138 0.289 1.00 1600
gamma[2,2,3] 0.117 0.079 0.007 0.057 0.104 0.164 0.300 1.00 4000
gamma[3,2,3] 0.435 0.105 0.219 0.370 0.440 0.509 0.629 1.01 750
gamma[4,2,3] 0.163 0.110 0.009 0.075 0.146 0.234 0.418 1.01 550
gamma[5,2,3] 0.187 0.110 0.012 0.101 0.181 0.263 0.428 1.00 970
gamma[6,2,3] 0.274 0.123 0.042 0.179 0.275 0.365 0.500 1.01 430
gamma[7,2,3] 0.492 0.113 0.256 0.417 0.497 0.573 0.703 1.01 220
gamma[8,2,3] 0.153 0.093 0.012 0.080 0.143 0.213 0.362 1.00 1100
gamma[9,2,3] 0.214 0.099 0.042 0.144 0.205 0.275 0.428 1.01 1200
gamma[10,2,3] 0.062 0.054 0.002 0.021 0.048 0.088 0.192 1.00 830
gamma[11,2,3] 0.378 0.053 0.273 0.342 0.379 0.414 0.482 1.00 3300
gamma[12,2,3] 0.048 0.038 0.002 0.018 0.039 0.069 0.147 1.00 910
gamma[13,2,3] 0.052 0.042 0.002 0.019 0.042 0.074 0.158 1.00 4000
gamma[14,2,3] 0.790 0.047 0.691 0.760 0.792 0.824 0.872 1.00 1100
gamma[15,2,3] 0.403 0.153 0.093 0.299 0.412 0.513 0.684 1.01 770
gamma[16,2,3] 0.908 0.025 0.850 0.892 0.910 0.926 0.950 1.00 1500
gamma[17,2,3] 0.705 0.069 0.555 0.661 0.708 0.755 0.825 1.00 640
gamma[18,2,3] 0.715 0.065 0.575 0.672 0.721 0.762 0.828 1.01 310
gamma[19,2,3] 0.030 0.029 0.001 0.009 0.021 0.042 0.110 1.00 940
gamma[20,2,3] 0.066 0.053 0.002 0.025 0.054 0.094 0.198 1.01 390
gamma[21,2,3] 0.047 0.042 0.002 0.015 0.035 0.064 0.160 1.00 2700
gamma[22,2,3] 0.058 0.045 0.003 0.023 0.049 0.081 0.170 1.01 370
gamma[23,2,3] 0.250 0.063 0.124 0.206 0.251 0.295 0.366 1.00 4000
gamma[24,2,3] 0.056 0.050 0.002 0.018 0.042 0.080 0.189 1.00 2800
gamma[25,2,3] 0.459 0.053 0.356 0.424 0.458 0.496 0.561 1.00 1900
gamma[1,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[2,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[3,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[4,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[5,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[6,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[7,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[8,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[9,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[10,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[11,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[12,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[13,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[14,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[15,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[16,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[17,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[18,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[19,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[20,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[21,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[22,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[23,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[24,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
gamma[25,3,3] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
inv.phi[1,1] 3.199 1.546 0.898 2.039 2.957 4.082 6.881 1.03 110
inv.phi[2,1] -0.518 1.063 -2.782 -1.166 -0.502 0.173 1.566 1.05 53
inv.phi[3,1] -1.166 1.121 -3.742 -1.794 -1.040 -0.415 0.718 1.06 54
inv.phi[4,1] -1.191 1.351 -4.239 -1.975 -1.037 -0.236 0.988 1.04 68
inv.phi[1,2] -0.518 1.063 -2.782 -1.166 -0.502 0.173 1.566 1.05 53
inv.phi[2,2] 2.927 1.511 0.675 1.831 2.641 3.788 6.543 1.10 34
inv.phi[3,2] -0.100 0.945 -2.180 -0.634 -0.064 0.502 1.649 1.03 82
inv.phi[4,2] -1.998 1.420 -5.256 -2.807 -1.752 -0.934 0.068 1.05 62
inv.phi[1,3] -1.166 1.121 -3.742 -1.794 -1.040 -0.415 0.718 1.06 54
inv.phi[2,3] -0.100 0.945 -2.180 -0.634 -0.064 0.502 1.649 1.03 82
inv.phi[3,3] 2.600 1.321 0.705 1.600 2.389 3.316 5.707 1.05 59
inv.phi[4,3] -0.823 1.267 -3.622 -1.597 -0.689 0.099 1.335 1.05 65
inv.phi[1,4] -1.191 1.351 -4.239 -1.975 -1.037 -0.236 0.988 1.04 68
inv.phi[2,4] -1.998 1.420 -5.256 -2.807 -1.752 -0.934 0.068 1.05 62
inv.phi[3,4] -0.823 1.267 -3.622 -1.597 -0.689 0.099 1.335 1.05 65
inv.phi[4,4] 3.886 2.180 0.770 2.237 3.498 5.155 9.043 1.03 95
lambda[1] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[2] 1.459 0.182 1.127 1.330 1.447 1.579 1.842 1.01 620
lambda[3] 1.359 0.178 1.047 1.234 1.344 1.471 1.735 1.01 460
lambda[4] 1.014 0.130 0.764 0.928 1.008 1.097 1.291 1.02 100
lambda[5] 1.127 0.125 0.904 1.040 1.122 1.212 1.384 1.01 500
lambda[6] 1.086 0.135 0.835 0.993 1.084 1.176 1.361 1.01 240
lambda[7] 1.415 0.184 1.098 1.281 1.401 1.537 1.796 1.01 330
lambda[8] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[9] 0.864 0.094 0.688 0.799 0.861 0.926 1.052 1.02 140
lambda[10] 0.756 0.095 0.585 0.690 0.749 0.817 0.962 1.01 230
lambda[11] 0.763 0.101 0.578 0.692 0.758 0.828 0.974 1.01 290
lambda[12] 0.923 0.088 0.767 0.861 0.920 0.980 1.108 1.01 290
lambda[13] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[14] 0.827 0.130 0.576 0.740 0.823 0.915 1.086 1.02 110
lambda[15] 0.490 0.074 0.358 0.439 0.485 0.537 0.646 1.02 180
lambda[16] 1.398 0.247 0.963 1.227 1.384 1.559 1.917 1.02 120
