Load the spatial rotation data

N = dim(Design_array)[1]
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = dim(Design_array)[3]

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

tau <- numeric(K)
for(k in 1:K){
  tau[k] <- runif(1,.2,.6)
}
R = matrix(0,K,K)
# Initial alphas
p_mastery <- c(.5,.5,.4,.4)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
  for(k in 1:K){
    prereqs <- which(R[k,]==1)
    if(length(prereqs)==0){
      Alphas_0[i,k] <- rbinom(1,1,p_mastery[k])
    }
    if(length(prereqs)>0){
      Alphas_0[i,k] <- prod(Alphas_0[i,prereqs])*rbinom(1,1,p_mastery)
    }
  }
}
Alphas <- sim_alphas(model="indept",taus=tau,N=N,L=L,R=R,alpha0=Alphas_0)
table(rowSums(Alphas[,,5]) - rowSums(Alphas[,,1])) # used to see how much transition has taken place
#> 
#>   0   1   2   3   4 
#>  23 111 139  64  13
Svec <- runif(K,.1,.3)
Gvec <- runif(K,.1,.3)

Y_sim <- sim_hmcdm(model="NIDA",Alphas,Q_matrix,Design_array,
                   Svec=Svec,Gvec=Gvec)

(2) Run the MCMC to sample parameters from the posterior distribution

output_NIDA_indept = hmcdm(Y_sim, Q_matrix, "NIDA_indept", Design_array,
                           100, 30, R = R)
#> 0
output_NIDA_indept
#> 
#> Model: NIDA_indept 
#> 
#> Sample Size: 350
#> Number of Items: 
#> Number of Time Points: 
#> 
#> Chain Length: 100, burn-in: 50
summary(output_NIDA_indept)
#> 
#> Model: NIDA_indept 
#> 
#> Item Parameters:
#>  ss_EAP gs_EAP
#>  0.2344 0.2044
#>  0.1098 0.1313
#>  0.2169 0.2628
#>  0.2688 0.1426
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.2394
#> τ2   0.2876
#> τ3   0.4735
#> τ4   0.5251
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.05722
#> 0001 0.04660
#> 0010 0.07692
#> 0011 0.04191
#> 0100 0.10985
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 21825.83 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5036
#> M2:  0.49
#> total scores:  0.6088
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.2343828
#> [2,] 0.1097769
#> [3,] 0.2168630
#> [4,] 0.2688473

(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] 0.8771429 0.9107143 0.9492857 0.9642857 0.9735714

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] 0.5942857 0.6828571 0.8171429 0.8657143 0.9057143

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2061.939            NA 17234.58 1890.680 21187.19
#> D(theta_bar)   1947.064            NA 16704.23 1897.271 20548.56
#> DIC            2176.815            NA 17764.92 1884.089 21825.83
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 1.00 1.00 1.00 1.00
#> [2,] 0.78 0.34 0.72 0.48 0.42
#> [3,] 0.82 0.04 0.80 0.80 0.56
#> [4,] 0.58 0.42 0.74 0.78 0.00
#> [5,] 0.64 0.34 0.98 0.70 0.48
#> [6,] 0.58 0.44 0.96 0.94 0.06
head(a$PPP_item_means)
#> [1] 0.84 0.60 0.92 0.46 0.08 0.16
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.82 0.76 0.14 0.70 0.96 0.72 0.62 0.52  0.70  0.12  0.20  0.76  0.72
#> [2,]   NA   NA 0.86 0.86 0.76 0.44 0.70 0.96 0.90  0.62  0.24  1.00  0.52  0.84
#> [3,]   NA   NA   NA 0.62 0.68 0.36 0.74 0.34 0.96  0.82  0.22  0.16  0.22  0.24
#> [4,]   NA   NA   NA   NA 0.64 0.54 0.38 0.88 0.92  0.48  0.52  0.24  0.06  0.48
#> [5,]   NA   NA   NA   NA   NA 0.42 0.90 0.94 0.52  0.82  0.96  0.86  0.98  0.94
#> [6,]   NA   NA   NA   NA   NA   NA 0.08 1.00 0.86  0.42  0.34  0.94  0.42  0.58
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.14  0.46  0.28  0.28  0.70  0.52  0.66  0.80  0.30  0.70  0.92  0.92
#> [2,]  0.58  0.58  0.90  0.06  0.12  0.50  0.54  0.52  0.32  0.38  0.32  1.00
#> [3,]  0.56  0.12  0.36  0.02  0.68  0.22  0.64  0.00  0.00  0.46  0.36  0.92
#> [4,]  0.28  0.60  0.60  0.44  0.22  0.30  0.76  0.38  0.50  0.94  0.76  0.32
#> [5,]  0.50  0.30  0.86  0.76  0.40  0.40  0.34  0.68  0.56  0.24  0.22  0.16
#> [6,]  0.36  0.46  0.62  0.02  0.24  0.16  0.28  0.40  0.02  0.56  0.94  0.94
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.92  0.20  0.62  0.14  0.22  0.58  0.02  0.04  0.28  0.04  0.40  0.64
#> [2,]  0.44  0.88  0.76  0.48  0.92  0.24  0.46  0.38  0.64  0.56  0.94  0.96
#> [3,]  0.06  0.22  0.38  0.04  0.92  0.96  0.80  0.56  0.66  0.42  0.86  0.06
#> [4,]  0.70  0.88  0.94  0.62  0.84  0.82  0.96  0.46  0.62  0.26  0.26  0.36
#> [5,]  0.82  1.00  0.58  0.42  0.78  0.10  0.90  0.26  0.32  0.62  0.54  0.44
#> [6,]  0.12  0.84  0.34  0.38  0.32  0.46  0.86  0.40  0.48  0.20  0.92  0.64
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.34  0.86  0.90  0.96  0.14  0.22  0.50  0.82  0.52  0.98  0.64  0.98
#> [2,]  0.14  0.94  0.42  0.52  0.78  0.30  0.78  0.64  0.10  0.32  0.70  0.90
#> [3,]  0.30  0.76  0.98  0.22  0.32  0.50  0.82  0.16  0.70  0.66  0.38  0.30
#> [4,]  0.32  0.34  0.64  0.14  0.52  0.64  0.52  0.30  0.36  0.94  0.64  0.02
#> [5,]  0.08  0.88  0.74  0.70  0.12  0.56  0.86  0.88  0.20  1.00  0.98  0.88
#> [6,]  0.18  0.68  0.42  0.24  0.84  0.50  0.12  0.70  0.34  0.28  0.64  0.70