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
#> 30 52 77 148 43
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
#> 0.18456 0.09599
#> 0.18986 0.23256
#> 0.10523 0.11852
#> 0.22187 0.11923
#> 0.08775 0.13346
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.02575
#> λ1 1.92896
#> λ2 0.22174
#> λ3 0.07975
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1709
#> 0001 0.1591
#> 0010 0.2098
#> 0011 0.1986
#> 0100 0.1834
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 18605.04
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5229
#> M2: 0.49
#> total scores: 0.6302
a <- summary(output_HMDCM)
a$ss_EAP
#> [,1]
#> [1,] 0.18455920
#> [2,] 0.18985962
#> [3,] 0.10523367
#> [4,] 0.22187448
#> [5,] 0.08774954
#> [6,] 0.18334949
#> [7,] 0.15500344
#> [8,] 0.25699268
#> [9,] 0.16032694
#> [10,] 0.19798400
#> [11,] 0.15091004
#> [12,] 0.23838443
#> [13,] 0.19094157
#> [14,] 0.15684118
#> [15,] 0.13672126
#> [16,] 0.15502856
#> [17,] 0.18063339
#> [18,] 0.24262112
#> [19,] 0.32292283
#> [20,] 0.14510435
#> [21,] 0.14889412
#> [22,] 0.07661825
#> [23,] 0.14082709
#> [24,] 0.12106204
#> [25,] 0.14925641
#> [26,] 0.16347773
#> [27,] 0.14617290
#> [28,] 0.20115715
#> [29,] 0.21154647
#> [30,] 0.14097770
#> [31,] 0.09529711
#> [32,] 0.14364558
#> [33,] 0.15099546
#> [34,] 0.13072970
#> [35,] 0.18600964
#> [36,] 0.09437936
#> [37,] 0.10013465
#> [38,] 0.12919356
#> [39,] 0.18406826
#> [40,] 0.16559404
#> [41,] 0.18872822
#> [42,] 0.15684492
#> [43,] 0.13504935
#> [44,] 0.16509263
#> [45,] 0.19118848
#> [46,] 0.10418668
#> [47,] 0.13092962
#> [48,] 0.21973501
#> [49,] 0.09414186
#> [50,] 0.13772416
a$lambdas_EAP
#> [,1]
#> λ0 -1.02575127
#> λ1 1.92896215
#> λ2 0.22174249
#> λ3 0.07974873
mean(a$PPP_total_scores)
#> [1] 0.6298286
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.5285714
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2073.743 NA 14473.65 1278.919 17826.31
#> D(theta_bar) 1813.953 NA 13996.32 1237.305 17047.58
#> DIC 2333.532 NA 14950.98 1320.532 18605.04
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.5714286 1.0000000 0.9428571 0.8000000 0.9428571
#> [2,] 0.5428571 0.8714286 0.5571429 0.8857143 0.8000000
#> [3,] 0.7285714 0.6571429 0.8857143 0.8142857 0.3714286
#> [4,] 0.2857143 0.4571429 0.5571429 0.7142857 0.7142857
#> [5,] 0.3714286 0.8000000 0.7857143 0.6571429 0.7857143
#> [6,] 0.4714286 0.5428571 0.8857143 0.4857143 1.0000000
head(a$PPP_item_means)
#> [1] 0.5000000 0.4714286 0.4714286 0.5285714 0.5285714 0.6285714
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] NA 0.5285714 0.9285714 0.9571429 0.2285714 0.7428571 0.5285714 0.4571429
#> [2,] NA NA 0.4571429 0.4571429 0.5571429 0.7428571 0.5857143 0.6571429
#> [3,] NA NA NA 0.8714286 0.9571429 0.7714286 0.7571429 0.1285714
#> [4,] NA NA NA NA 0.6428571 0.5714286 0.8428571 0.4142857
#> [5,] NA NA NA NA NA 0.5714286 0.3142857 0.5857143
#> [6,] NA NA NA NA NA NA 0.4714286 0.5428571
#> [,9] [,10] [,11] [,12] [,13] [,14] [,15]
#> [1,] 0.7571429 0.2857143 0.1857143 0.7285714 0.52857143 0.3428571 0.2285714
