Adapted from the sirt package examples (data.read).
library(mirt)
library(sirt)
library(mvtnorm)
data(data.read)
dat <- data.read
I <- ncol(dat)
# use 10th item as the reference item
ref.item <- 10
# ability grid
theta.k <- seq(-4,4,len=9)
#-- M12a: rasch.mirtlc (in sirt)
mod12a <- sirt::rasch.mirtlc(dat , Nclasses=3, modeltype="MLC1" , ref.item=ref.item,
progress = FALSE )
summary(mod12a)
## ----------------------------------------------------------------------------------------------------------
## sirt 3.12-66 (2022-05-16 12:27:54)
##
## Date of Analysis: 2023-07-05 16:11:56
## Time difference of 0.2820177 secs
## Computation time: 0.2820177
##
## Multidimensional Item Response Latent Class Model
##
## Multidimensional Latent Class Rasch Model with
## 3 Classes , 1 Group(s) , 1 Dimension(s)
## ----------------------------------------------------------------------------------------------------------
## Number of iterations= 67
## Deviance= 3934.46 | Log Likelihood= -1967.23
## Number of persons= 328
## Number of estimated item parameters= 11
## Number of estimated distribution parameters= 5
## Number of estimated parameters= 16
## AIC= 3966.46 | penalty= 32 | AIC=-2*LL + 2*p
## AICc= 3968.21 | penalty= 33.75 | AICc=-2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## BIC= 4027.15 | penalty= 92.69 | BIC=-2*LL + log(n)*p
## CAIC= 4043.15 | penalty= 108.69 | CAIC=-2*LL + [log(n)+1]*p (consistent AIC)
##
## ----------------------------------------------------------------------------------------------------------
## Trait Distribution
## theta prob
## des.theta1 -1.696 0.029
## des.theta2 0.242 0.460
## des.theta3 2.019 0.510
##
## M Trait: 1.092
## SD Trait: 1
## Skewness Trait: -0.513
## ----------------------------------------------------------------------------------------------------------
## Item Parameters
## Item Probabilities
## Class1 Class2 Class3
## A1 0.328 0.771 0.952
## A2 0.176 0.597 0.897
## A3 0.078 0.368 0.775
## A4 0.047 0.255 0.670
## B1 0.156 0.561 0.883
## B2 0.058 0.301 0.718
## B3 0.475 0.862 0.974
## B4 0.134 0.517 0.864
## C1 0.569 0.902 0.982
## C2 0.156 0.561 0.883
## C3 0.371 0.804 0.960
## C4 0.173 0.592 0.895
##
## Item Parameter
## b a thresh
## A1 -0.973 1 -0.973
## A2 -0.149 1 -0.149
## A3 0.783 1 0.783
## A4 1.313 1 1.313
## B1 -0.002 1 -0.002
## B2 1.088 1 1.088
## B3 -1.591 1 -1.591
## B4 0.174 1 0.174
## C1 -1.971 1 -1.971
## C2 0.000 1 0.000
## C3 -1.166 1 -1.166
## C4 -0.127 1 -0.127
#-- M12b: gdm (in CDM)
theta.k <- seq(-1 , 1 , len=3)
# initial matrix
b.constraint <- matrix( c(10,1,0) , nrow=1,ncol=3)
# estimate model
mod12b <- CDM::gdm( dat , theta.k = theta.k , skillspace="est" , irtmodel="1PL",
b.constraint=b.constraint , maxiter=200)