lambda[17] 1.295 0.209 0.927 1.136 1.281 1.452 1.697 1.04 71
lambda[18] 0.907 0.139 0.657 0.811 0.900 0.993 1.206 1.02 160
lambda[19] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
lambda[20] 1.197 0.129 0.969 1.107 1.190 1.282 1.472 1.01 760
lambda[21] 0.957 0.102 0.769 0.884 0.952 1.024 1.165 1.00 870
lambda[22] 1.111 0.101 0.925 1.041 1.108 1.175 1.319 1.01 240
lambda[23] 0.935 0.112 0.731 0.857 0.928 1.005 1.179 1.01 270
lambda[24] 0.911 0.090 0.754 0.847 0.903 0.965 1.109 1.01 430
lambda[25] 0.840 0.101 0.655 0.770 0.836 0.904 1.055 1.01 250
lambda.std[1] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[2] 0.821 0.033 0.748 0.799 0.823 0.845 0.879 1.01 840
lambda.std[3] 0.801 0.037 0.723 0.777 0.802 0.827 0.866 1.01 390
lambda.std[4] 0.708 0.045 0.607 0.680 0.710 0.739 0.791 1.02 110
lambda.std[5] 0.745 0.037 0.671 0.721 0.747 0.771 0.810 1.01 420
lambda.std[6] 0.731 0.042 0.641 0.705 0.735 0.762 0.806 1.01 270
lambda.std[7] 0.812 0.036 0.739 0.788 0.814 0.838 0.874 1.01 290
lambda.std[8] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[9] 0.651 0.041 0.567 0.624 0.652 0.680 0.725 1.02 140
lambda.std[10] 0.600 0.048 0.505 0.568 0.599 0.633 0.693 1.02 210
lambda.std[11] 0.603 0.050 0.500 0.569 0.604 0.638 0.698 1.01 290
lambda.std[12] 0.676 0.035 0.609 0.652 0.677 0.700 0.742 1.01 290
lambda.std[13] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[14] 0.632 0.060 0.499 0.595 0.635 0.675 0.736 1.03 110
lambda.std[15] 0.438 0.053 0.337 0.402 0.436 0.473 0.542 1.02 180
lambda.std[16] 0.805 0.050 0.694 0.775 0.811 0.842 0.887 1.02 140
lambda.std[17] 0.784 0.049 0.680 0.751 0.788 0.824 0.862 1.04 79
lambda.std[18] 0.666 0.056 0.549 0.630 0.669 0.705 0.770 1.03 140
lambda.std[19] 0.707 0.000 0.707 0.707 0.707 0.707 0.707 1.00 1
lambda.std[20] 0.764 0.034 0.696 0.742 0.765 0.789 0.827 1.01 820
lambda.std[21] 0.688 0.038 0.610 0.662 0.690 0.715 0.759 1.00 830
lambda.std[22] 0.741 0.030 0.679 0.721 0.742 0.762 0.797 1.01 220
lambda.std[23] 0.679 0.043 0.590 0.651 0.680 0.709 0.763 1.01 270
lambda.std[24] 0.671 0.036 0.602 0.646 0.670 0.694 0.743 1.01 420
lambda.std[25] 0.640 0.045 0.548 0.610 0.641 0.671 0.726 1.01 240
phi[1,1] 2.590 1.414 0.715 1.511 2.328 3.377 6.130 1.01 580
phi[2,1] 2.025 1.217 0.210 1.174 1.873 2.761 4.778 1.04 110
phi[3,1] 1.865 1.277 0.004 1.029 1.679 2.467 4.959 1.03 210
phi[4,1] 2.155 0.963 0.249 1.511 2.171 2.824 4.002 1.01 400
phi[1,2] 2.025 1.217 0.210 1.174 1.873 2.761 4.778 1.04 110
phi[2,2] 3.217 2.517 0.965 1.891 2.635 3.774 9.479 1.13 32
phi[3,2] 1.776 1.279 -0.596 1.029 1.731 2.471 4.346 1.04 180
phi[4,2] 2.525 0.954 0.730 1.921 2.469 3.092 4.438 1.09 46
phi[1,3] 1.865 1.277 0.004 1.029 1.679 2.467 4.959 1.03 210
phi[2,3] 1.776 1.279 -0.596 1.029 1.731 2.471 4.346 1.04 180
phi[3,3] 2.586 1.680 0.702 1.541 2.233 3.137 6.440 1.04 120
phi[4,3] 1.914 1.134 -0.748 1.340 2.061 2.620 3.852 1.03 370
phi[1,4] 2.155 0.963 0.249 1.511 2.171 2.824 4.002 1.01 400
phi[2,4] 2.525 0.954 0.730 1.921 2.469 3.092 4.438 1.09 46
phi[3,4] 1.914 1.134 -0.748 1.340 2.061 2.620 3.852 1.03 370
phi[4,4] 2.958 0.307 2.408 2.740 2.942 3.166 3.592 1.01 220
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] 0.732 0.223 0.133 0.656 0.804 0.883 0.951 1.07 100
phi.cor[3,1] 0.721 0.241 0.003 0.646 0.793 0.884 0.955 1.02 170
phi.cor[4,1] 0.779 0.214 0.121 0.735 0.855 0.912 0.960 1.07 120
phi.cor[1,2] 0.732 0.223 0.133 0.656 0.804 0.883 0.951 1.07 100
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] 0.651 0.299 -0.245 0.566 0.757 0.848 0.930 1.05 170
phi.cor[4,2] 0.843 0.153 0.397 0.816 0.893 0.933 0.968 1.04 160
phi.cor[1,3] 0.721 0.241 0.003 0.646 0.793 0.884 0.955 1.02 170
phi.cor[2,3] 0.651 0.299 -0.245 0.566 0.757 0.848 0.930 1.05 170
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] 0.698 0.321 -0.348 0.655 0.818 0.892 0.947 1.06 97
phi.cor[1,4] 0.779 0.214 0.121 0.735 0.855 0.912 0.960 1.07 120
phi.cor[2,4] 0.843 0.153 0.397 0.816 0.893 0.933 0.968 1.04 160
phi.cor[3,4] 0.698 0.321 -0.348 0.655 0.818 0.892 0.947 1.06 97
phi.cor[4,4] 1.000 0.000 1.000 1.000 1.000 1.000 1.000 1.00 1
reli.omega[1] 0.910 0.009 0.891 0.904 0.911 0.917 0.927 1.01 660
reli.omega[2] 0.824 0.012 0.799 0.815 0.824 0.833 0.846 1.03 95
reli.omega[3] 0.852 0.020 0.812 0.838 0.853 0.866 0.888 1.02 230
reli.omega[4] 0.861 0.012 0.837 0.853 0.861 0.869 0.884 1.02 190
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] 3.126 0.166 2.802 3.013 3.125 3.242 3.455 1.00 890
tau[2,2] 4.009 0.364 3.375 3.754 3.987 4.244 4.812 1.01 230
tau[3,2] 3.623 0.317 3.038 3.399 3.610 3.831 4.283 1.00 2500
tau[4,2] 2.206 0.181 1.865 2.085 2.204 2.316 2.583 1.02 150
tau[5,2] 2.736 0.210 2.348 2.591 2.726 2.871 3.163 1.01 540
tau[6,2] 3.155 0.253 2.685 2.981 3.145 3.317 3.694 1.01 420
tau[7,2] 4.327 0.388 3.642 4.053 4.297 4.565 5.171 1.01 240
tau[8,2] 2.049 0.130 1.796 1.961 2.049 2.137 2.308 1.00 1300
tau[9,2] 0.955 0.141 0.656 0.869 0.965 1.054 1.198 1.00 4000
tau[10,2] 1.510 0.115 1.289 1.430 1.508 1.587 1.744 1.00 890
tau[11,2] 0.079 0.062 0.003 0.029 0.065 0.119 0.226 1.00 4000