#> [2,] 0.3571429 0.4714286 0.1428571 0.9428571 0.01428571 0.2857143 0.3714286
#> [3,] 0.8571429 0.2000000 0.3142857 0.5857143 0.24285714 0.1142857 0.7428571
#> [4,] 0.6857143 0.9000000 0.3428571 0.6857143 0.48571429 0.4571429 0.9571429
#> [5,] 0.6142857 0.3857143 0.6285714 0.5000000 0.41428571 0.2285714 0.3285714
#> [6,] 0.6714286 0.7000000 0.1571429 0.8857143 0.58571429 0.4285714 0.5000000
#> [,16] [,17] [,18] [,19] [,20] [,21] [,22]
#> [1,] 0.2000000 0.4428571 0.6142857 0.22857143 0.9571429 0.27142857 0.5571429
#> [2,] 0.5285714 0.7714286 0.8714286 0.28571429 0.9428571 0.17142857 0.1285714
#> [3,] 0.2571429 0.7428571 0.9285714 0.51428571 0.8428571 0.10000000 0.3000000
#> [4,] 0.2428571 0.5571429 0.1285714 0.91428571 0.9285714 0.52857143 0.1428571
#> [5,] 0.2714286 0.3142857 0.8000000 0.05714286 0.8428571 0.04285714 0.5714286
#> [6,] 0.7000000 0.8714286 0.7857143 0.14285714 0.9857143 0.28571429 0.1428571
#> [,23] [,24] [,25] [,26] [,27] [,28] [,29]
#> [1,] 0.35714286 0.5428571 0.9142857 0.4428571 0.42857143 0.07142857 0.08571429
#> [2,] 0.62857143 0.5571429 0.6571429 0.4285714 0.85714286 0.40000000 0.38571429
#> [3,] 0.77142857 0.5428571 0.8714286 0.8428571 0.10000000 0.67142857 0.48571429
#> [4,] 0.08571429 0.6000000 0.5857143 0.5857143 0.27142857 0.37142857 0.58571429
#> [5,] 0.88571429 0.3571429 0.9714286 0.4571429 0.87142857 0.15714286 0.00000000
#> [6,] 0.32857143 0.1000000 0.8857143 0.6571429 0.05714286 0.05714286 0.11428571
#> [,30] [,31] [,32] [,33] [,34] [,35] [,36]
#> [1,] 0.4571429 0.3571429 0.4000000 0.37142857 0.8000000 0.7571429 0.6857143
#> [2,] 0.6857143 0.4000000 0.3714286 0.80000000 0.4857143 0.2857143 0.5000000
#> [3,] 0.8142857 0.2000000 0.6285714 0.31428571 0.3857143 0.8857143 0.3857143
#> [4,] 0.4571429 0.1714286 0.2571429 0.04285714 0.5428571 0.2571429 0.4714286
#> [5,] 0.5000000 0.1714286 0.2714286 0.48571429 0.9142857 0.3142857 0.3428571
#> [6,] 0.3142857 0.2285714 0.5857143 0.72857143 0.5714286 0.2000000 0.6285714
#> [,37] [,38] [,39] [,40] [,41] [,42] [,43]
#> [1,] 0.7000000 0.6571429 0.5571429 0.4857143 0.7428571 0.5428571 0.1857143
#> [2,] 0.5857143 0.2000000 0.8571429 0.4571429 0.8857143 0.6857143 0.9142857
#> [3,] 0.9714286 0.2285714 0.6428571 0.3285714 0.6142857 0.7571429 0.9000000
#> [4,] 0.6714286 0.5571429 0.4571429 0.6714286 0.5571429 0.5571429 0.2857143
#> [5,] 0.2857143 0.7142857 0.8285714 0.1714286 0.4285714 0.9571429 0.3714286
#> [6,] 0.9142857 0.6285714 0.7000000 0.6142857 0.6571429 0.8000000 0.9857143
#> [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.7142857 0.7714286 0.3428571 0.3000000 0.3714286 0.24285714 0.5571429
#> [2,] 0.4571429 0.9142857 0.9714286 0.8428571 0.9571429 0.61428571 1.0000000
#> [3,] 0.6142857 0.4285714 0.5857143 0.8000000 0.7571429 0.11428571 0.7285714
#> [4,] 0.8428571 0.5142857 0.5428571 0.1571429 0.2428571 0.01428571 0.2000000
#> [5,] 0.7142857 0.4857143 0.8714286 0.8142857 0.6857143 0.14285714 0.3285714
#> [6,] 0.5714286 0.3000000 0.8714286 0.8285714 0.5714286 0.17142857 0.9857143
library(bayesplot)
pp_check(output_HMDCM)
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)