## ......................................................................
## Iteration 1 2023-07-05 16:11:56
## Deviance = 3975.4685
## Maximum item intercept parameter change = 0.891647
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.055752
## ......................................................................
## Iteration 2 2023-07-05 16:11:56
## Deviance = 4001.393 | Deviance change = -25.924515 Deviance increases!
## Maximum item intercept parameter change = 0.167581
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.013919
## ......................................................................
## Iteration 3 2023-07-05 16:11:56
## Deviance = 3988.1822 | Deviance change = 13.210775
## Maximum item intercept parameter change = 0.113534
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002636
## ......................................................................
## Iteration 4 2023-07-05 16:11:56
## Deviance = 3979.4418 | Deviance change = 8.740395
## Maximum item intercept parameter change = 0.088862
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001584
## ......................................................................
## Iteration 5 2023-07-05 16:11:56
## Deviance = 3972.6152 | Deviance change = 6.826611
## Maximum item intercept parameter change = 0.076322
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002068
## ......................................................................
## Iteration 6 2023-07-05 16:11:56
## Deviance = 3967.19 | Deviance change = 5.425235
## Maximum item intercept parameter change = 0.068515
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002242
## ......................................................................
## Iteration 7 2023-07-05 16:11:56
## Deviance = 3962.874 | Deviance change = 4.316009
## Maximum item intercept parameter change = 0.061335
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00231
## ......................................................................
## Iteration 8 2023-07-05 16:11:56
## Deviance = 3959.4385 | Deviance change = 3.435474
## Maximum item intercept parameter change = 0.054841
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002341
## ......................................................................
## Iteration 9 2023-07-05 16:11:56
## Deviance = 3956.7009 | Deviance change = 2.737591
## Maximum item intercept parameter change = 0.049077
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002358
## ......................................................................
## Iteration 10 2023-07-05 16:11:56
## Deviance = 3954.5161 | Deviance change = 2.184807
## Maximum item intercept parameter change = 0.043998
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002373
## ......................................................................
## Iteration 11 2023-07-05 16:11:56
## Deviance = 3952.7693 | Deviance change = 1.746833
## Maximum item intercept parameter change = 0.039509
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002387
## ......................................................................
## Iteration 12 2023-07-05 16:11:56
## Deviance = 3951.3697 | Deviance change = 1.399576
## Maximum item intercept parameter change = 0.035536
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002405
## ......................................................................
## Iteration 13 2023-07-05 16:11:56
## Deviance = 3950.2457 | Deviance change = 1.124021
## Maximum item intercept parameter change = 0.032019
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002425
## ......................................................................
## Iteration 14 2023-07-05 16:11:56
## Deviance = 3949.3405 | Deviance change = 0.905207
## Maximum item intercept parameter change = 0.028888
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002447
## ......................................................................
## Iteration 15 2023-07-05 16:11:56
## Deviance = 3948.6091 | Deviance change = 0.731375
## Maximum item intercept parameter change = 0.026106
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002473
## ......................................................................
## Iteration 16 2023-07-05 16:11:56
## Deviance = 3948.0158 | Deviance change = 0.593273
## Maximum item intercept parameter change = 0.023627
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002502
## ......................................................................
## Iteration 17 2023-07-05 16:11:56
## Deviance = 3947.5322 | Deviance change = 0.48361
## Maximum item intercept parameter change = 0.021408
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002533
## ......................................................................
## Iteration 18 2023-07-05 16:11:56
## Deviance = 3947.1356 | Deviance change = 0.396627
## Maximum item intercept parameter change = 0.01942
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002567
## ......................................................................
## Iteration 19 2023-07-05 16:11:56
## Deviance = 3946.8078 | Deviance change = 0.327767
## Maximum item intercept parameter change = 0.017637
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002604
## ......................................................................
## Iteration 20 2023-07-05 16:11:56
## Deviance = 3946.5344 | Deviance change = 0.273415
## Maximum item intercept parameter change = 0.016039
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002642
## ......................................................................
## Iteration 21 2023-07-05 16:11:56
## Deviance = 3946.3037 | Deviance change = 0.230697
## Maximum item intercept parameter change = 0.014603
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002683
## ......................................................................
## Iteration 22 2023-07-05 16:11:56
## Deviance = 3946.1064 | Deviance change = 0.197326
## Maximum item intercept parameter change = 0.013314
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002726
## ......................................................................
## Iteration 23 2023-07-05 16:11:56
## Deviance = 3945.9349 | Deviance change = 0.171477
## Maximum item intercept parameter change = 0.012155
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002772
## ......................................................................
## Iteration 24 2023-07-05 16:11:56
## Deviance = 3945.7832 | Deviance change = 0.151691
## Maximum item intercept parameter change = 0.011115
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002818
## ......................................................................
## Iteration 25 2023-07-05 16:11:56
## Deviance = 3945.6464 | Deviance change = 0.136802
## Maximum item intercept parameter change = 0.010179
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002867
## ......................................................................
## Iteration 26 2023-07-05 16:11:56
## Deviance = 3945.5205 | Deviance change = 0.125875
## Maximum item intercept parameter change = 0.009337
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002917
## ......................................................................
## Iteration 27 2023-07-05 16:11:56
## Deviance = 3945.4024 | Deviance change = 0.118162
## Maximum item intercept parameter change = 0.00858
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002969
## ......................................................................
## Iteration 28 2023-07-05 16:11:56
## Deviance = 3945.2893 | Deviance change = 0.113061
## Maximum item intercept parameter change = 0.007898
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003022
## ......................................................................
## Iteration 29 2023-07-05 16:11:56
## Deviance = 3945.1792 | Deviance change = 0.11009
## Maximum item intercept parameter change = 0.007283
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003076
## ......................................................................
## Iteration 30 2023-07-05 16:11:56
## Deviance = 3945.0704 | Deviance change = 0.108864
## Maximum item intercept parameter change = 0.006728
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003131
## ......................................................................
## Iteration 31 2023-07-05 16:11:56
## Deviance = 3944.9613 | Deviance change = 0.109072
## Maximum item intercept parameter change = 0.006228
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003187
## ......................................................................
## Iteration 32 2023-07-05 16:11:56
## Deviance = 3944.8508 | Deviance change = 0.110466
## Maximum item intercept parameter change = 0.005775
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003244
## ......................................................................
## Iteration 33 2023-07-05 16:11:56
## Deviance = 3944.738 | Deviance change = 0.112848
## Maximum item intercept parameter change = 0.005367
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003301
## ......................................................................
## Iteration 34 2023-07-05 16:11:56
## Deviance = 3944.6219 | Deviance change = 0.11606
## Maximum item intercept parameter change = 0.004997
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003359
## ......................................................................
## Iteration 35 2023-07-05 16:11:56
## Deviance = 3944.5019 | Deviance change = 0.119975
## Maximum item intercept parameter change = 0.004662
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003416
## ......................................................................
## Iteration 36 2023-07-05 16:11:56
## Deviance = 3944.3774 | Deviance change = 0.124495
## Maximum item intercept parameter change = 0.004358
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003474
## ......................................................................
## Iteration 37 2023-07-05 16:11:56
## Deviance = 3944.2479 | Deviance change = 0.129541
## Maximum item intercept parameter change = 0.004083
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003531
## ......................................................................
## Iteration 38 2023-07-05 16:11:56
## Deviance = 3944.1128 | Deviance change = 0.135051
## Maximum item intercept parameter change = 0.003834
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003587
## ......................................................................
## Iteration 39 2023-07-05 16:11:56
## Deviance = 3943.9719 | Deviance change = 0.140979
## Maximum item intercept parameter change = 0.003606
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003643