tau[12,2] 1.746 0.110 1.534 1.671 1.744 1.819 1.966 1.00 680
tau[13,2] 1.813 0.104 1.611 1.741 1.814 1.883 2.014 1.00 4000
tau[14,2] 2.922 0.222 2.520 2.762 2.918 3.069 3.380 1.01 230
tau[15,2] 1.424 0.137 1.167 1.330 1.423 1.516 1.701 1.00 1100
tau[16,2] 4.979 0.535 4.054 4.596 4.942 5.324 6.106 1.03 100
tau[17,2] 3.798 0.341 3.181 3.554 3.783 4.024 4.520 1.04 81
tau[18,2] 3.220 0.253 2.742 3.047 3.207 3.382 3.733 1.01 340
tau[19,2] 2.147 0.115 1.926 2.069 2.146 2.227 2.371 1.00 1600
tau[20,2] 2.988 0.208 2.608 2.844 2.972 3.119 3.424 1.00 560
tau[21,2] 1.770 0.122 1.537 1.687 1.768 1.853 2.014 1.00 2200
tau[22,2] 2.152 0.137 1.904 2.057 2.147 2.243 2.431 1.00 1000
tau[23,2] 0.138 0.079 0.009 0.074 0.135 0.193 0.299 1.00 4000
tau[24,2] 1.979 0.124 1.748 1.893 1.976 2.060 2.232 1.00 2100
tau[25,2] 0.046 0.040 0.001 0.016 0.035 0.066 0.145 1.00 1100
theta[1] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[2] 3.161 0.542 2.269 2.770 3.094 3.492 4.392 1.01 540
theta[3] 2.878 0.496 2.096 2.523 2.807 3.164 4.009 1.00 510
theta[4] 2.045 0.269 1.584 1.860 2.017 2.203 2.666 1.03 100
theta[5] 2.287 0.286 1.818 2.081 2.259 2.468 2.915 1.01 570
theta[6] 2.198 0.298 1.697 1.986 2.175 2.383 2.851 1.01 220
theta[7] 3.035 0.534 2.206 2.641 2.963 3.364 4.227 1.01 350
theta[8] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[9] 1.756 0.166 1.473 1.638 1.741 1.858 2.107 1.02 140
theta[10] 1.581 0.148 1.342 1.476 1.561 1.667 1.926 1.01 270
theta[11] 1.592 0.158 1.334 1.479 1.574 1.686 1.949 1.01 290
theta[12] 1.860 0.164 1.588 1.741 1.846 1.961 2.227 1.01 280
theta[13] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[14] 1.702 0.219 1.332 1.547 1.677 1.838 2.179 1.02 120
theta[15] 1.246 0.075 1.128 1.192 1.235 1.289 1.417 1.02 180
theta[16] 3.016 0.714 1.928 2.504 2.915 3.431 4.677 1.03 110
theta[17] 2.720 0.553 1.860 2.291 2.640 3.109 3.881 1.04 68
theta[18] 1.842 0.263 1.432 1.657 1.810 1.987 2.455 1.02 200
theta[19] 2.000 0.000 2.000 2.000 2.000 2.000 2.000 1.00 1
theta[20] 2.451 0.314 1.939 2.226 2.415 2.644 3.168 1.01 710
theta[21] 1.926 0.197 1.591 1.781 1.907 2.049 2.357 1.00 920
theta[22] 2.244 0.228 1.855 2.083 2.228 2.381 2.740 1.01 250
theta[23] 1.886 0.214 1.534 1.735 1.861 2.011 2.390 1.01 270
theta[24] 1.837 0.169 1.568 1.718 1.816 1.931 2.231 1.01 450
theta[25] 1.716 0.174 1.430 1.594 1.699 1.818 2.113 1.01 280

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_model3_lambda_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "lambda.std"); ggsave("fig/pools_model3_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_model3_lambda_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "lambda.std"); ggsave("fig/pools_model3_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_m3.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 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_model3_omega_dens.pdf")

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bayesplot::mcmc_acf(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model3_omega_acf.pdf")

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bayesplot::mcmc_trace(fit.mcmc, regex_pars = "reli.omega"); ggsave("fig/pools_model3_omega_trace.pdf")

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ggmcmc::ggs_grb(fit.mcmc.ggs, family = "reli.omega"); ggsave("fig/pools_model3_omega_grb.pdf")

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# extract omega posterior for results comparison
extracted_omega <- data.frame(model_3_f1 = fit.mcmc$`reli.omega[1]`,
                              model_3_f2 = fit.mcmc$`reli.omega[2]`,
                              model_3_f3 = fit.mcmc$`reli.omega[3]`,
                              model_3_f4 = fit.mcmc$`reli.omega[4]`)
write.csv(x=extracted_omega, file=paste0(getwd(),"/data/pools/extracted_omega_m3.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 3 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 04:17:43 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
  \toprule
 & mean & sd & 2.5\% & 25\% & 50\% & 75\% & 97.5\% & Rhat & n.eff \\ 
  \midrule
deviance & 15491.43 & 122.19 & 15248.15 & 15413.53 & 15490.96 & 15574.98 & 15725.50 & 1.00 & 780.00 \\ 
  gamma[1,1,1] & 0.79 & 0.07 & 0.64 & 0.74 & 0.79 & 0.84 & 0.91 & 1.00 & 4000.00 \\ 
  gamma[2,1,1] & 0.83 & 0.06 & 0.70 & 0.79 & 0.83 & 0.87 & 0.93 & 1.01 & 390.00 \\ 
  gamma[3,1,1] & 0.62 & 0.09 & 0.44 & 0.55 & 0.62 & 0.68 & 0.79 & 1.01 & 410.00 \\ 
  gamma[4,1,1] & 0.59 & 0.10 & 0.40 & 0.52 & 0.59 & 0.65 & 0.78 & 1.01 & 300.00 \\ 
  gamma[5,1,1] & 0.76 & 0.08 & 0.60 & 0.71 & 0.77 & 0.82 & 0.91 & 1.00 & 780.00 \\ 
  gamma[6,1,1] & 0.76 & 0.08 & 0.58 & 0.70 & 0.76 & 0.82 & 0.91 & 1.00 & 910.00 \\ 
  gamma[7,1,1] & 0.80 & 0.07 & 0.65 & 0.75 & 0.80 & 0.85 & 0.92 & 1.01 & 470.00 \\ 
  gamma[8,1,1] & 0.76 & 0.09 & 0.57 & 0.71 & 0.77 & 0.83 & 0.92 & 1.00 & 1400.00 \\ 
  gamma[9,1,1] & 0.86 & 0.12 & 0.57 & 0.82 & 0.89 & 0.95 & 0.99 & 1.01 & 370.00 \\ 
  gamma[10,1,1] & 0.78 & 0.11 & 0.52 & 0.70 & 0.79 & 0.86 & 0.96 & 1.00 & 1000.00 \\ 
