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class_0 <- sample(1:2^K, N, replace = L)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1))
}
thetas_true = rnorm(N)
lambdas_true = c(-1, 1.8, .277, .055)
Alphas <- sim_alphas(model="HO_sep",
lambdas=lambdas_true,
thetas=thetas_true,
Q_matrix=Q_matrix,
Design_array=Design_array)
table(rowSums(Alphas[,,5]) - rowSums(Alphas[,,1])) # used to see how much transition has taken place
#>
#> 0 1 2 3 4
#> 29 29 103 143 46
itempars_true <- matrix(runif(J*2,.1,.2), ncol=2)
Y_sim <- sim_hmcdm(model="DINA",Alphas,Q_matrix,Design_array,
itempars=itempars_true)
output_HMDCM = hmcdm(Y_sim,Q_matrix,"DINA_HO",Test_order = Test_order, Test_versions = Test_versions,
chain_length=100,burn_in=30,
theta_propose = 2,deltas_propose = c(.45,.35,.25,.06))
#> 0
output_HMDCM = hmcdm(Y_sim,Q_matrix,"DINA_HO",Design_array,
chain_length=100,burn_in=30,
theta_propose = 2,deltas_propose = c(.45,.35,.25,.06))
#> 0
output_HMDCM
#>
#> Model: DINA_HO
#>
#> Sample Size: 350
#> Number of Items:
#> Number of Time Points:
#>
#> Chain Length: 100, burn-in: 30
summary(output_HMDCM)
#>
#> Model: DINA_HO
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.07685 0.17243
#> 0.18488 0.07224
#> 0.11893 0.09148
#> 0.11457 0.25188
#> 0.23254 0.14521
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.3192
#> λ1 1.8989
#> λ2 0.2050
#> λ3 0.1283
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1459
#> 0001 0.1697
#> 0010 0.1465
#> 0011 0.2256
#> 0100 0.2020
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 19338.99
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4997
#> M2: 0.49
#> total scores: 0.6243
a <- summary(output_HMDCM)
a$ss_EAP
#> [,1]
#> [1,] 0.07685255
#> [2,] 0.18488425
#> [3,] 0.11892786
#> [4,] 0.11456749
#> [5,] 0.23254269
#> [6,] 0.18006215
#> [7,] 0.12160810
#> [8,] 0.21652203
#> [9,] 0.19235236
#> [10,] 0.14879741
#> [11,] 0.20244524
#> [12,] 0.15301554
#> [13,] 0.14864318
#> [14,] 0.16782918
#> [15,] 0.08299005
#> [16,] 0.12658188
#> [17,] 0.17201443
#> [18,] 0.11441438
#> [19,] 0.21313259
#> [20,] 0.15480563
#> [21,] 0.23201792
#> [22,] 0.22040852
#> [23,] 0.18641166
#> [24,] 0.15644341
#> [25,] 0.15068218
#> [26,] 0.14069133
#> [27,] 0.15763156
#> [28,] 0.26286838
#> [29,] 0.20866321
#> [30,] 0.16014609
#> [31,] 0.20695261
#> [32,] 0.18302578
#> [33,] 0.16749500
#> [34,] 0.19857339
#> [35,] 0.17062041
#> [36,] 0.11672392
#> [37,] 0.19205306
#> [38,] 0.11277445
#> [39,] 0.16949512
#> [40,] 0.15137924
#> [41,] 0.22840721
#> [42,] 0.17458218
#> [43,] 0.11333775
#> [44,] 0.16533007
#> [45,] 0.15727484
#> [46,] 0.22936398
#> [47,] 0.13081081
#> [48,] 0.18149035
#> [49,] 0.22000283
#> [50,] 0.19266879
a$lambdas_EAP
#> [,1]
#> λ0 -1.3191652
#> λ1 1.8988731
#> λ2 0.2049675
#> λ3 0.1282824
mean(a$PPP_total_scores)
#> [1] 0.6232245
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.4968571
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2133.712 NA 15036.72 1323.997 18494.42
#> D(theta_bar) 1891.812 NA 14468.75 1289.299 17649.86
#> DIC 2375.612 NA 15604.68 1358.694 19338.99
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.3857143 1.0000000 0.67142857 0.4714286 0.8000000
#> [2,] 0.5000000 0.8714286 0.02857143 1.0000000 0.2285714
#> [3,] 0.5571429 0.5000000 1.00000000 1.0000000 0.7714286
#> [4,] 0.3857143 0.8000000 0.81428571 0.9714286 0.5142857
#> [5,] 0.8857143 0.5428571 0.88571429 0.5428571 0.7714286
#> [6,] 0.9285714 0.6142857 0.92857143 0.1142857 1.0000000
head(a$PPP_item_means)
#> [1] 0.3714286 0.5142857 0.4714286 0.5285714 0.3571429 0.4000000
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] NA 0.6857143 0.9857143 0.5428571 0.3714286 0.6857143 0.3857143 0.5285714
#> [2,] NA NA 0.3285714 0.8000000 0.2571429 0.7571429 0.6428571 0.6285714
#> [3,] NA NA NA 0.4000000 0.7285714 0.1285714 0.8142857 0.9142857
#> [4,] NA NA NA NA 0.9142857 0.6571429 0.9285714 0.4142857
#> [5,] NA NA NA NA NA 0.5714286 0.5285714 0.9142857
#> [6,] NA NA NA NA NA NA 0.8571429 0.5285714
#> [,9] [,10] [,11] [,12] [,13] [,14] [,15]
#> [1,] 0.4285714 0.1285714 0.6285714 0.74285714 0.57142857 0.4857143 0.6428571