## ......................................................................
## Iteration 40 2023-07-05 16:11:56
## Deviance = 3943.8246 | Deviance change = 0.147286
## Maximum item intercept parameter change = 0.003399
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003697
## ......................................................................
## Iteration 41 2023-07-05 16:11:56
## Deviance = 3943.6706 | Deviance change = 0.153944
## Maximum item intercept parameter change = 0.00321
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00375
## ......................................................................
## Iteration 42 2023-07-05 16:11:56
## Deviance = 3943.5097 | Deviance change = 0.160932
## Maximum item intercept parameter change = 0.003036
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003801
## ......................................................................
## Iteration 43 2023-07-05 16:11:56
## Deviance = 3943.3415 | Deviance change = 0.168229
## Maximum item intercept parameter change = 0.002877
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003849
## ......................................................................
## Iteration 44 2023-07-05 16:11:56
## Deviance = 3943.1657 | Deviance change = 0.175821
## Maximum item intercept parameter change = 0.00273
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003895
## ......................................................................
## Iteration 45 2023-07-05 16:11:56
## Deviance = 3942.982 | Deviance change = 0.183692
## Maximum item intercept parameter change = 0.002594
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003938
## ......................................................................
## Iteration 46 2023-07-05 16:11:56
## Deviance = 3942.7901 | Deviance change = 0.191825
## Maximum item intercept parameter change = 0.002468
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003977
## ......................................................................
## Iteration 47 2023-07-05 16:11:56
## Deviance = 3942.5899 | Deviance change = 0.2002
## Maximum item intercept parameter change = 0.00235
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004012
## ......................................................................
## Iteration 48 2023-07-05 16:11:56
## Deviance = 3942.3811 | Deviance change = 0.208792
## Maximum item intercept parameter change = 0.002239
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004042
## ......................................................................
## Iteration 49 2023-07-05 16:11:56
## Deviance = 3942.1636 | Deviance change = 0.217566
## Maximum item intercept parameter change = 0.002134
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004066
## ......................................................................
## Iteration 50 2023-07-05 16:11:56
## Deviance = 3941.9371 | Deviance change = 0.226478
## Maximum item intercept parameter change = 0.002033
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004085
## ......................................................................
## Iteration 51 2023-07-05 16:11:56
## Deviance = 3941.7016 | Deviance change = 0.235469
## Maximum item intercept parameter change = 0.001936
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004096
## ......................................................................
## Iteration 52 2023-07-05 16:11:56
## Deviance = 3941.4572 | Deviance change = 0.244463
## Maximum item intercept parameter change = 0.00184
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.0041
## ......................................................................
## Iteration 53 2023-07-05 16:11:56
## Deviance = 3941.2038 | Deviance change = 0.253365
## Maximum item intercept parameter change = 0.001745
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004095
## ......................................................................
## Iteration 54 2023-07-05 16:11:56
## Deviance = 3940.9418 | Deviance change = 0.262053
## Maximum item intercept parameter change = 0.00165
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004081
## ......................................................................
## Iteration 55 2023-07-05 16:11:56
## Deviance = 3940.6714 | Deviance change = 0.27038
## Maximum item intercept parameter change = 0.001551
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.004056
## ......................................................................
## Iteration 56 2023-07-05 16:11:56
## Deviance = 3940.3932 | Deviance change = 0.278171
## Maximum item intercept parameter change = 0.001449
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00402
## ......................................................................
## Iteration 57 2023-07-05 16:11:56
## Deviance = 3940.108 | Deviance change = 0.285219
## Maximum item intercept parameter change = 0.001341
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003971
## ......................................................................
## Iteration 58 2023-07-05 16:11:56
## Deviance = 3939.8167 | Deviance change = 0.291292
## Maximum item intercept parameter change = 0.001225
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00391
## ......................................................................
## Iteration 59 2023-07-05 16:11:56
## Deviance = 3939.5206 | Deviance change = 0.296137
## Maximum item intercept parameter change = 0.001099
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003834
## ......................................................................
## Iteration 60 2023-07-05 16:11:56
## Deviance = 3939.2211 | Deviance change = 0.299488
## Maximum item intercept parameter change = 0.000963
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003745
## ......................................................................
## Iteration 61 2023-07-05 16:11:56
## Deviance = 3938.92 | Deviance change = 0.301081
## Maximum item intercept parameter change = 0.000813
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003641
## ......................................................................
## Iteration 62 2023-07-05 16:11:56
## Deviance = 3938.6193 | Deviance change = 0.300677
## Maximum item intercept parameter change = 0.00065
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003523
## ......................................................................
## Iteration 63 2023-07-05 16:11:56
## Deviance = 3938.3212 | Deviance change = 0.29808
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003392
## ......................................................................
## Iteration 64 2023-07-05 16:11:56
## Deviance = 3938.0284 | Deviance change = 0.292863
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003248
## ......................................................................
## Iteration 65 2023-07-05 16:11:56
## Deviance = 3937.7432 | Deviance change = 0.285183
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.003093
## ......................................................................
## Iteration 66 2023-07-05 16:11:56
## Deviance = 3937.4678 | Deviance change = 0.275345
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002928
## ......................................................................
## Iteration 67 2023-07-05 16:11:56
## Deviance = 3937.2046 | Deviance change = 0.263203
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002757
## ......................................................................
## Iteration 68 2023-07-05 16:11:56
## Deviance = 3936.9557 | Deviance change = 0.248965
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002582
## ......................................................................
## Iteration 69 2023-07-05 16:11:56
## Deviance = 3936.7226 | Deviance change = 0.233044
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002405
## ......................................................................
## Iteration 70 2023-07-05 16:11:56
## Deviance = 3936.5077 | Deviance change = 0.214918
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002228
## ......................................................................
## Iteration 71 2023-07-05 16:11:56
## Deviance = 3936.3114 | Deviance change = 0.196316
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00212
## ......................................................................
## Iteration 72 2023-07-05 16:11:56
## Deviance = 3936.1336 | Deviance change = 0.177762
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002082
## ......................................................................
## Iteration 73 2023-07-05 16:11:56
## Deviance = 3935.974 | Deviance change = 0.159667
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.002037
## ......................................................................
## Iteration 74 2023-07-05 16:11:56
## Deviance = 3935.8316 | Deviance change = 0.142363
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001983
## ......................................................................
## Iteration 75 2023-07-05 16:11:56
## Deviance = 3935.7055 | Deviance change = 0.126098
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001921
## ......................................................................
## Iteration 76 2023-07-05 16:11:56
## Deviance = 3935.5945 | Deviance change = 0.111036
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001853
## ......................................................................
## Iteration 77 2023-07-05 16:11:56
## Deviance = 3935.4972 | Deviance change = 0.097267
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001779
## ......................................................................
## Iteration 78 2023-07-05 16:11:56
## Deviance = 3935.4124 | Deviance change = 0.084819
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.0017
## ......................................................................
## Iteration 79 2023-07-05 16:11:56
## Deviance = 3935.3387 | Deviance change = 0.073677
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001617
## ......................................................................
## Iteration 80 2023-07-05 16:11:56
## Deviance = 3935.2749 | Deviance change = 0.063789
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001531
## ......................................................................
## Iteration 81 2023-07-05 16:11:56
## Deviance = 3935.2198 | Deviance change = 0.055084
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001445
## ......................................................................
## Iteration 82 2023-07-05 16:11:56
## Deviance = 3935.1724 | Deviance change = 0.047472
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001358