  gamma[11,1,1] & 0.23 & 0.06 & 0.12 & 0.19 & 0.23 & 0.27 & 0.36 & 1.00 & 1200.00 \\ 
  gamma[12,1,1] & 0.96 & 0.03 & 0.87 & 0.94 & 0.96 & 0.98 & 1.00 & 1.00 & 1500.00 \\ 
  gamma[13,1,1] & 0.96 & 0.03 & 0.89 & 0.95 & 0.97 & 0.98 & 1.00 & 1.00 & 3200.00 \\ 
  gamma[14,1,1] & 0.63 & 0.13 & 0.38 & 0.54 & 0.62 & 0.72 & 0.87 & 1.00 & 790.00 \\ 
  gamma[15,1,1] & 0.82 & 0.11 & 0.58 & 0.75 & 0.84 & 0.91 & 0.98 & 1.01 & 300.00 \\ 
  gamma[16,1,1] & 0.63 & 0.11 & 0.39 & 0.55 & 0.63 & 0.71 & 0.84 & 1.01 & 340.00 \\ 
  gamma[17,1,1] & 0.70 & 0.10 & 0.48 & 0.63 & 0.70 & 0.77 & 0.89 & 1.01 & 250.00 \\ 
  gamma[18,1,1] & 0.75 & 0.11 & 0.53 & 0.68 & 0.76 & 0.83 & 0.94 & 1.01 & 230.00 \\ 
  gamma[19,1,1] & 0.95 & 0.03 & 0.87 & 0.94 & 0.96 & 0.98 & 0.99 & 1.00 & 1300.00 \\ 
  gamma[20,1,1] & 0.87 & 0.06 & 0.73 & 0.83 & 0.87 & 0.91 & 0.96 & 1.01 & 450.00 \\ 
  gamma[21,1,1] & 0.88 & 0.06 & 0.74 & 0.84 & 0.89 & 0.93 & 0.98 & 1.00 & 700.00 \\ 
  gamma[22,1,1] & 0.97 & 0.02 & 0.91 & 0.96 & 0.98 & 0.99 & 1.00 & 1.01 & 760.00 \\ 
  gamma[23,1,1] & 0.11 & 0.04 & 0.04 & 0.08 & 0.10 & 0.13 & 0.19 & 1.00 & 4000.00 \\ 
  gamma[24,1,1] & 0.96 & 0.03 & 0.87 & 0.94 & 0.96 & 0.98 & 1.00 & 1.01 & 560.00 \\ 
  gamma[25,1,1] & 0.13 & 0.04 & 0.07 & 0.11 & 0.13 & 0.16 & 0.21 & 1.01 & 460.00 \\ 
  gamma[1,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,2,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,3,1] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,1,2] & 0.19 & 0.07 & 0.07 & 0.14 & 0.19 & 0.23 & 0.33 & 1.01 & 1100.00 \\ 
  gamma[2,1,2] & 0.15 & 0.05 & 0.05 & 0.11 & 0.14 & 0.18 & 0.27 & 1.00 & 4000.00 \\ 
  gamma[3,1,2] & 0.35 & 0.09 & 0.18 & 0.28 & 0.34 & 0.41 & 0.54 & 1.01 & 280.00 \\ 
  gamma[4,1,2] & 0.34 & 0.11 & 0.12 & 0.26 & 0.34 & 0.41 & 0.54 & 1.01 & 750.00 \\ 
  gamma[5,1,2] & 0.22 & 0.08 & 0.06 & 0.16 & 0.21 & 0.27 & 0.38 & 1.01 & 1800.00 \\ 
  gamma[6,1,2] & 0.23 & 0.09 & 0.07 & 0.16 & 0.22 & 0.28 & 0.40 & 1.01 & 430.00 \\ 
  gamma[7,1,2] & 0.17 & 0.07 & 0.05 & 0.13 & 0.17 & 0.21 & 0.32 & 1.08 & 88.00 \\ 
  gamma[8,1,2] & 0.19 & 0.10 & 0.01 & 0.12 & 0.18 & 0.25 & 0.39 & 1.11 & 91.00 \\ 
  gamma[9,1,2] & 0.12 & 0.11 & 0.00 & 0.04 & 0.09 & 0.17 & 0.41 & 1.02 & 350.00 \\ 
  gamma[10,1,2] & 0.16 & 0.11 & 0.01 & 0.07 & 0.14 & 0.23 & 0.43 & 1.02 & 270.00 \\ 
  gamma[11,1,2] & 0.75 & 0.06 & 0.63 & 0.71 & 0.75 & 0.79 & 0.86 & 1.00 & 4000.00 \\ 
  gamma[12,1,2] & 0.03 & 0.03 & 0.00 & 0.01 & 0.02 & 0.04 & 0.10 & 1.01 & 450.00 \\ 
  gamma[13,1,2] & 0.03 & 0.03 & 0.00 & 0.01 & 0.02 & 0.04 & 0.10 & 1.00 & 3100.00 \\ 
  gamma[14,1,2] & 0.35 & 0.12 & 0.10 & 0.26 & 0.35 & 0.43 & 0.59 & 1.00 & 610.00 \\ 
  gamma[15,1,2] & 0.13 & 0.10 & 0.00 & 0.05 & 0.11 & 0.20 & 0.38 & 1.01 & 400.00 \\ 
  gamma[16,1,2] & 0.35 & 0.11 & 0.15 & 0.27 & 0.34 & 0.42 & 0.58 & 1.00 & 830.00 \\ 
  gamma[17,1,2] & 0.26 & 0.10 & 0.09 & 0.19 & 0.26 & 0.33 & 0.47 & 1.01 & 330.00 \\ 
  gamma[18,1,2] & 0.23 & 0.10 & 0.05 & 0.15 & 0.22 & 0.30 & 0.45 & 1.03 & 140.00 \\ 
  gamma[19,1,2] & 0.03 & 0.03 & 0.00 & 0.01 & 0.02 & 0.04 & 0.10 & 1.01 & 590.00 \\ 
  gamma[20,1,2] & 0.06 & 0.04 & 0.00 & 0.02 & 0.05 & 0.08 & 0.16 & 1.01 & 550.00 \\ 
  gamma[21,1,2] & 0.05 & 0.05 & 0.00 & 0.02 & 0.04 & 0.07 & 0.18 & 1.01 & 4000.00 \\ 
  gamma[22,1,2] & 0.02 & 0.02 & 0.00 & 0.01 & 0.01 & 0.03 & 0.07 & 1.00 & 2300.00 \\ 
  gamma[23,1,2] & 0.89 & 0.04 & 0.80 & 0.87 & 0.89 & 0.92 & 0.96 & 1.00 & 1900.00 \\ 
  gamma[24,1,2] & 0.03 & 0.02 & 0.00 & 0.01 & 0.02 & 0.04 & 0.09 & 1.00 & 1100.00 \\ 
  gamma[25,1,2] & 0.86 & 0.04 & 0.78 & 0.84 & 0.86 & 0.89 & 0.93 & 1.00 & 560.00 \\ 
  gamma[1,2,2] & 0.91 & 0.08 & 0.71 & 0.86 & 0.93 & 0.97 & 1.00 & 1.00 & 1400.00 \\ 
  gamma[2,2,2] & 0.88 & 0.08 & 0.70 & 0.84 & 0.90 & 0.94 & 0.99 & 1.00 & 2300.00 \\ 
  gamma[3,2,2] & 0.56 & 0.10 & 0.37 & 0.49 & 0.56 & 0.63 & 0.78 & 1.00 & 740.00 \\ 
  gamma[4,2,2] & 0.84 & 0.11 & 0.58 & 0.77 & 0.85 & 0.92 & 0.99 & 1.01 & 540.00 \\ 
  gamma[5,2,2] & 0.81 & 0.11 & 0.57 & 0.74 & 0.82 & 0.90 & 0.99 & 1.00 & 1700.00 \\ 
  gamma[6,2,2] & 0.73 & 0.12 & 0.50 & 0.64 & 0.72 & 0.82 & 0.96 & 1.01 & 460.00 \\ 
  gamma[7,2,2] & 0.51 & 0.11 & 0.30 & 0.43 & 0.50 & 0.58 & 0.74 & 1.02 & 140.00 \\ 
  gamma[8,2,2] & 0.85 & 0.09 & 0.64 & 0.79 & 0.86 & 0.92 & 0.99 & 1.00 & 1000.00 \\ 
  gamma[9,2,2] & 0.79 & 0.10 & 0.57 & 0.73 & 0.79 & 0.86 & 0.96 & 1.00 & 3400.00 \\ 
  gamma[10,2,2] & 0.94 & 0.05 & 0.81 & 0.91 & 0.95 & 0.98 & 1.00 & 1.01 & 740.00 \\ 
  gamma[11,2,2] & 0.62 & 0.05 & 0.52 & 0.59 & 0.62 & 0.66 & 0.73 & 1.00 & 3100.00 \\ 
  gamma[12,2,2] & 0.95 & 0.04 & 0.85 & 0.93 & 0.96 & 0.98 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[13,2,2] & 0.95 & 0.04 & 0.84 & 0.93 & 0.96 & 0.98 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[14,2,2] & 0.21 & 0.05 & 0.13 & 0.18 & 0.21 & 0.24 & 0.31 & 1.00 & 1200.00 \\ 
  gamma[15,2,2] & 0.60 & 0.15 & 0.32 & 0.49 & 0.59 & 0.70 & 0.91 & 1.00 & 770.00 \\ 
  gamma[16,2,2] & 0.09 & 0.03 & 0.05 & 0.07 & 0.09 & 0.11 & 0.15 & 1.00 & 1300.00 \\ 
  gamma[17,2,2] & 0.30 & 0.07 & 0.17 & 0.25 & 0.29 & 0.34 & 0.44 & 1.00 & 590.00 \\ 
