DINA_FOHM

library(hmcdm)

Load the spatial rotation data

N = length(Test_versions)
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = nrow(Test_order)
Jt = J/L

(1) Simulate responses and response times based on the DINA_FOHM model

TP <- TPmat(K)
Omega_true <- rOmega(TP)
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))
}
Alphas <- sim_alphas(model="FOHM", Omega = Omega_true, N=N, L=L)
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_FOHM = hmcdm(Y_sim,Q_matrix,"DINA_FOHM",Design_array,100,30)
#> 0
output_FOHM
#> 
#> Model: DINA_FOHM 
#> 
#> Sample Size: 350
#> Number of Items: 
#> Number of Time Points: 
#> 
#> Chain Length: 100, burn-in: 50
summary(output_FOHM)
#> 
#> Model: DINA_FOHM 
#> 
#> Item Parameters:
#>  ss_EAP  gs_EAP
#>  0.1993 0.08784
#>  0.1749 0.06718
#>  0.1449 0.25210
#>  0.1244 0.11229
#>  0.1680 0.19368
#>    ... 45 more items
#> 
#> Transition Parameters:
#>  [1] 0.14043 0.03141 0.05562 0.17925 0.03888 0.02903 0.07963 0.07601 0.09427
#> [10] 0.02723 0.02334 0.08122 0.02682 0.02063 0.04316 0.05308
#>    ... 15 more rows
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.2026
#> 0001  0.1897
#> 0010  0.2048
#> 0011  0.1926
#> 0100  0.1598
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 18304.54 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5212
#> M2:  0.49
#> total scores:  0.6319
a <- summary(output_FOHM)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1993277
#> [2,] 0.1749079
#> [3,] 0.1449463
#> [4,] 0.1244004
#> [5,] 0.1680391
#> [6,] 0.1537029

(3) Check for parameter estimation accuracy

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9371429 0.9414286 0.9614286 0.9857143 0.9914286

PAR_vec <- numeric(L)
for(t in 1:L){
  PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.7771429 0.8085714 0.8600000 0.9457143 0.9657143

(4) Evaluate the fit of the model to the observed response

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2395.374            NA 14158.34 1210.126 17763.84
#> D(theta_bar)   2317.826            NA 13715.50 1189.808 17223.14
#> DIC            2472.921            NA 14601.18 1230.444 18304.54
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.38 0.78 0.32 0.12 0.40
#> [2,] 0.86 0.86 0.40 0.88 0.80
#> [3,] 0.86 0.56 0.56 0.52 0.84
#> [4,] 0.48 0.60 0.88 0.58 0.74
#> [5,] 0.34 0.36 0.54 0.24 0.80
#> [6,] 0.90 0.52 0.56 0.42 1.00
head(a$PPP_item_means)
#> [1] 0.52 0.58 0.56 0.36 0.56 0.48
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.62 0.22 0.66 0.60 0.24 0.64 0.72 0.42  0.28  0.30  0.66  0.92  0.54
#> [2,]   NA   NA 0.22 0.48 0.66 0.82 0.78 0.68 0.68  0.94  0.60  0.28  0.10  0.88
#> [3,]   NA   NA   NA 0.74 0.88 0.38 0.28 0.42 0.86  0.52  0.36  0.36  0.66  0.62
#> [4,]   NA   NA   NA   NA 0.86 0.62 0.78 0.84 0.56  0.84  0.82  0.72  0.72  0.62
#> [5,]   NA   NA   NA   NA   NA 0.26 0.46 0.62 0.72  0.52  0.72  0.16  0.62  0.94
#> [6,]   NA   NA   NA   NA   NA   NA 0.50 0.54 0.86  0.70  0.90  0.94  0.66  0.38
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.82  0.92  0.56  0.20  0.68  0.42  0.42  0.78  0.68  0.90  0.86  0.74
#> [2,]  0.82  0.84  0.74  0.64  0.58  0.10  0.08  0.02  0.58  0.08  0.20  0.26
#> [3,]  0.48  0.52  0.12  0.00  0.08  0.64  0.30  0.56  0.52  0.64  0.68  0.84
#> [4,]  0.64  0.82  0.22  0.58  0.32  0.40  0.70  0.96  0.60  1.00  0.54  0.68
#> [5,]  0.48  0.50  1.00  0.88  0.98  0.62  0.80  0.14  0.44  0.54  0.38  0.94
#> [6,]  0.90  0.92  0.92  1.00  0.52  0.26  0.20  0.28  0.84  0.32  0.18  0.74
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.44  1.00  0.64  0.98  0.78  0.26  0.80  0.60  0.14  0.28  0.24  0.12
#> [2,]  0.18  0.56  0.38  0.14  0.20  0.36  0.70  0.60  0.14  0.18  0.30  0.60
#> [3,]  0.48  0.74  0.82  0.84  0.74  0.10  0.56  0.36  0.16  0.20  0.48  0.62
#> [4,]  1.00  0.98  1.00  0.58  0.78  0.14  0.04  0.92  0.08  0.66  0.36  0.96
#> [5,]  0.20  0.90  0.86  0.44  0.28  0.10  0.20  0.50  0.20  0.36  0.18  0.66
#> [6,]  0.42  0.86  1.00  0.08  0.68  0.46  0.42  0.18  0.60  0.94  0.14  0.66
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.28  0.12  0.60  0.44  0.88  0.54  0.70  1.00  0.76  0.36  0.54  0.84
#> [2,]  0.48  0.20  0.86  0.26  0.68  0.76  0.18  0.80  0.96  0.74  0.32  0.16
#> [3,]  0.00  0.16  0.50  0.72  0.08  0.46  0.94  0.16  0.22  0.58  0.08  0.56
#> [4,]  0.18  0.52  1.00  0.14  0.52  0.06  0.92  0.34  0.22  0.46  0.38  0.18
#> [5,]  0.48  0.32  0.76  0.52  0.58  0.12  0.66  0.16  0.28  0.14  0.22  0.28
#> [6,]  0.04  0.70  0.98  0.48  0.80  0.16  0.64  0.36  0.26  0.42  0.16  0.20