## ......................................................................
## Iteration 83 2023-07-05 16:11:56
## Deviance = 3935.1315 | Deviance change = 0.04086
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001271
## ......................................................................
## Iteration 84 2023-07-05 16:11:56
## Deviance = 3935.0963 | Deviance change = 0.035151
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001186
## ......................................................................
## Iteration 85 2023-07-05 16:11:56
## Deviance = 3935.0661 | Deviance change = 0.030247
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001104
## ......................................................................
## Iteration 86 2023-07-05 16:11:56
## Deviance = 3935.04 | Deviance change = 0.026056
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.001024
## ......................................................................
## Iteration 87 2023-07-05 16:11:56
## Deviance = 3935.0176 | Deviance change = 0.02249
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000947
## ......................................................................
## Iteration 88 2023-07-05 16:11:56
## Deviance = 3934.9984 | Deviance change = 0.019162
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000874
## ......................................................................
## Iteration 89 2023-07-05 16:11:56
## Deviance = 3934.9815 | Deviance change = 0.016925
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000805
## ......................................................................
## Iteration 90 2023-07-05 16:11:56
## Deviance = 3934.9667 | Deviance change = 0.014782
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00074
## ......................................................................
## Iteration 91 2023-07-05 16:11:56
## Deviance = 3934.9537 | Deviance change = 0.012985
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000678
## ......................................................................
## Iteration 92 2023-07-05 16:11:56
## Deviance = 3934.9422 | Deviance change = 0.011483
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000621
## ......................................................................
## Iteration 93 2023-07-05 16:11:56
## Deviance = 3934.932 | Deviance change = 0.010231
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000567
## ......................................................................
## Iteration 94 2023-07-05 16:11:56
## Deviance = 3934.9228 | Deviance change = 0.009188
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000518
## ......................................................................
## Iteration 95 2023-07-05 16:11:56
## Deviance = 3934.9145 | Deviance change = 0.008322
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000472
## ......................................................................
## Iteration 96 2023-07-05 16:11:56
## Deviance = 3934.9069 | Deviance change = 0.007603
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000429
## ......................................................................
## Iteration 97 2023-07-05 16:11:56
## Deviance = 3934.8999 | Deviance change = 0.007007
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00039
## ......................................................................
## Iteration 98 2023-07-05 16:11:56
## Deviance = 3934.8934 | Deviance change = 0.006513
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000355
## ......................................................................
## Iteration 99 2023-07-05 16:11:56
## Deviance = 3934.8872 | Deviance change = 0.006104
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000322
## ......................................................................
## Iteration 100 2023-07-05 16:11:56
## Deviance = 3934.8815 | Deviance change = 0.005764
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000292
## ......................................................................
## Iteration 101 2023-07-05 16:11:56
## Deviance = 3934.876 | Deviance change = 0.005482
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000264
## ......................................................................
## Iteration 102 2023-07-05 16:11:56
## Deviance = 3934.8708 | Deviance change = 0.005248
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000239
## ......................................................................
## Iteration 103 2023-07-05 16:11:56
## Deviance = 3934.8657 | Deviance change = 0.005052
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000216
## ......................................................................
## Iteration 104 2023-07-05 16:11:56
## Deviance = 3934.8608 | Deviance change = 0.004888
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000196
## ......................................................................
## Iteration 105 2023-07-05 16:11:56
## Deviance = 3934.8561 | Deviance change = 0.004751
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000177
## ......................................................................
## Iteration 106 2023-07-05 16:11:56
## Deviance = 3934.8514 | Deviance change = 0.004635
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00016
## ......................................................................
## Iteration 107 2023-07-05 16:11:56
## Deviance = 3934.8469 | Deviance change = 0.004537
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000144
## ......................................................................
## Iteration 108 2023-07-05 16:11:56
## Deviance = 3934.8424 | Deviance change = 0.004452
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.00013
## ......................................................................
## Iteration 109 2023-07-05 16:11:56
## Deviance = 3934.8381 | Deviance change = 0.00438
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000118
## ......................................................................
## Iteration 110 2023-07-05 16:11:56
## Deviance = 3934.8337 | Deviance change = 0.004317
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 0.000106
## ......................................................................
## Iteration 111 2023-07-05 16:11:56
## Deviance = 3934.8295 | Deviance change = 0.004261
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 9.6e-05
## ......................................................................
## Iteration 112 2023-07-05 16:11:56
## Deviance = 3934.8253 | Deviance change = 0.004212
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 8.6e-05
## ......................................................................
## Iteration 113 2023-07-05 16:11:56
## Deviance = 3934.8211 | Deviance change = 0.004168
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 7.8e-05
## ......................................................................
## Iteration 114 2023-07-05 16:11:56
## Deviance = 3934.8172 | Deviance change = 0.00387
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 7e-05
## ......................................................................
## Iteration 115 2023-07-05 16:11:56
## Deviance = 3934.8134 | Deviance change = 0.003825
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 6.3e-05
## ......................................................................
## Iteration 116 2023-07-05 16:11:56
## Deviance = 3934.8093 | Deviance change = 0.004062
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 5.7e-05
## ......................................................................
## Iteration 117 2023-07-05 16:11:56
## Deviance = 3934.8053 | Deviance change = 0.00403
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 5.1e-05
## ......................................................................
## Iteration 118 2023-07-05 16:11:56
## Deviance = 3934.8013 | Deviance change = 0.004001
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 4.6e-05
## ......................................................................
## Iteration 119 2023-07-05 16:11:56
## Deviance = 3934.7973 | Deviance change = 0.003972
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 4.2e-05
## ......................................................................
## Iteration 120 2023-07-05 16:11:56
## Deviance = 3934.7934 | Deviance change = 0.003945
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3.8e-05
## ......................................................................
## Iteration 121 2023-07-05 16:11:56
## Deviance = 3934.7895 | Deviance change = 0.003919
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3.4e-05
## ......................................................................
## Iteration 122 2023-07-05 16:11:56
## Deviance = 3934.7856 | Deviance change = 0.003894
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3.1e-05
## ......................................................................
## Iteration 123 2023-07-05 16:11:56
## Deviance = 3934.7817 | Deviance change = 0.003869
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2.8e-05
## ......................................................................
## Iteration 124 2023-07-05 16:11:56
## Deviance = 3934.7779 | Deviance change = 0.003845
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2.5e-05
## ......................................................................
## Iteration 125 2023-07-05 16:11:56
## Deviance = 3934.774 | Deviance change = 0.003821
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2.2e-05
## ......................................................................
## Iteration 126 2023-07-05 16:11:56
## Deviance = 3934.7702 | Deviance change = 0.003797
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-05
## ......................................................................
## Iteration 127 2023-07-05 16:11:56
## Deviance = 3934.7665 | Deviance change = 0.003774
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.8e-05
## ......................................................................
## Iteration 128 2023-07-05 16:11:56
## Deviance = 3934.7627 | Deviance change = 0.003751
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.7e-05
## ......................................................................
## Iteration 129 2023-07-05 16:11:56
## Deviance = 3934.759 | Deviance change = 0.003728
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.5e-05
## ......................................................................
## Iteration 130 2023-07-05 16:11:56
## Deviance = 3934.7553 | Deviance change = 0.003706
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.3e-05
## ......................................................................
## Iteration 131 2023-07-05 16:11:56
## Deviance = 3934.7516 | Deviance change = 0.003683
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.2e-05