  gamma[18,2,2] & 0.28 & 0.06 & 0.17 & 0.24 & 0.28 & 0.33 & 0.42 & 1.01 & 290.00 \\ 
  gamma[19,2,2] & 0.97 & 0.03 & 0.89 & 0.96 & 0.98 & 0.99 & 1.00 & 1.00 & 1100.00 \\ 
  gamma[20,2,2] & 0.93 & 0.05 & 0.80 & 0.91 & 0.95 & 0.97 & 1.00 & 1.02 & 220.00 \\ 
  gamma[21,2,2] & 0.95 & 0.04 & 0.84 & 0.94 & 0.97 & 0.98 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[22,2,2] & 0.94 & 0.04 & 0.83 & 0.92 & 0.95 & 0.98 & 1.00 & 1.00 & 1100.00 \\ 
  gamma[23,2,2] & 0.75 & 0.06 & 0.63 & 0.70 & 0.75 & 0.79 & 0.88 & 1.00 & 2300.00 \\ 
  gamma[24,2,2] & 0.94 & 0.05 & 0.81 & 0.92 & 0.96 & 0.98 & 1.00 & 1.00 & 4000.00 \\ 
  gamma[25,2,2] & 0.54 & 0.05 & 0.44 & 0.50 & 0.54 & 0.58 & 0.64 & 1.00 & 2200.00 \\ 
  gamma[1,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[2,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[3,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[4,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[5,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[6,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[7,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[8,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[9,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[10,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[11,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[12,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[13,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[14,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[15,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[16,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[17,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[18,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[19,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[20,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[21,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[22,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[23,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[24,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[25,3,2] & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 \\ 
  gamma[1,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.11 & 1.01 & 330.00 \\ 
  gamma[2,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.03 & 170.00 \\ 
  gamma[3,1,3] & 0.03 & 0.05 & 0.00 & 0.00 & 0.02 & 0.05 & 0.17 & 1.02 & 280.00 \\ 
  gamma[4,1,3] & 0.08 & 0.06 & 0.00 & 0.02 & 0.06 & 0.11 & 0.23 & 1.03 & 140.00 \\ 
  gamma[5,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.09 & 56.00 \\ 
  gamma[6,1,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.08 & 1.01 & 200.00 \\ 
  gamma[7,1,3] & 0.03 & 0.03 & 0.00 & 0.00 & 0.02 & 0.04 & 0.13 & 1.06 & 57.00 \\ 
  gamma[8,1,3] & 0.05 & 0.05 & 0.00 & 0.01 & 0.03 & 0.07 & 0.19 & 1.11 & 45.00 \\ 
  gamma[9,1,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.07 & 1.01 & 460.00 \\ 
  gamma[10,1,3] & 0.06 & 0.06 & 0.00 & 0.02 & 0.05 & 0.10 & 0.22 & 1.02 & 170.00 \\ 
  gamma[11,1,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.06 & 1.05 & 110.00 \\ 
  gamma[12,1,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.02 & 0.08 & 1.00 & 1300.00 \\ 
  gamma[13,1,3] & 0.01 & 0.02 & 0.00 & 0.00 & 0.01 & 0.01 & 0.05 & 1.03 & 150.00 \\ 
  gamma[14,1,3] & 0.03 & 0.03 & 0.00 & 0.00 & 0.01 & 0.04 & 0.12 & 1.02 & 240.00 \\ 
  gamma[15,1,3] & 0.04 & 0.05 & 0.00 & 0.01 & 0.02 & 0.06 & 0.21 & 1.01 & 390.00 \\ 
  gamma[16,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.12 & 1.03 & 110.00 \\ 
  gamma[17,1,3] & 0.04 & 0.04 & 0.00 & 0.01 & 0.02 & 0.05 & 0.16 & 1.03 & 180.00 \\ 
  gamma[18,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.11 & 63.00 \\ 
  gamma[19,1,3] & 0.02 & 0.02 & 0.00 & 0.00 & 0.01 & 0.03 & 0.08 & 1.03 & 150.00 \\ 
  gamma[20,1,3] & 0.08 & 0.06 & 0.00 & 0.03 & 0.06 & 0.11 & 0.21 & 1.01 & 540.00 \\ 
  gamma[21,1,3] & 0.07 & 0.05 & 0.00 & 0.03 & 0.06 & 0.10 & 0.19 & 1.02 & 520.00 \\ 
  gamma[22,1,3] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.05 & 1.12 & 63.00 \\ 
  gamma[23,1,3] & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.02 & 1.06 & 340.00 \\ 
  gamma[24,1,3] & 0.02 & 0.03 & 0.00 & 0.00 & 0.01 & 0.03 & 0.10 & 1.01 & 280.00 \\ 
  gamma[25,1,3] & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 & 0.03 & 1.02 & 250.00 \\ 
  gamma[1,2,3] & 0.09 & 0.08 & 0.00 & 0.03 & 0.07 & 0.14 & 0.29 & 1.01 & 1600.00 \\ 
  gamma[2,2,3] & 0.12 & 0.08 & 0.01 & 0.06 & 0.10 & 0.16 & 0.30 & 1.00 & 4000.00 \\ 
  gamma[3,2,3] & 0.44 & 0.10 & 0.22 & 0.37 & 0.44 & 0.51 & 0.63 & 1.01 & 750.00 \\ 
  gamma[4,2,3] & 0.16 & 0.11 & 0.01 & 0.08 & 0.15 & 0.23 & 0.42 & 1.01 & 550.00 \\ 
  gamma[5,2,3] & 0.19 & 0.11 & 0.01 & 0.10 & 0.18 & 0.26 & 0.43 & 1.01 & 970.00 \\ 
  gamma[6,2,3] & 0.27 & 0.12 & 0.04 & 0.18 & 0.28 & 0.36 & 0.50 & 1.01 & 430.00 \\ 
  gamma[7,2,3] & 0.49 & 0.11 & 0.26 & 0.42 & 0.50 & 0.57 & 0.70 & 1.01 & 220.00 \\ 
  gamma[8,2,3] & 0.15 & 0.09 & 0.01 & 0.08 & 0.14 & 0.21 & 0.36 & 1.00 & 1100.00 \\ 
  gamma[9,2,3] & 0.21 & 0.10 & 0.04 & 0.14 & 0.21 & 0.27 & 0.43 & 1.01 & 1200.00 \\ 
