HMDCM
Load the spatial rotation data
(1) Simulate responses based on the HMDCM model
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
#> 36 41 87 140 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)(2) Run the MCMC to sample parameters from the posterior distribution
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
#> 0.21358 0.1295
#> 0.12764 0.1291
#> 0.13752 0.1891
#> 0.16142 0.2463
#> 0.09328 0.1028
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -0.87888
#> λ1 1.58656
#> λ2 0.27205
#> λ3 0.04635
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1954
#> 0001 0.1828
#> 0010 0.1725
#> 0011 0.1633
#> 0100 0.2049
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 18918.4
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5186
#> M2: 0.49
#> total scores: 0.6267
a <- summary(output_HMDCM)
a$ss_EAP
#> [,1]
#> [1,] 0.21358253
#> [2,] 0.12764328
#> [3,] 0.13752461
#> [4,] 0.16142071
#> [5,] 0.09327540
#> [6,] 0.11639334
#> [7,] 0.17008166
#> [8,] 0.13363641
#> [9,] 0.09202580
#> [10,] 0.21317484
#> [11,] 0.18044225
#> [12,] 0.13340315
#> [13,] 0.25253290
#> [14,] 0.19863744
#> [15,] 0.09045943
#> [16,] 0.18132641
#> [17,] 0.14035492
#> [18,] 0.13874298
#> [19,] 0.22679362
#> [20,] 0.14854039
#> [21,] 0.17433503
#> [22,] 0.14927752
#> [23,] 0.11550883
#> [24,] 0.10220618
#> [25,] 0.12419254
#> [26,] 0.14270303
#> [27,] 0.20507627
#> [28,] 0.17655728
#> [29,] 0.14276231
#> [30,] 0.12151921
#> [31,] 0.13087156
#> [32,] 0.11924670
#> [33,] 0.15372113
#> [34,] 0.21141074
#> [35,] 0.08586200
#> [36,] 0.15638653
#> [37,] 0.18941353
#> [38,] 0.16143471
#> [39,] 0.16002566
#> [40,] 0.10842000
#> [41,] 0.11254295
#> [42,] 0.08257697
#> [43,] 0.20037207
#> [44,] 0.12738953
#> [45,] 0.16641782
#> [46,] 0.16370288
#> [47,] 0.13573702
#> [48,] 0.13486301
#> [49,] 0.22782097
#> [50,] 0.18130822
a$lambdas_EAP
#> [,1]
#> λ0 -0.87888032
#> λ1 1.58655746
#> λ2 0.27204642
#> λ3 0.04634614
mean(a$PPP_total_scores)
#> [1] 0.6288571
mean(upper.tri(a$PPP_item_ORs))
#> [1] 0.49
mean(a$PPP_item_means)
#> [1] 0.518(3) Evaluate the accuracy of estimated parameters
Attribute-wise agreement rate between true and estimated alphas
(4) Evaluate the fit of the model to the observed response
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2289.555 NA 14499.59 1271.778 18060.92
#> D(theta_bar) 2008.706 NA 13948.75 1245.992 17203.45
#> DIC 2570.405 NA 15050.43 1297.564 18918.40
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.6285714 0.6285714 0.8000000 0.07142857 0.78571429
#> [2,] 0.9142857 0.8142857 0.4428571 0.52857143 0.85714286
#> [3,] 0.4142857 0.2428571 0.8571429 0.85714286 1.00000000
#> [4,] 0.9714286 0.3714286 0.5714286 0.97142857 0.75714286
#> [5,] 0.9857143 0.9571429 0.6285714 0.47142857 0.85714286
#> [6,] 0.6857143 0.2000000 0.1428571 1.00000000 0.08571429
head(a$PPP_item_means)
#> [1] 0.4285714 0.4714286 0.5571429 0.5428571 0.5285714 0.5428571
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] NA 0.7714286 0.8142857 0.8857143 0.7571429 0.7000000 0.4142857
#> [2,] NA NA 0.6571429 0.9857143 0.5285714 0.7142857 0.7142857
#> [3,] NA NA NA 0.8571429 0.7285714 0.7000000 0.4428571
#> [4,] NA NA NA NA 0.6285714 0.8857143 0.8428571
#> [5,] NA NA NA NA NA 0.4142857 0.5000000
#> [6,] NA NA NA NA NA NA 0.3571429
#> [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0.90000000 0.68571429 0.9285714 0.14285714 0.5714286 0.7428571 0.02857143