## ......................................................................
## Iteration 132 2023-07-05 16:11:56
## Deviance = 3934.7479 | Deviance change = 0.003661
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1.1e-05
## ......................................................................
## Iteration 133 2023-07-05 16:11:56
## Deviance = 3934.7443 | Deviance change = 0.003638
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-05
## ......................................................................
## Iteration 134 2023-07-05 16:11:56
## Deviance = 3934.7407 | Deviance change = 0.003616
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 9e-06
## ......................................................................
## Iteration 135 2023-07-05 16:11:56
## Deviance = 3934.7371 | Deviance change = 0.003594
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 8e-06
## ......................................................................
## Iteration 136 2023-07-05 16:11:56
## Deviance = 3934.7335 | Deviance change = 0.003571
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 7e-06
## ......................................................................
## Iteration 137 2023-07-05 16:11:56
## Deviance = 3934.73 | Deviance change = 0.003549
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 7e-06
## ......................................................................
## Iteration 138 2023-07-05 16:11:56
## Deviance = 3934.7264 | Deviance change = 0.003527
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 6e-06
## ......................................................................
## Iteration 139 2023-07-05 16:11:56
## Deviance = 3934.7229 | Deviance change = 0.003505
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 6e-06
## ......................................................................
## Iteration 140 2023-07-05 16:11:56
## Deviance = 3934.7195 | Deviance change = 0.003483
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 5e-06
## ......................................................................
## Iteration 141 2023-07-05 16:11:56
## Deviance = 3934.716 | Deviance change = 0.00346
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 5e-06
## ......................................................................
## Iteration 142 2023-07-05 16:11:56
## Deviance = 3934.7126 | Deviance change = 0.003438
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 4e-06
## ......................................................................
## Iteration 143 2023-07-05 16:11:56
## Deviance = 3934.7091 | Deviance change = 0.003416
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 4e-06
## ......................................................................
## Iteration 144 2023-07-05 16:11:56
## Deviance = 3934.7058 | Deviance change = 0.003394
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 4e-06
## ......................................................................
## Iteration 145 2023-07-05 16:11:56
## Deviance = 3934.7024 | Deviance change = 0.003372
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3e-06
## ......................................................................
## Iteration 146 2023-07-05 16:11:56
## Deviance = 3934.699 | Deviance change = 0.00335
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3e-06
## ......................................................................
## Iteration 147 2023-07-05 16:11:56
## Deviance = 3934.6957 | Deviance change = 0.003327
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3e-06
## ......................................................................
## Iteration 148 2023-07-05 16:11:56
## Deviance = 3934.6924 | Deviance change = 0.003305
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 3e-06
## ......................................................................
## Iteration 149 2023-07-05 16:11:56
## Deviance = 3934.6891 | Deviance change = 0.003283
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 150 2023-07-05 16:11:56
## Deviance = 3934.6859 | Deviance change = 0.003261
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 151 2023-07-05 16:11:56
## Deviance = 3934.6826 | Deviance change = 0.003239
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 152 2023-07-05 16:11:56
## Deviance = 3934.6794 | Deviance change = 0.003217
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 153 2023-07-05 16:11:56
## Deviance = 3934.6762 | Deviance change = 0.003195
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 154 2023-07-05 16:11:56
## Deviance = 3934.673 | Deviance change = 0.003172
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 155 2023-07-05 16:11:56
## Deviance = 3934.6699 | Deviance change = 0.00315
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 156 2023-07-05 16:11:56
## Deviance = 3934.6668 | Deviance change = 0.003128
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 2e-06
## ......................................................................
## Iteration 157 2023-07-05 16:11:56
## Deviance = 3934.6636 | Deviance change = 0.003106
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 158 2023-07-05 16:11:56
## Deviance = 3934.6606 | Deviance change = 0.003084
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 159 2023-07-05 16:11:56
## Deviance = 3934.6575 | Deviance change = 0.003062
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 160 2023-07-05 16:11:56
## Deviance = 3934.6545 | Deviance change = 0.003039
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 161 2023-07-05 16:11:56
## Deviance = 3934.6514 | Deviance change = 0.003017
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 162 2023-07-05 16:11:56
## Deviance = 3934.6485 | Deviance change = 0.002995
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 163 2023-07-05 16:11:56
## Deviance = 3934.6455 | Deviance change = 0.002973
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 164 2023-07-05 16:11:56
## Deviance = 3934.6425 | Deviance change = 0.002951
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 165 2023-07-05 16:11:56
## Deviance = 3934.6396 | Deviance change = 0.002929
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 166 2023-07-05 16:11:56
## Deviance = 3934.6367 | Deviance change = 0.002906
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 167 2023-07-05 16:11:56
## Deviance = 3934.6338 | Deviance change = 0.002884
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 168 2023-07-05 16:11:56
## Deviance = 3934.6309 | Deviance change = 0.002862
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 169 2023-07-05 16:11:56
## Deviance = 3934.6281 | Deviance change = 0.00284
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 170 2023-07-05 16:11:56
## Deviance = 3934.6253 | Deviance change = 0.002818
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 171 2023-07-05 16:11:56
## Deviance = 3934.6225 | Deviance change = 0.002795
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 172 2023-07-05 16:11:56
## Deviance = 3934.6197 | Deviance change = 0.002773
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 173 2023-07-05 16:11:56
## Deviance = 3934.617 | Deviance change = 0.002751
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 174 2023-07-05 16:11:56
## Deviance = 3934.6142 | Deviance change = 0.002729
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 175 2023-07-05 16:11:56
## Deviance = 3934.6115 | Deviance change = 0.002707
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 176 2023-07-05 16:11:56
## Deviance = 3934.6089 | Deviance change = 0.002684
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 177 2023-07-05 16:11:56
## Deviance = 3934.6062 | Deviance change = 0.002662
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 178 2023-07-05 16:11:56
## Deviance = 3934.6035 | Deviance change = 0.00264
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 179 2023-07-05 16:11:56
## Deviance = 3934.6009 | Deviance change = 0.002618
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 180 2023-07-05 16:11:56
## Deviance = 3934.5983 | Deviance change = 0.002596
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 181 2023-07-05 16:11:56
## Deviance = 3934.5958 | Deviance change = 0.002573
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 182 2023-07-05 16:11:56
## Deviance = 3934.5932 | Deviance change = 0.002551
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 183 2023-07-05 16:11:56
## Deviance = 3934.5907 | Deviance change = 0.002529
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 184 2023-07-05 16:11:56
## Deviance = 3934.5882 | Deviance change = 0.002507
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 185 2023-07-05 16:11:56
## Deviance = 3934.5857 | Deviance change = 0.002484
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 186 2023-07-05 16:11:56
## Deviance = 3934.5832 | Deviance change = 0.002462
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 187 2023-07-05 16:11:56
## Deviance = 3934.5808 | Deviance change = 0.00244
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 188 2023-07-05 16:11:56
## Deviance = 3934.5784 | Deviance change = 0.002418
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 189 2023-07-05 16:11:56
## Deviance = 3934.576 | Deviance change = 0.002395
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 190 2023-07-05 16:11:56
## Deviance = 3934.5736 | Deviance change = 0.002373
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 191 2023-07-05 16:11:56
## Deviance = 3934.5713 | Deviance change = 0.002351
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 192 2023-07-05 16:11:56
## Deviance = 3934.5689 | Deviance change = 0.002329
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 193 2023-07-05 16:11:56
## Deviance = 3934.5666 | Deviance change = 0.002306
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 194 2023-07-05 16:11:56
## Deviance = 3934.5643 | Deviance change = 0.002284
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 195 2023-07-05 16:11:56
## Deviance = 3934.5621 | Deviance change = 0.002262
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 196 2023-07-05 16:11:56
## Deviance = 3934.5598 | Deviance change = 0.00224
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 197 2023-07-05 16:11:56
## Deviance = 3934.5576 | Deviance change = 0.002217
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 198 2023-07-05 16:11:56
## Deviance = 3934.5554 | Deviance change = 0.002195
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 199 2023-07-05 16:11:56
## Deviance = 3934.5532 | Deviance change = 0.002173
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## ......................................................................