  gamma[10,2,3] & 0.06 & 0.05 & 0.00 & 0.02 & 0.05 & 0.09 & 0.19 & 1.00 & 830.00 \\ 
  gamma[11,2,3] & 0.38 & 0.05 & 0.27 & 0.34 & 0.38 & 0.41 & 0.48 & 1.00 & 3300.00 \\ 
  gamma[12,2,3] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.15 & 1.01 & 910.00 \\ 
  gamma[13,2,3] & 0.05 & 0.04 & 0.00 & 0.02 & 0.04 & 0.07 & 0.16 & 1.00 & 4000.00 \\ 
  gamma[14,2,3] & 0.79 & 0.05 & 0.69 & 0.76 & 0.79 & 0.82 & 0.87 & 1.00 & 1100.00 \\ 
  gamma[15,2,3] & 0.40 & 0.15 & 0.09 & 0.30 & 0.41 & 0.51 & 0.68 & 1.01 & 770.00 \\ 
  gamma[16,2,3] & 0.91 & 0.03 & 0.85 & 0.89 & 0.91 & 0.93 & 0.95 & 1.00 & 1500.00 \\ 
  gamma[17,2,3] & 0.70 & 0.07 & 0.56 & 0.66 & 0.71 & 0.75 & 0.83 & 1.00 & 640.00 \\ 
  gamma[18,2,3] & 0.72 & 0.06 & 0.58 & 0.67 & 0.72 & 0.76 & 0.83 & 1.01 & 310.00 \\ 
  gamma[19,2,3] & 0.03 & 0.03 & 0.00 & 0.01 & 0.02 & 0.04 & 0.11 & 1.00 & 940.00 \\ 
  gamma[20,2,3] & 0.07 & 0.05 & 0.00 & 0.03 & 0.05 & 0.09 & 0.20 & 1.01 & 390.00 \\ 
  gamma[21,2,3] & 0.05 & 0.04 & 0.00 & 0.02 & 0.03 & 0.06 & 0.16 & 1.00 & 2700.00 \\ 
  gamma[22,2,3] & 0.06 & 0.04 & 0.00 & 0.02 & 0.05 & 0.08 & 0.17 & 1.01 & 370.00 \\ 
  gamma[23,2,3] & 0.25 & 0.06 & 0.12 & 0.21 & 0.25 & 0.30 & 0.37 & 1.00 & 4000.00 \\ 
  gamma[24,2,3] & 0.06 & 0.05 & 0.00 & 0.02 & 0.04 & 0.08 & 0.19 & 1.00 & 2800.00 \\ 
  gamma[25,2,3] & 0.46 & 0.05 & 0.36 & 0.42 & 0.46 & 0.50 & 0.56 & 1.00 & 1900.00 \\ 
  gamma[1,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[2,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[3,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[4,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[5,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[6,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[7,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[8,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[9,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[10,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[11,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[12,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[13,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[14,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[15,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[16,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[17,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[18,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[19,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[20,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[21,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[22,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[23,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[24,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  gamma[25,3,3] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  inv.phi[1,1] & 3.20 & 1.55 & 0.90 & 2.04 & 2.96 & 4.08 & 6.88 & 1.03 & 110.00 \\ 
  inv.phi[2,1] & -0.52 & 1.06 & -2.78 & -1.17 & -0.50 & 0.17 & 1.57 & 1.05 & 53.00 \\ 
  inv.phi[3,1] & -1.17 & 1.12 & -3.74 & -1.79 & -1.04 & -0.42 & 0.72 & 1.06 & 54.00 \\ 
  inv.phi[4,1] & -1.19 & 1.35 & -4.24 & -1.97 & -1.04 & -0.24 & 0.99 & 1.04 & 68.00 \\ 
  inv.phi[1,2] & -0.52 & 1.06 & -2.78 & -1.17 & -0.50 & 0.17 & 1.57 & 1.05 & 53.00 \\ 
  inv.phi[2,2] & 2.93 & 1.51 & 0.68 & 1.83 & 2.64 & 3.79 & 6.54 & 1.10 & 34.00 \\ 
  inv.phi[3,2] & -0.10 & 0.95 & -2.18 & -0.63 & -0.06 & 0.50 & 1.65 & 1.03 & 82.00 \\ 
  inv.phi[4,2] & -2.00 & 1.42 & -5.26 & -2.81 & -1.75 & -0.93 & 0.07 & 1.05 & 62.00 \\ 
  inv.phi[1,3] & -1.17 & 1.12 & -3.74 & -1.79 & -1.04 & -0.42 & 0.72 & 1.06 & 54.00 \\ 
  inv.phi[2,3] & -0.10 & 0.95 & -2.18 & -0.63 & -0.06 & 0.50 & 1.65 & 1.03 & 82.00 \\ 
  inv.phi[3,3] & 2.60 & 1.32 & 0.70 & 1.60 & 2.39 & 3.32 & 5.71 & 1.05 & 59.00 \\ 
  inv.phi[4,3] & -0.82 & 1.27 & -3.62 & -1.60 & -0.69 & 0.10 & 1.34 & 1.05 & 65.00 \\ 
  inv.phi[1,4] & -1.19 & 1.35 & -4.24 & -1.97 & -1.04 & -0.24 & 0.99 & 1.04 & 68.00 \\ 
  inv.phi[2,4] & -2.00 & 1.42 & -5.26 & -2.81 & -1.75 & -0.93 & 0.07 & 1.05 & 62.00 \\ 
  inv.phi[3,4] & -0.82 & 1.27 & -3.62 & -1.60 & -0.69 & 0.10 & 1.34 & 1.05 & 65.00 \\ 
  inv.phi[4,4] & 3.89 & 2.18 & 0.77 & 2.24 & 3.50 & 5.15 & 9.04 & 1.03 & 95.00 \\ 
  lambda[1] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[2] & 1.46 & 0.18 & 1.13 & 1.33 & 1.45 & 1.58 & 1.84 & 1.01 & 620.00 \\ 
  lambda[3] & 1.36 & 0.18 & 1.05 & 1.23 & 1.34 & 1.47 & 1.73 & 1.01 & 460.00 \\ 
  lambda[4] & 1.01 & 0.13 & 0.76 & 0.93 & 1.01 & 1.10 & 1.29 & 1.02 & 100.00 \\ 
  lambda[5] & 1.13 & 0.13 & 0.90 & 1.04 & 1.12 & 1.21 & 1.38 & 1.01 & 500.00 \\ 
  lambda[6] & 1.09 & 0.14 & 0.83 & 0.99 & 1.08 & 1.18 & 1.36 & 1.01 & 240.00 \\ 
  lambda[7] & 1.41 & 0.18 & 1.10 & 1.28 & 1.40 & 1.54 & 1.80 & 1.01 & 330.00 \\ 
  lambda[8] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[9] & 0.86 & 0.09 & 0.69 & 0.80 & 0.86 & 0.93 & 1.05 & 1.02 & 140.00 \\ 
  lambda[10] & 0.76 & 0.10 & 0.58 & 0.69 & 0.75 & 0.82 & 0.96 & 1.01 & 230.00 \\ 
  lambda[11] & 0.76 & 0.10 & 0.58 & 0.69 & 0.76 & 0.83 & 0.97 & 1.01 & 290.00 \\ 
