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
#>  0.1855 0.1066
#>  0.1933 0.2048
#>  0.1149 0.3250
#>  0.1640 0.1535
#>  0.1286 0.1638
#>    ... 45 more items
#> 
#> Transition Parameters:
#>  [1] 0.05762 0.04467 0.05999 0.01714 0.06578 0.16154 0.05479 0.13594 0.01879
#> [10] 0.03274 0.08537 0.03498 0.07110 0.03772 0.03262 0.08921
#>    ... 15 more rows
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1848
#> 0001  0.2160
#> 0010  0.1621
#> 0011  0.1710
#> 0100  0.1798
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 18951.72 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5056
#> M2:  0.49
#> total scores:  0.6264
a <- summary(output_FOHM)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1854844
#> [2,] 0.1932964
#> [3,] 0.1148948
#> [4,] 0.1640345
#> [5,] 0.1285565
#> [6,] 0.1303325

(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] 0.9207143 0.9407143 0.9778571 0.9814286 0.9850000

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] 0.7285714 0.7885714 0.9200000 0.9285714 0.9457143

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2242.214            NA 14843.61 1288.915 18374.74
#> D(theta_bar)   2152.713            NA 14383.76 1261.286 17797.76
#> DIC            2331.714            NA 15303.46 1316.543 18951.72
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.86 0.68 0.16 0.68 0.30
#> [2,] 0.58 0.54 0.14 0.44 0.52
#> [3,] 0.72 0.16 0.48 0.20 0.14
#> [4,] 0.92 0.58 1.00 1.00 1.00
#> [5,] 0.92 0.68 0.76 0.10 0.46
#> [6,] 0.50 0.78 0.46 1.00 0.74
head(a$PPP_item_means)
#> [1] 0.44 0.40 0.48 0.64 0.46 0.58
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.58 0.90 0.70 0.52 0.78 0.38 0.48 0.72  0.28  0.62  0.32  0.64  0.86
#> [2,]   NA   NA 0.82 0.60 0.80 0.76 0.84 0.70 0.66  0.88  0.72  0.88  0.30  0.22
#> [3,]   NA   NA   NA 0.36 0.56 0.92 0.80 0.96 0.74  0.76  0.12  0.06  0.26  0.84
#> [4,]   NA   NA   NA   NA 0.74 0.86 0.64 0.78 0.96  0.88  0.54  0.22  0.20  0.62
#> [5,]   NA   NA   NA   NA   NA 0.80 0.82 0.38 0.88  0.88  1.00  0.48  0.10  0.80
#> [6,]   NA   NA   NA   NA   NA   NA 0.56 0.46 0.48  0.66  0.80  0.94  0.02  0.66
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.84  0.26  0.82  0.32  0.28  0.52  0.12  0.84  0.30  0.52  0.80  0.44
#> [2,]  0.84  0.86  0.74  0.80  0.70  0.86  0.98  0.86  0.98  0.88  0.84  0.90
#> [3,]  0.46  0.70  0.88  0.02  0.36  0.34  0.80  0.42  0.12  0.36  0.28  0.24
#> [4,]  0.56  0.46  0.24  0.72  0.18  0.44  0.30  0.84  0.98  0.06  0.86  0.86
#> [5,]  0.98  0.76  0.86  0.80  0.48  0.98  0.20  0.96  0.98  0.40  0.26  0.76
#> [6,]  0.98  0.98  0.70  0.48  0.52  0.32  0.24  0.84  1.00  0.60  0.96  0.42
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.38  0.56  0.36  0.88  0.20  0.32  0.70  0.80  0.70  0.84  0.94  0.02
#> [2,]  0.12  0.84  0.98  0.64  0.84  0.04  0.76  0.18  0.54  0.28  0.32  0.24
#> [3,]  0.10  0.50  0.26  0.76  0.98  0.56  0.90  0.50  0.40  0.88  0.50  0.88
#> [4,]  0.66  0.52  0.64  0.66  0.16  0.04  0.92  0.62  0.62  0.10  0.54  0.62
#> [5,]  0.20  0.54  0.88  0.80  0.60  0.06  0.76  0.40  0.14  0.82  0.84  0.18
#> [6,]  0.18  0.60  1.00  0.68  0.16  0.26  0.96  0.22  0.00  0.82  0.28  0.46
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.84  0.46  0.24  0.14  0.48  0.02  0.84  0.08  0.60  0.18  0.16  0.44
#> [2,]  0.06  0.90  0.02  0.86  0.82  0.32  0.10  0.56  0.60  0.64  0.52  0.54
#> [3,]  0.28  0.38  0.72  0.48  0.98  0.42  0.76  0.76  0.60  0.72  0.20  0.80
#> [4,]  0.50  0.78  0.36  0.96  0.92  0.10  0.18  0.22  0.98  0.86  0.24  0.70
#> [5,]  0.18  0.20  0.18  0.38  0.26  0.02  0.30  0.18  0.88  0.68  0.92  0.18
#> [6,]  0.52  0.78  0.52  0.38  0.24  0.20  0.10  0.80  0.72  0.26  0.14  0.42