#> [2,] 0.5571429 0.5428571 0.8000000 0.80000000 0.17142857 0.3857143 0.4428571
#> [3,] 0.8285714 0.2857143 0.8285714 0.18571429 0.37142857 0.7000000 0.9142857
#> [4,] 0.6714286 0.2428571 0.4000000 0.80000000 0.37142857 0.5142857 0.4571429
#> [5,] 0.5857143 0.5571429 0.5428571 0.01428571 0.21428571 0.6142857 0.2000000
#> [6,] 0.8000000 0.6857143 0.8571429 0.60000000 0.01428571 0.3428571 0.2428571
#> [,16] [,17] [,18] [,19] [,20] [,21] [,22]
#> [1,] 0.7571429 0.75714286 0.9285714 0.6000000 0.5571429 0.2285714 0.25714286
#> [2,] 0.4571429 0.24285714 0.8857143 0.1857143 0.7857143 0.5142857 0.34285714
#> [3,] 0.6714286 0.25714286 0.8571429 0.7571429 0.7571429 0.6571429 0.42857143
#> [4,] 0.6142857 0.62857143 0.7571429 0.6857143 0.7285714 0.6571429 0.50000000
#> [5,] 0.5285714 0.02857143 0.9571429 0.2285714 0.7428571 0.6428571 0.42857143
#> [6,] 0.4428571 0.62857143 0.8000000 0.5285714 0.6000000 0.2142857 0.08571429
#> [,23] [,24] [,25] [,26] [,27] [,28] [,29]
#> [1,] 0.5000000 0.01428571 0.08571429 0.04285714 0.8714286 0.08571429 0.8000000
#> [2,] 0.2857143 0.31428571 0.52857143 0.18571429 0.1285714 0.42857143 0.1857143
#> [3,] 0.8142857 0.82857143 0.32857143 0.41428571 0.9285714 0.20000000 0.8571429
#> [4,] 0.2000000 0.38571429 0.15714286 0.00000000 1.0000000 0.88571429 0.8857143
#> [5,] 0.5142857 0.20000000 0.54285714 0.17142857 0.9857143 0.54285714 0.6857143
#> [6,] 0.2000000 0.28571429 0.01428571 0.10000000 0.5142857 0.07142857 0.1857143
#> [,30] [,31] [,32] [,33] [,34] [,35] [,36]
#> [1,] 0.1142857 0.18571429 0.4285714 0.8714286 0.2714286 0.45714286 0.47142857
#> [2,] 0.2000000 0.45714286 0.3714286 0.7714286 0.2571429 0.52857143 0.47142857
#> [3,] 0.4428571 0.04285714 0.5285714 0.6000000 0.7000000 0.08571429 0.07142857
#> [4,] 0.7428571 0.64285714 0.2142857 0.1571429 0.1285714 0.44285714 0.27142857
#> [5,] 0.8714286 0.67142857 0.7142857 0.7571429 0.8285714 0.60000000 0.92857143
#> [6,] 0.4714286 0.18571429 0.3142857 0.5857143 0.1857143 0.54285714 0.47142857
#> [,37] [,38] [,39] [,40] [,41] [,42] [,43]
#> [1,] 0.3142857 0.15714286 0.7142857 0.3285714 0.45714286 0.9857143 0.1000000
#> [2,] 0.3142857 0.64285714 0.4714286 0.6571429 0.07142857 0.5285714 0.5857143
#> [3,] 0.3285714 0.04285714 0.2142857 0.6285714 0.51428571 0.7285714 0.5000000
#> [4,] 0.2285714 0.72857143 0.1142857 0.8000000 0.78571429 0.5857143 0.2000000
#> [5,] 0.9857143 0.45714286 0.4571429 0.4571429 0.62857143 0.2428571 0.2857143
#> [6,] 0.1571429 0.88571429 0.2000000 0.6285714 0.14285714 0.7000000 0.8857143
#> [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.4142857 0.9428571 0.5428571 0.57142857 0.2571429 0.17142857 0.6571429
#> [2,] 0.7000000 0.3571429 0.5857143 0.28571429 0.2571429 0.40000000 0.3428571
#> [3,] 0.4857143 0.8142857 0.7142857 0.91428571 0.4428571 0.17142857 0.8571429
#> [4,] 0.7000000 0.5571429 0.3142857 0.04285714 0.1285714 0.78571429 0.6714286
#> [5,] 0.4000000 0.8714286 0.7142857 0.85714286 0.5428571 0.54285714 0.4428571
#> [6,] 0.8428571 0.5714286 0.4571429 0.04285714 0.2000000 0.08571429 0.4285714
library(bayesplot)
pp_check(output_HMDCM)
pp_check(output_HMDCM, plotfun="hist", type="item_OR")
#> Note: in most cases the default test statistic 'mean' is too weak to detect anything of interest.
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
pp_check(output_HMDCM, plotfun="stat_2d", type="item_mean")
#> Note: in most cases the default test statistic 'mean' is too weak to detect anything of interest.
Checking convergence of the two independent MCMC chains with
different initial values using coda
package.
# output_HMDCM1 = hmcdm(Y_sim, Q_matrix, "DINA_HO", Design_array,
# chain_length=100, burn_in=30,
# theta_propose = 2, deltas_propose = c(.45,.35,.25,.06))
# output_HMDCM2 = hmcdm(Y_sim, Q_matrix, "DINA_HO", Design_array,
# chain_length=100, burn_in=30,
# theta_propose = 2, deltas_propose = c(.45,.35,.25,.06))
#
# library(coda)
#
# x <- mcmc.list(mcmc(t(rbind(output_HMDCM1$ss, output_HMDCM1$gs, output_HMDCM1$lambdas))),
# mcmc(t(rbind(output_HMDCM2$ss, output_HMDCM2$gs, output_HMDCM2$lambdas))))
#
# gelman.diag(x, autoburnin=F)
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