  lambda[12] & 0.92 & 0.09 & 0.77 & 0.86 & 0.92 & 0.98 & 1.11 & 1.01 & 290.00 \\ 
  lambda[13] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[14] & 0.83 & 0.13 & 0.58 & 0.74 & 0.82 & 0.92 & 1.09 & 1.03 & 110.00 \\ 
  lambda[15] & 0.49 & 0.07 & 0.36 & 0.44 & 0.48 & 0.54 & 0.65 & 1.02 & 180.00 \\ 
  lambda[16] & 1.40 & 0.25 & 0.96 & 1.23 & 1.38 & 1.56 & 1.92 & 1.02 & 120.00 \\ 
  lambda[17] & 1.29 & 0.21 & 0.93 & 1.14 & 1.28 & 1.45 & 1.70 & 1.04 & 71.00 \\ 
  lambda[18] & 0.91 & 0.14 & 0.66 & 0.81 & 0.90 & 0.99 & 1.21 & 1.02 & 160.00 \\ 
  lambda[19] & 1.00 & 0.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\ 
  lambda[20] & 1.20 & 0.13 & 0.97 & 1.11 & 1.19 & 1.28 & 1.47 & 1.01 & 760.00 \\ 
  lambda[21] & 0.96 & 0.10 & 0.77 & 0.88 & 0.95 & 1.02 & 1.16 & 1.00 & 870.00 \\ 
  lambda[22] & 1.11 & 0.10 & 0.92 & 1.04 & 1.11 & 1.18 & 1.32 & 1.01 & 240.00 \\ 
  lambda[23] & 0.93 & 0.11 & 0.73 & 0.86 & 0.93 & 1.01 & 1.18 & 1.01 & 270.00 \\ 
  lambda[24] & 0.91 & 0.09 & 0.75 & 0.85 & 0.90 & 0.97 & 1.11 & 1.01 & 430.00 \\ 
  lambda[25] & 0.84 & 0.10 & 0.66 & 0.77 & 0.84 & 0.90 & 1.05 & 1.01 & 250.00 \\ 
  lambda.std[1] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[2] & 0.82 & 0.03 & 0.75 & 0.80 & 0.82 & 0.84 & 0.88 & 1.01 & 840.00 \\ 
  lambda.std[3] & 0.80 & 0.04 & 0.72 & 0.78 & 0.80 & 0.83 & 0.87 & 1.01 & 390.00 \\ 
  lambda.std[4] & 0.71 & 0.05 & 0.61 & 0.68 & 0.71 & 0.74 & 0.79 & 1.02 & 110.00 \\ 
  lambda.std[5] & 0.74 & 0.04 & 0.67 & 0.72 & 0.75 & 0.77 & 0.81 & 1.01 & 420.00 \\ 
  lambda.std[6] & 0.73 & 0.04 & 0.64 & 0.70 & 0.73 & 0.76 & 0.81 & 1.01 & 270.00 \\ 
  lambda.std[7] & 0.81 & 0.04 & 0.74 & 0.79 & 0.81 & 0.84 & 0.87 & 1.01 & 290.00 \\ 
  lambda.std[8] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[9] & 0.65 & 0.04 & 0.57 & 0.62 & 0.65 & 0.68 & 0.72 & 1.02 & 140.00 \\ 
  lambda.std[10] & 0.60 & 0.05 & 0.50 & 0.57 & 0.60 & 0.63 & 0.69 & 1.02 & 210.00 \\ 
  lambda.std[11] & 0.60 & 0.05 & 0.50 & 0.57 & 0.60 & 0.64 & 0.70 & 1.01 & 290.00 \\ 
  lambda.std[12] & 0.68 & 0.03 & 0.61 & 0.65 & 0.68 & 0.70 & 0.74 & 1.01 & 290.00 \\ 
  lambda.std[13] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[14] & 0.63 & 0.06 & 0.50 & 0.59 & 0.64 & 0.68 & 0.74 & 1.03 & 110.00 \\ 
  lambda.std[15] & 0.44 & 0.05 & 0.34 & 0.40 & 0.44 & 0.47 & 0.54 & 1.02 & 180.00 \\ 
  lambda.std[16] & 0.80 & 0.05 & 0.69 & 0.78 & 0.81 & 0.84 & 0.89 & 1.02 & 140.00 \\ 
  lambda.std[17] & 0.78 & 0.05 & 0.68 & 0.75 & 0.79 & 0.82 & 0.86 & 1.04 & 79.00 \\ 
  lambda.std[18] & 0.67 & 0.06 & 0.55 & 0.63 & 0.67 & 0.70 & 0.77 & 1.03 & 140.00 \\ 
  lambda.std[19] & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.71 & 0.71 & 1.00 & 1.00 \\ 
  lambda.std[20] & 0.76 & 0.03 & 0.70 & 0.74 & 0.77 & 0.79 & 0.83 & 1.01 & 820.00 \\ 
  lambda.std[21] & 0.69 & 0.04 & 0.61 & 0.66 & 0.69 & 0.72 & 0.76 & 1.00 & 830.00 \\ 
  lambda.std[22] & 0.74 & 0.03 & 0.68 & 0.72 & 0.74 & 0.76 & 0.80 & 1.01 & 220.00 \\ 
  lambda.std[23] & 0.68 & 0.04 & 0.59 & 0.65 & 0.68 & 0.71 & 0.76 & 1.01 & 270.00 \\ 
  lambda.std[24] & 0.67 & 0.04 & 0.60 & 0.65 & 0.67 & 0.69 & 0.74 & 1.01 & 420.00 \\ 
  lambda.std[25] & 0.64 & 0.05 & 0.55 & 0.61 & 0.64 & 0.67 & 0.73 & 1.01 & 240.00 \\ 
  phi[1,1] & 2.59 & 1.41 & 0.72 & 1.51 & 2.33 & 3.38 & 6.13 & 1.01 & 580.00 \\ 
  phi[2,1] & 2.02 & 1.22 & 0.21 & 1.17 & 1.87 & 2.76 & 4.78 & 1.04 & 110.00 \\ 
  phi[3,1] & 1.87 & 1.28 & 0.00 & 1.03 & 1.68 & 2.47 & 4.96 & 1.03 & 210.00 \\ 
  phi[4,1] & 2.16 & 0.96 & 0.25 & 1.51 & 2.17 & 2.82 & 4.00 & 1.01 & 400.00 \\ 
  phi[1,2] & 2.02 & 1.22 & 0.21 & 1.17 & 1.87 & 2.76 & 4.78 & 1.04 & 110.00 \\ 
  phi[2,2] & 3.22 & 2.52 & 0.97 & 1.89 & 2.64 & 3.77 & 9.48 & 1.13 & 32.00 \\ 
  phi[3,2] & 1.78 & 1.28 & -0.60 & 1.03 & 1.73 & 2.47 & 4.35 & 1.04 & 180.00 \\ 
  phi[4,2] & 2.53 & 0.95 & 0.73 & 1.92 & 2.47 & 3.09 & 4.44 & 1.09 & 46.00 \\ 
  phi[1,3] & 1.87 & 1.28 & 0.00 & 1.03 & 1.68 & 2.47 & 4.96 & 1.03 & 210.00 \\ 
  phi[2,3] & 1.78 & 1.28 & -0.60 & 1.03 & 1.73 & 2.47 & 4.35 & 1.04 & 180.00 \\ 
  phi[3,3] & 2.59 & 1.68 & 0.70 & 1.54 & 2.23 & 3.14 & 6.44 & 1.04 & 120.00 \\ 
  phi[4,3] & 1.91 & 1.13 & -0.75 & 1.34 & 2.06 & 2.62 & 3.85 & 1.03 & 370.00 \\ 
  phi[1,4] & 2.16 & 0.96 & 0.25 & 1.51 & 2.17 & 2.82 & 4.00 & 1.01 & 400.00 \\ 
  phi[2,4] & 2.53 & 0.95 & 0.73 & 1.92 & 2.47 & 3.09 & 4.44 & 1.09 & 46.00 \\ 
  phi[3,4] & 1.91 & 1.13 & -0.75 & 1.34 & 2.06 & 2.62 & 3.85 & 1.03 & 370.00 \\ 
  phi[4,4] & 2.96 & 0.31 & 2.41 & 2.74 & 2.94 & 3.17 & 3.59 & 1.01 & 220.00 \\ 
  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] & 0.73 & 0.22 & 0.13 & 0.66 & 0.80 & 0.88 & 0.95 & 1.07 & 100.00 \\ 
  phi.cor[3,1] & 0.72 & 0.24 & 0.00 & 0.65 & 0.79 & 0.88 & 0.95 & 1.02 & 170.00 \\ 
  phi.cor[4,1] & 0.78 & 0.21 & 0.12 & 0.73 & 0.86 & 0.91 & 0.96 & 1.07 & 120.00 \\ 
  phi.cor[1,2] & 0.73 & 0.22 & 0.13 & 0.66 & 0.80 & 0.88 & 0.95 & 1.07 & 100.00 \\ 
  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 & 0.30 & -0.25 & 0.57 & 0.76 & 0.85 & 0.93 & 1.05 & 170.00 \\ 
  phi.cor[4,2] & 0.84 & 0.15 & 0.40 & 0.82 & 0.89 & 0.93 & 0.97 & 1.04 & 160.00 \\ 