## Iteration 200 2023-07-05 16:11:56
## Deviance = 3934.5511 | Deviance change = 0.002151
## Maximum item intercept parameter change = 0.000473
## Maximum item slope parameter change = 0
## Maximum distribution parameter change = 1e-06
## -----------------------------------
## Start: 2023-07-05 16:11:56
## End: 2023-07-05 16:11:56
## Time difference of 0.2806468 secs
## Difference: 0.2806468
## -----------------------------------
summary(mod12b)
## -----------------------------------------------------------------------------
## CDM 8.2-6 (2022-08-25 15:43:23)
##
## Date of Analysis: 2023-07-05 16:11:56
## Time difference of 0.2806468 secs
## Computation Time: 0.2806468
##
## General Diagnostic Model
##
## Call:
## CDM::gdm(data = dat, theta.k = theta.k, irtmodel = "1PL", skillspace = "est",
## b.constraint = b.constraint, maxiter = 200)
##
## 328 Cases, 12 Items, 1 Group(s) , 1 Dimension(s)
## Saturated skill space with estimated trait grid
##
## -----------------------------------------------------------------------------
## Number of iterations= 200
## Maximum number of iterations was reached.
##
## Deviance = 3934.55 | Log Likelihood = -1967.28
## Number of persons = 328
## Number of estimated parameters = 16
## Number of estimated item parameters = 11
## 11 Intercepts and 0 Slopes
## 0 centered intercepts and 0 centered slopes
## Number of estimated distribution parameters = 5
##
## AIC = 3967 | penalty = 32 | AIC = -2*LL + 2*p
## AICc = 3968 | penalty = 33.75 | AICc = -2*LL + 2*p + 2*p*(p+1)/(n-p-1) (bias corrected AIC)
## BIC = 4027 | penalty = 92.69 | BIC = -2*LL + log(n)*p
## CAIC = 4043 | penalty = 108.69 | CAIC = -2*LL + [log(n)+1]*p (consistent AIC)
##
## -----------------------------------------------------------------------------
## Trait Distribution
##
## M Trait:
## F1
## Group1 1.137
##
## SD Trait:
## F1
## Group1 1.004
##
## Skewness Trait:
## F1
## Group1 -0.505
##
## Correlations Trait:
## Group 1
## F1
## F1 1
##
##
## Estimated Skill Distribution
## F1 pi.k
## 1 -1.673 0.02885
## 2 0.284 0.46255
## 3 2.072 0.50860
##
## EAP Reliability:
## F1
## [1,] 0.72
## -----------------------------------------------------------------------------
## Item Parameters
## item N M b.Cat1 a.F1 itemfit.rmsea
## 1 A1 328 0.851 0.926 1 0.083
## 2 A2 328 0.738 0.103 1 0.065
## 3 A3 328 0.567 -0.829 1 0.039
## 4 A4 328 0.460 -1.362 1 0.022
## 5 B1 328 0.713 -0.043 1 0.060
## 6 B2 328 0.506 -1.135 1 0.077
## 7 B3 328 0.909 1.547 1 0.027
## 8 B4 328 0.683 -0.218 1 0.006
## 9 C1 328 0.933 1.913 1 0.053
## 10 C2 328 0.713 0.000 1 0.031
## 11 C3 328 0.872 1.128 1 0.041
## 12 C4 328 0.735 0.085 1 0.045
##
## Mean of RMSEA item fit: 0.046
#-- M12c: mirt (in mirt)
items <- colnames(dat)
# define three latent classes
Theta <- diag(3)
# define mirt model
I <- ncol(dat) # I = 12
mirtmodel <- mirt::mirt.model("
C1 = 1-12
C2 = 1-12
C3 = 1-12
CONSTRAIN = (1-12,a1),(1-12,a2),(1-12,a3)
")
# get parameters
mod.pars <- mirt(dat, model=mirtmodel , pars = "values")
# set starting values for class specific item probabilities
mod.pars[ mod.pars$name == "d" ,"value" ] <- qlogis( colMeans(dat,na.rm=TRUE) )
# set item difficulty of reference item to zero
ind <- which( ( paste(mod.pars$item) == items[ref.item] ) &
( ( paste(mod.pars$name) == "d" ) ) )
mod.pars[ ind ,"value" ] <- 0
mod.pars[ ind ,"est" ] <- FALSE
# initial values for a1, a2 and a3
mod.pars[ mod.pars$name %in% c("a1","a2","a3") ,"value" ] <- c(-1,0,1)
mod.pars