#> [2,] 0.92857143 0.70000000 0.9428571 0.70000000 1.0000000 1.0000000 0.87142857
#> [3,] 0.07142857 0.62857143 0.2428571 0.84285714 0.4142857 0.4714286 0.55714286
#> [4,] 0.88571429 0.50000000 0.9714286 0.05714286 0.5285714 0.9000000 0.22857143
#> [5,] 0.27142857 0.05714286 0.3000000 0.54285714 0.8571429 0.7857143 0.28571429
#> [6,] 0.78571429 0.21428571 0.3428571 0.47142857 0.8428571 0.6857143 0.88571429
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21]
#> [1,] 0.5142857 0.9571429 0.6428571 0.6428571 0.5428571 0.6857143 0.5142857
#> [2,] 0.8428571 0.3000000 0.6714286 0.8857143 0.8000000 0.9571429 0.9142857
#> [3,] 0.7000000 0.3714286 0.1857143 0.3000000 0.5571429 0.4714286 0.9571429
#> [4,] 0.6428571 0.8857143 0.6000000 0.6142857 0.5428571 0.6142857 0.3142857
#> [5,] 0.3714286 0.4857143 0.2285714 0.3714286 0.7428571 0.6142857 0.6285714
#> [6,] 0.7000000 0.9000000 0.4714286 0.4142857 0.6000000 0.4714286 0.7857143
#> [,22] [,23] [,24] [,25] [,26] [,27] [,28]
#> [1,] 0.95714286 0.7000000 0.5142857 0.2714286 0.4714286 0.2142857 0.02857143
#> [2,] 0.80000000 0.8857143 0.4571429 0.6285714 0.9142857 0.5714286 0.44285714
#> [3,] 0.07142857 0.1571429 0.1571429 0.7571429 0.5714286 0.3428571 0.30000000
#> [4,] 0.08571429 0.9142857 0.4428571 0.5285714 0.6285714 0.5142857 0.20000000
#> [5,] 0.88571429 0.5714286 0.1571429 0.4000000 0.7285714 0.3571429 0.11428571
#> [6,] 0.32857143 0.6714286 0.3714286 0.5000000 0.8714286 0.6714286 0.22857143
#> [,29] [,30] [,31] [,32] [,33] [,34] [,35]
#> [1,] 0.1142857 0.9714286 0.9142857 0.2714286 0.5428571 0.9857143 0.4142857
#> [2,] 0.8000000 0.9285714 0.3571429 0.8571429 0.2142857 1.0000000 0.3571429
#> [3,] 0.4000000 0.3285714 0.2571429 0.2428571 0.2428571 0.3142857 0.3285714
#> [4,] 0.4142857 0.1428571 0.7571429 0.6142857 0.8428571 0.6571429 0.5285714
#> [5,] 0.0000000 0.5857143 0.2000000 0.1714286 0.6428571 0.6571429 0.8000000
#> [6,] 0.3428571 0.9000000 0.6714286 0.8142857 0.6142857 0.8142857 0.7000000
#> [,36] [,37] [,38] [,39] [,40] [,41] [,42]
#> [1,] 0.2857143 0.3285714 0.7285714 0.4285714 0.9428571 0.6571429 0.7857143
#> [2,] 0.3428571 0.9428571 0.4857143 0.9000000 0.4857143 0.6142857 0.7714286
#> [3,] 0.3714286 0.2142857 0.6428571 0.2428571 0.5571429 0.6857143 0.2000000
#> [4,] 0.5857143 0.4428571 0.5285714 0.3571429 0.1142857 0.2142857 0.4428571
#> [5,] 0.6000000 0.5857143 0.5285714 0.4571429 0.7142857 0.8285714 0.9571429
#> [6,] 0.9142857 0.9428571 0.7000000 0.2714286 0.6428571 0.8714286 0.3714286
#> [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.28571429 0.8857143 0.3714286 0.45714286 0.9714286 0.7571429 0.4142857
#> [2,] 0.20000000 0.3142857 0.6857143 0.04285714 0.5714286 0.7000000 0.1571429
#> [3,] 0.65714286 0.8000000 0.8857143 0.67142857 0.6428571 0.9714286 0.9428571
#> [4,] 0.01428571 0.4142857 0.4000000 0.32857143 0.8142857 0.7714286 0.8142857
#> [5,] 0.58571429 0.9714286 0.6000000 0.52857143 0.7428571 1.0000000 0.7000000
#> [6,] 0.24285714 0.4857143 0.5428571 0.17142857 0.8000000 0.8285714 0.5428571
#> [,50]
#> [1,] 0.5571429
#> [2,] 0.3142857
#> [3,] 0.3285714
#> [4,] 0.7285714
#> [5,] 0.6714286
#> [6,] 0.5714286
library(bayesplot)
pp_check(output_HMDCM)
pp_check(output_HMDCM, plotfun="hist", type="item_OR")
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Convergence checking
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)