  phi.cor[1,3] & 0.72 & 0.24 & 0.00 & 0.65 & 0.79 & 0.88 & 0.95 & 1.02 & 170.00 \\ 
  phi.cor[2,3] & 0.65 & 0.30 & -0.25 & 0.57 & 0.76 & 0.85 & 0.93 & 1.05 & 170.00 \\ 
  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] & 0.70 & 0.32 & -0.35 & 0.66 & 0.82 & 0.89 & 0.95 & 1.06 & 97.00 \\ 
  phi.cor[1,4] & 0.78 & 0.21 & 0.12 & 0.73 & 0.86 & 0.91 & 0.96 & 1.07 & 120.00 \\ 
  phi.cor[2,4] & 0.84 & 0.15 & 0.40 & 0.82 & 0.89 & 0.93 & 0.97 & 1.04 & 160.00 \\ 
  phi.cor[3,4] & 0.70 & 0.32 & -0.35 & 0.66 & 0.82 & 0.89 & 0.95 & 1.06 & 97.00 \\ 
  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] & 0.91 & 0.01 & 0.89 & 0.90 & 0.91 & 0.92 & 0.93 & 1.01 & 660.00 \\ 
  reli.omega[2] & 0.82 & 0.01 & 0.80 & 0.82 & 0.82 & 0.83 & 0.85 & 1.03 & 95.00 \\ 
  reli.omega[3] & 0.85 & 0.02 & 0.81 & 0.84 & 0.85 & 0.87 & 0.89 & 1.02 & 230.00 \\ 
  reli.omega[4] & 0.86 & 0.01 & 0.84 & 0.85 & 0.86 & 0.87 & 0.88 & 1.02 & 190.00 \\ 
  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] & 3.13 & 0.17 & 2.80 & 3.01 & 3.12 & 3.24 & 3.45 & 1.00 & 890.00 \\ 
  tau[2,2] & 4.01 & 0.36 & 3.38 & 3.75 & 3.99 & 4.24 & 4.81 & 1.01 & 230.00 \\ 
  tau[3,2] & 3.62 & 0.32 & 3.04 & 3.40 & 3.61 & 3.83 & 4.28 & 1.00 & 2500.00 \\ 
  tau[4,2] & 2.21 & 0.18 & 1.87 & 2.09 & 2.20 & 2.32 & 2.58 & 1.02 & 150.00 \\ 
  tau[5,2] & 2.74 & 0.21 & 2.35 & 2.59 & 2.73 & 2.87 & 3.16 & 1.01 & 540.00 \\ 
  tau[6,2] & 3.16 & 0.25 & 2.68 & 2.98 & 3.14 & 3.32 & 3.69 & 1.01 & 420.00 \\ 
  tau[7,2] & 4.33 & 0.39 & 3.64 & 4.05 & 4.30 & 4.57 & 5.17 & 1.01 & 240.00 \\ 
  tau[8,2] & 2.05 & 0.13 & 1.80 & 1.96 & 2.05 & 2.14 & 2.31 & 1.00 & 1300.00 \\ 
  tau[9,2] & 0.95 & 0.14 & 0.66 & 0.87 & 0.97 & 1.05 & 1.20 & 1.00 & 4000.00 \\ 
  tau[10,2] & 1.51 & 0.11 & 1.29 & 1.43 & 1.51 & 1.59 & 1.74 & 1.00 & 890.00 \\ 
  tau[11,2] & 0.08 & 0.06 & 0.00 & 0.03 & 0.06 & 0.12 & 0.23 & 1.00 & 4000.00 \\ 
  tau[12,2] & 1.75 & 0.11 & 1.53 & 1.67 & 1.74 & 1.82 & 1.97 & 1.00 & 680.00 \\ 
  tau[13,2] & 1.81 & 0.10 & 1.61 & 1.74 & 1.81 & 1.88 & 2.01 & 1.00 & 4000.00 \\ 
  tau[14,2] & 2.92 & 0.22 & 2.52 & 2.76 & 2.92 & 3.07 & 3.38 & 1.01 & 230.00 \\ 
  tau[15,2] & 1.42 & 0.14 & 1.17 & 1.33 & 1.42 & 1.52 & 1.70 & 1.00 & 1100.00 \\ 
  tau[16,2] & 4.98 & 0.54 & 4.05 & 4.60 & 4.94 & 5.32 & 6.11 & 1.03 & 100.00 \\ 
  tau[17,2] & 3.80 & 0.34 & 3.18 & 3.55 & 3.78 & 4.02 & 4.52 & 1.04 & 81.00 \\ 
  tau[18,2] & 3.22 & 0.25 & 2.74 & 3.05 & 3.21 & 3.38 & 3.73 & 1.01 & 340.00 \\ 
  tau[19,2] & 2.15 & 0.11 & 1.93 & 2.07 & 2.15 & 2.23 & 2.37 & 1.00 & 1600.00 \\ 
  tau[20,2] & 2.99 & 0.21 & 2.61 & 2.84 & 2.97 & 3.12 & 3.42 & 1.00 & 560.00 \\ 
  tau[21,2] & 1.77 & 0.12 & 1.54 & 1.69 & 1.77 & 1.85 & 2.01 & 1.00 & 2200.00 \\ 
  tau[22,2] & 2.15 & 0.14 & 1.90 & 2.06 & 2.15 & 2.24 & 2.43 & 1.00 & 1000.00 \\ 
  tau[23,2] & 0.14 & 0.08 & 0.01 & 0.07 & 0.14 & 0.19 & 0.30 & 1.00 & 4000.00 \\ 
  tau[24,2] & 1.98 & 0.12 & 1.75 & 1.89 & 1.98 & 2.06 & 2.23 & 1.00 & 2100.00 \\ 
  tau[25,2] & 0.05 & 0.04 & 0.00 & 0.02 & 0.03 & 0.07 & 0.14 & 1.00 & 1100.00 \\ 
  theta[1] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[2] & 3.16 & 0.54 & 2.27 & 2.77 & 3.09 & 3.49 & 4.39 & 1.01 & 540.00 \\ 
  theta[3] & 2.88 & 0.50 & 2.10 & 2.52 & 2.81 & 3.16 & 4.01 & 1.01 & 510.00 \\ 
  theta[4] & 2.04 & 0.27 & 1.58 & 1.86 & 2.02 & 2.20 & 2.67 & 1.03 & 100.00 \\ 
  theta[5] & 2.29 & 0.29 & 1.82 & 2.08 & 2.26 & 2.47 & 2.91 & 1.01 & 570.00 \\ 
  theta[6] & 2.20 & 0.30 & 1.70 & 1.99 & 2.17 & 2.38 & 2.85 & 1.01 & 220.00 \\ 
  theta[7] & 3.04 & 0.53 & 2.21 & 2.64 & 2.96 & 3.36 & 4.23 & 1.01 & 350.00 \\ 
  theta[8] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[9] & 1.76 & 0.17 & 1.47 & 1.64 & 1.74 & 1.86 & 2.11 & 1.02 & 140.00 \\ 
  theta[10] & 1.58 & 0.15 & 1.34 & 1.48 & 1.56 & 1.67 & 1.93 & 1.01 & 270.00 \\ 
  theta[11] & 1.59 & 0.16 & 1.33 & 1.48 & 1.57 & 1.69 & 1.95 & 1.01 & 290.00 \\ 
  theta[12] & 1.86 & 0.16 & 1.59 & 1.74 & 1.85 & 1.96 & 2.23 & 1.01 & 280.00 \\ 
  theta[13] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[14] & 1.70 & 0.22 & 1.33 & 1.55 & 1.68 & 1.84 & 2.18 & 1.02 & 120.00 \\ 
  theta[15] & 1.25 & 0.08 & 1.13 & 1.19 & 1.23 & 1.29 & 1.42 & 1.02 & 180.00 \\ 
  theta[16] & 3.02 & 0.71 & 1.93 & 2.50 & 2.92 & 3.43 & 4.68 & 1.03 & 110.00 \\ 
  theta[17] & 2.72 & 0.55 & 1.86 & 2.29 & 2.64 & 3.11 & 3.88 & 1.04 & 68.00 \\ 
  theta[18] & 1.84 & 0.26 & 1.43 & 1.66 & 1.81 & 1.99 & 2.46 & 1.02 & 200.00 \\ 
  theta[19] & 2.00 & 0.00 & 2.00 & 2.00 & 2.00 & 2.00 & 2.00 & 1.00 & 1.00 \\ 
  theta[20] & 2.45 & 0.31 & 1.94 & 2.23 & 2.42 & 2.64 & 3.17 & 1.01 & 710.00 \\ 
  theta[21] & 1.93 & 0.20 & 1.59 & 1.78 & 1.91 & 2.05 & 2.36 & 1.00 & 920.00 \\ 
  theta[22] & 2.24 & 0.23 & 1.86 & 2.08 & 2.23 & 2.38 & 2.74 & 1.01 & 250.00 \\ 
  theta[23] & 1.89 & 0.21 & 1.53 & 1.74 & 1.86 & 2.01 & 2.39 & 1.01 & 270.00 \\ 
  theta[24] & 1.84 & 0.17 & 1.57 & 1.72 & 1.82 & 1.93 & 2.23 & 1.01 & 450.00 \\ 
  theta[25] & 1.72 & 0.17 & 1.43 & 1.59 & 1.70 & 1.82 & 2.11 & 1.01 & 280.00 \\ 
   \bottomrule
\end{tabular}
\caption{pools Model 3 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