## group item class name parnum value lbound ubound est
## 1 all A1 dich a1 1 -1.00000000 -Inf Inf TRUE
## 2 all A1 dich a2 2 0.00000000 -Inf Inf TRUE
## 3 all A1 dich a3 3 1.00000000 -Inf Inf TRUE
## 4 all A1 dich d 4 1.73939148 -Inf Inf TRUE
## 5 all A1 dich g 5 0.00000000 0e+00 1 FALSE
## 6 all A1 dich u 6 1.00000000 0e+00 1 FALSE
## 7 all A2 dich a1 7 -1.00000000 -Inf Inf TRUE
## 8 all A2 dich a2 8 0.00000000 -Inf Inf TRUE
## 9 all A2 dich a3 9 1.00000000 -Inf Inf TRUE
## 10 all A2 dich d 10 1.03459043 -Inf Inf TRUE
## 11 all A2 dich g 11 0.00000000 0e+00 1 FALSE
## 12 all A2 dich u 12 1.00000000 0e+00 1 FALSE
## 13 all A3 dich a1 13 -1.00000000 -Inf Inf TRUE
## 14 all A3 dich a2 14 0.00000000 -Inf Inf TRUE
## 15 all A3 dich a3 15 1.00000000 -Inf Inf TRUE
## 16 all A3 dich d 16 0.26991962 -Inf Inf TRUE
## 17 all A3 dich g 17 0.00000000 0e+00 1 FALSE
## 18 all A3 dich u 18 1.00000000 0e+00 1 FALSE
## 19 all A4 dich a1 19 -1.00000000 -Inf Inf TRUE
## 20 all A4 dich a2 20 0.00000000 -Inf Inf TRUE
## 21 all A4 dich a3 21 1.00000000 -Inf Inf TRUE
## 22 all A4 dich d 22 -0.15886990 -Inf Inf TRUE
## 23 all A4 dich g 23 0.00000000 0e+00 1 FALSE
## 24 all A4 dich u 24 1.00000000 0e+00 1 FALSE
## 25 all B1 dich a1 25 -1.00000000 -Inf Inf TRUE
## 26 all B1 dich a2 26 0.00000000 -Inf Inf TRUE
## 27 all B1 dich a3 27 1.00000000 -Inf Inf TRUE
## 28 all B1 dich d 28 0.91202633 -Inf Inf TRUE
## 29 all B1 dich g 29 0.00000000 0e+00 1 FALSE
## 30 all B1 dich u 30 1.00000000 0e+00 1 FALSE
## 31 all B2 dich a1 31 -1.00000000 -Inf Inf TRUE
## 32 all B2 dich a2 32 0.00000000 -Inf Inf TRUE
## 33 all B2 dich a3 33 1.00000000 -Inf Inf TRUE
## 34 all B2 dich d 34 0.02439145 -Inf Inf TRUE
## 35 all B2 dich g 35 0.00000000 0e+00 1 FALSE
## 36 all B2 dich u 36 1.00000000 0e+00 1 FALSE
## 37 all B3 dich a1 37 -1.00000000 -Inf Inf TRUE
## 38 all B3 dich a2 38 0.00000000 -Inf Inf TRUE
## 39 all B3 dich a3 39 1.00000000 -Inf Inf TRUE
## 40 all B3 dich d 40 2.29589610 -Inf Inf TRUE
## 41 all B3 dich g 41 0.00000000 0e+00 1 FALSE
## 42 all B3 dich u 42 1.00000000 0e+00 1 FALSE
## 43 all B4 dich a1 43 -1.00000000 -Inf Inf TRUE
## 44 all B4 dich a2 44 0.00000000 -Inf Inf TRUE
## 45 all B4 dich a3 45 1.00000000 -Inf Inf TRUE
## 46 all B4 dich d 46 0.76725515 -Inf Inf TRUE
## 47 all B4 dich g 47 0.00000000 0e+00 1 FALSE
## 48 all B4 dich u 48 1.00000000 0e+00 1 FALSE
## 49 all C1 dich a1 49 -1.00000000 -Inf Inf TRUE
## 50 all C1 dich a2 50 0.00000000 -Inf Inf TRUE
## 51 all C1 dich a3 51 1.00000000 -Inf Inf TRUE
## 52 all C1 dich d 52 2.63254265 -Inf Inf TRUE
## 53 all C1 dich g 53 0.00000000 0e+00 1 FALSE
## 54 all C1 dich u 54 1.00000000 0e+00 1 FALSE
## 55 all C2 dich a1 55 -1.00000000 -Inf Inf TRUE
## 56 all C2 dich a2 56 0.00000000 -Inf Inf TRUE
## 57 all C2 dich a3 57 1.00000000 -Inf Inf TRUE
## 58 all C2 dich d 58 0.00000000 -Inf Inf FALSE
## 59 all C2 dich g 59 0.00000000 0e+00 1 FALSE
## 60 all C2 dich u 60 1.00000000 0e+00 1 FALSE
## 61 all C3 dich a1 61 -1.00000000 -Inf Inf TRUE
## 62 all C3 dich a2 62 0.00000000 -Inf Inf TRUE
## 63 all C3 dich a3 63 1.00000000 -Inf Inf TRUE
## 64 all C3 dich d 64 1.91832219 -Inf Inf TRUE
## 65 all C3 dich g 65 0.00000000 0e+00 1 FALSE
## 66 all C3 dich u 66 1.00000000 0e+00 1 FALSE
## 67 all C4 dich a1 67 -1.00000000 -Inf Inf TRUE
## 68 all C4 dich a2 68 0.00000000 -Inf Inf TRUE
## 69 all C4 dich a3 69 1.00000000 -Inf Inf TRUE
## 70 all C4 dich d 70 1.01888881 -Inf Inf TRUE
## 71 all C4 dich g 71 0.00000000 0e+00 1 FALSE
## 72 all C4 dich u 72 1.00000000 0e+00 1 FALSE
## 73 all GROUP GroupPars MEAN_1 73 0.00000000 -Inf Inf FALSE
## 74 all GROUP GroupPars MEAN_2 74 0.00000000 -Inf Inf FALSE
## 75 all GROUP GroupPars MEAN_3 75 0.00000000 -Inf Inf FALSE
## 76 all GROUP GroupPars COV_11 76 1.00000000 1e-04 Inf FALSE
## 77 all GROUP GroupPars COV_21 77 0.00000000 -Inf Inf FALSE
## 78 all GROUP GroupPars COV_31 78 0.00000000 -Inf Inf FALSE
## 79 all GROUP GroupPars COV_22 79 1.00000000 1e-04 Inf FALSE
## 80 all GROUP GroupPars COV_32 80 0.00000000 -Inf Inf FALSE
## 81 all GROUP GroupPars COV_33 81 1.00000000 1e-04 Inf FALSE
## prior.type prior_1 prior_2
## 1 none NaN NaN
## 2 none NaN NaN
## 3 none NaN NaN
## 4 none NaN NaN
## 5 none NaN NaN
## 6 none NaN NaN
## 7 none NaN NaN
## 8 none NaN NaN
## 9 none NaN NaN
## 10 none NaN NaN
## 11 none NaN NaN
## 12 none NaN NaN
## 13 none NaN NaN
## 14 none NaN NaN
## 15 none NaN NaN
## 16 none NaN NaN
## 17 none NaN NaN
## 18 none NaN NaN
## 19 none NaN NaN
## 20 none NaN NaN
## 21 none NaN NaN
## 22 none NaN NaN
## 23 none NaN NaN
## 24 none NaN NaN
## 25 none NaN NaN
## 26 none NaN NaN
## 27 none NaN NaN
## 28 none NaN NaN
## 