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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
#>  0.1608 0.1285
#>  0.1918 0.2048
#>  0.1378 0.2567
#>  0.2098 0.2158
#>  0.1816 0.1293
#>    ... 45 more items
#> 
#> Transition Parameters:
#>  [1] 0.02909 0.04587 0.03618 0.04830 0.15715 0.03313 0.05721 0.02544 0.03755
#> [10] 0.06410 0.06371 0.03695 0.04014 0.05010 0.25844 0.01663
#>    ... 15 more rows
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1944
#> 0001  0.1329
#> 0010  0.2160
#> 0011  0.2464
#> 0100  0.1279
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 18901.53 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5036
#> M2:  0.49
#> total scores:  0.6264
a <- summary(output_FOHM)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1608014
#> [2,] 0.1918233
#> [3,] 0.1378178
#> [4,] 0.2097728
#> [5,] 0.1816050
#> [6,] 0.2081184

(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] 0.9250000 0.9371429 0.9728571 0.9878571 0.9921429

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] 0.7342857 0.7800000 0.8971429 0.9514286 0.9685714

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2089.519            NA 14968.72 1259.491 18317.73
#> D(theta_bar)   2041.764            NA 14487.14 1205.031 17733.93
#> DIC            2137.274            NA 15450.31 1313.952 18901.53
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.26 0.72 0.26 0.70 0.92
#> [2,] 0.92 0.98 0.86 0.04 0.94
#> [3,] 0.56 0.86 0.08 1.00 0.28
#> [4,] 0.82 0.60 0.92 0.60 0.76
#> [5,] 0.54 0.48 0.38 0.54 0.70
#> [6,] 0.62 0.04 0.72 0.62 0.94
head(a$PPP_item_means)
#> [1] 0.52 0.40 0.50 0.44 0.40 0.52
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.24 0.74 0.82 0.48 0.66 0.76 0.78 0.74  0.82  0.50  0.66  0.26  0.34
#> [2,]   NA   NA 0.26 0.42 0.44 0.50 0.62 0.30 0.24  0.32  1.00  0.24  0.22  0.96
#> [3,]   NA   NA   NA 0.98 0.46 0.84 0.24 0.36 0.30  0.64  0.96  0.58  0.56  0.66
#> [4,]   NA   NA   NA   NA 0.68 0.44 0.54 0.96 0.66  0.70  1.00  0.20  0.94  0.94
#> [5,]   NA   NA   NA   NA   NA 0.78 0.58 0.12 0.60  0.62  0.54  0.80  0.24  0.86
#> [6,]   NA   NA   NA   NA   NA   NA 0.30 0.84 0.34  0.34  0.92  0.80  0.40  1.00
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.56  0.10  0.62  0.98  0.50  0.48  0.58  0.24  0.48  0.64  0.62  0.84
#> [2,]  0.94  0.54  0.60  0.44  0.94  0.86  0.80  0.02  0.50  0.78  0.58  0.80
#> [3,]  0.68  0.78  0.50  0.64  0.72  0.96  0.26  0.14  0.88  0.60  0.90  0.12
#> [4,]  0.64  0.86  0.12  0.68  0.18  1.00  0.62  0.04  0.78  0.54  0.74  0.12
#> [5,]  0.60  0.44  0.20  0.66  0.82  0.70  0.16  0.10  0.40  0.62  0.34  0.10
#> [6,]  0.78  0.50  0.48  0.72  0.68  0.96  0.78  0.08  0.12  1.00  0.16  0.54
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.76  0.14  0.56  0.58  0.54  0.16  0.38  0.54  0.76  0.80  0.52  0.64
#> [2,]  0.26  0.60  0.38  0.32  0.78  0.00  0.00  0.36  0.80  0.58  0.06  0.24
#> [3,]  0.02  0.40  0.28  1.00  0.70  0.16  0.24  0.64  0.58  0.42  0.18  0.34
#> [4,]  0.86  0.22  0.48  0.72  0.68  0.20  0.12  0.04  0.70  0.22  0.16  0.06
#> [5,]  0.34  0.82  0.90  0.68  0.80  0.08  0.38  0.52  0.90  0.58  0.94  0.62
#> [6,]  0.00  0.62  0.96  0.16  0.62  0.04  0.06  0.08  0.98  0.40  0.10  0.46
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  1.00  0.32  0.32  0.68  0.82  0.86  0.74  0.64  0.72  1.00  0.90  0.94
#> [2,]  0.50  0.22  0.62  0.60  0.38  0.38  0.20  0.12  0.64  0.70  0.84  0.62
#> [3,]  0.62  0.56  0.54  0.46  0.54  0.60  0.90  0.22  0.66  0.58  0.80  0.36
#> [4,]  0.98  0.32  0.56  0.58  0.22  0.28  1.00  0.56  0.74  0.34  0.64  0.28
#> [5,]  0.72  0.22  0.04  0.46  0.42  0.08  0.24  0.56  0.82  0.28  0.66  0.32
#> [6,]  0.68  0.34  0.20  0.62  0.80  0.66  0.50  0.62  0.54  0.24  0.74  0.24

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They may not be fully stable and should be used with caution. We make no claims about them.