29 none NaN NaN
## 30 none NaN NaN
## 31 none NaN NaN
## 32 none NaN NaN
## 33 none NaN NaN
## 34 none NaN NaN
## 35 none NaN NaN
## 36 none NaN NaN
## 37 none NaN NaN
## 38 none NaN NaN
## 39 none NaN NaN
## 40 none NaN NaN
## 41 none NaN NaN
## 42 none NaN NaN
## 43 none NaN NaN
## 44 none NaN NaN
## 45 none NaN NaN
## 46 none NaN NaN
## 47 none NaN NaN
## 48 none NaN NaN
## 49 none NaN NaN
## 50 none NaN NaN
## 51 none NaN NaN
## 52 none NaN NaN
## 53 none NaN NaN
## 54 none NaN NaN
## 55 none NaN NaN
## 56 none NaN NaN
## 57 none NaN NaN
## 58 none NaN NaN
## 59 none NaN NaN
## 60 none NaN NaN
## 61 none NaN NaN
## 62 none NaN NaN
## 63 none NaN NaN
## 64 none NaN NaN
## 65 none NaN NaN
## 66 none NaN NaN
## 67 none NaN NaN
## 68 none NaN NaN
## 69 none NaN NaN
## 70 none NaN NaN
## 71 none NaN NaN
## 72 none NaN NaN
## 73 none NaN NaN
## 74 none NaN NaN
## 75 none NaN NaN
## 76 none NaN NaN
## 77 none NaN NaN
## 78 none NaN NaN
## 79 none NaN NaN
## 80 none NaN NaN
## 81 none NaN NaN
#* define prior for latent class analysis
lca_prior <- function(Theta,Etable){
# number of latent Theta classes
TP <- nrow(Theta)
# prior in initial iteration
if ( is.null(Etable) ){
prior <- rep( 1/TP , TP )
}
# process Etable (this is correct for datasets without missing data)
if ( ! is.null(Etable) ){
# sum over correct and incorrect expected responses
prior <- ( rowSums( Etable[ , seq(1,2*I,2)] ) + rowSums( Etable[ , seq(2,2*I,2)]))}
prior <- prior / sum(prior)
return(prior)
}
#* estimate model
mod12c <- mirt(dat, mirtmodel , technical = list(
customTheta=Theta , customPriorFun = lca_prior) ,
pars = mod.pars , verbose=FALSE )
print(mod12c)
##
## Call:
## mirt(data = dat, model = mirtmodel, pars = mod.pars, verbose = FALSE,
## technical = list(customTheta = Theta, customPriorFun = lca_prior))
##
## Full-information item factor analysis with 3 factor(s).
## Converged within 1e-04 tolerance after 80 EM iterations.
## mirt version: 1.39.4
## M-step optimizer: BFGS
## EM acceleration: Ramsay
## Number of rectangular quadrature: 3
## Latent density type: Gaussian
##
## Log-likelihood = -1967.22
## Estimated parameters: 47
## AIC = 3962.441
## BIC = 4015.543; SABIC = 3971.135
## G2 (4081) = 832.48, p = 1
## RMSEA = 0, CFI = NaN, TLI = NaN
# estimated parameters from the user customized prior distribution.
nest <- as.integer(sum(mod.pars$est) + 2)
#* extract item parameters
coef1 <- coef(mod12c, simplify=TRUE)$items
#* inspect estimated distribution
coef1
## a1 a2 a3 d g u
## A1 -1.706573 0.2463275 2.033385 0.970432213 0 1
## A2 -1.706573 0.2463275 2.033385 0.145888002 0 1
## A3 -1.706573 0.2463275 2.033385 -0.788138229 0 1
## A4 -1.706573 0.2463275 2.033385 -1.320002426 0 1
## B1 -1.706573 0.2463275 2.033385 -0.001154736 0 1
## B2 -1.706573 0.2463275 2.033385 -1.093086286 0 1
## B3 -1.706573 0.2463275 2.033385 1.599935802 0 1
## B4 -1.706573 0.2463275 2.033385 -0.176302606 0 1
## C1 -1.706573 0.2463275 2.033385 1.972606241 0 1
## C2 -1.706573 0.2463275 2.033385 0.000000000 0 1
## C3 -1.706573 0.2463275 2.033385 1.174713959 0 1
## C4 -1.706573 0.2463275 2.033385 0.127114430 0 1
extract.mirt(mod12c, "Prior")[[1]]
## [1] 0.02912642 0.46245139 0.50842219
sessionInfo()
## R version 4.2.2 Patched (2022-11-10 r83330)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.6 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] mvtnorm_1.2-2 sirt_3.12-66 ltm_1.2-0 polycor_0.8-1
## [5] msm_1.7 MASS_7.3-58.2 mirt_1.39.4 lattice_0.20-45
## [9] knitr_1.43
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.10 highr_0.10 compiler_4.2.2
## [4] dcurver_0.9.2 tools_4.2.2 evaluate_0.21
## [7] lifecycle_1.0.3 gtable_0.3.3 nlme_3.1-162
## [10] mgcv_1.8-41 rlang_1.1.1 Matrix_1.5-3
## [13] cli_3.6.1 rstudioapi_0.14 commonmark_1.9.0
## [16] parallel_4.2.2 TAM_4.1-4 expm_0.999-7
## [19] xfun_0.39 gridExtra_2.3 cluster_2.1.4
## [22] admisc_0.32 grid_4.2.2 glue_1.6.2
## [25] pbapply_1.7-0 survival_3.4-0 CDM_8.2-6
## [28] GPArotation_2023.3-1 splines_4.2.2 mime_0.12
## [31] permute_0.9-7 Deriv_4.1.3 markdown_1.7
## [34] vegan_2.6-4