NIDA_indept

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

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 
#>  20  93 129  91  17
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)

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
#>  0.1674 0.2199
#>  0.1247 0.3293
#>  0.2951 0.2565
#>  0.2388 0.2609
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.2331
#> τ2   0.4450
#> τ3   0.5775
#> τ4   0.4988
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.09508
#> 0001 0.04653
#> 0010 0.07996
#> 0011 0.02217
#> 0100 0.05203
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23391.34 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5356
#> M2:  0.49
#> total scores:  0.6037
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1673737
#> [2,] 0.1247369
#> [3,] 0.2950716
#> [4,] 0.2388467

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8264286 0.8742857 0.9221429 0.9464286 0.9714286

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] 0.4628571 0.5971429 0.7200000 0.8057143 0.8914286

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2153.662            NA 18664.79 1795.530 22613.98
#> D(theta_bar)   2030.082            NA 18021.98 1784.563 21836.63
#> DIC            2277.241            NA 19307.60 1806.498 23391.34
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.88 1.00 1.00 0.90 0.60
#> [2,] 0.28 0.26 0.62 0.32 0.64
#> [3,] 0.48 0.72 0.80 0.84 0.90
#> [4,] 0.66 0.46 1.00 0.74 0.96
#> [5,] 0.72 0.90 0.08 0.70 0.96
#> [6,] 0.60 0.96 0.28 0.20 0.56
head(a$PPP_item_means)
#> [1] 0.70 0.54 0.20 0.56 0.30 0.82
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.16 0.68 0.92 0.20 1.00 0.34 0.28 0.12  0.40  0.60  0.34  0.58  0.88
#> [2,]   NA   NA 0.28 0.58 0.60 0.52 0.20 0.78 0.32  0.96  0.02  0.90  0.44  0.40
#> [3,]   NA   NA   NA 0.74 0.98 0.72 0.12 0.52 0.30  0.72  0.24  0.46  0.90  0.76
#> [4,]   NA   NA   NA   NA 0.26 0.70 0.32 0.62 0.76  0.52  0.56  0.16  0.92  0.52
#> [5,]   NA   NA   NA   NA   NA 0.24 0.30 0.90 0.34  0.88  0.18  0.78  0.82  0.42
#> [6,]   NA   NA   NA   NA   NA   NA 0.06 0.74 0.06  0.06  0.10  0.12  0.70  1.00
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.86  0.60  0.72  0.88  0.24  0.84  0.18  0.96  0.04  0.18  0.64  0.30
#> [2,]  0.74  0.32  0.94  0.58  0.56  0.02  0.72  0.78  0.02  0.34  0.80  0.54
#> [3,]  0.18  0.40  0.32  0.60  0.62  0.50  0.26  0.64  0.84  0.44  0.20  0.66
#> [4,]  0.78  0.24  0.68  0.92  0.60  0.54  0.14  0.26  0.30  0.92  0.20  0.76
#> [5,]  0.80  0.16  0.14  0.02  0.14  0.10  0.12  0.28  0.54  0.16  0.50  0.40
#> [6,]  0.86  0.36  0.62  0.72  1.00  0.42  0.56  0.16  0.08  0.16  0.86  0.22
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.96  0.28  0.34  0.42  0.32  0.98  0.84  0.78  0.80  1.00  0.90  1.00
#> [2,]  0.44  0.76  0.86  0.48  0.76  0.72  0.06  0.96  0.84  0.24  0.70  0.92
#> [3,]  0.08  0.20  0.30  0.36  0.04  0.38  0.86  0.68  0.04  0.12  0.66  0.04
#> [4,]  0.32  0.84  0.48  0.72  0.16  0.14  0.14  0.16  0.46  0.60  0.88  0.14
#> [5,]  0.40  0.18  0.56  0.08  0.40  0.16  0.62  0.88  0.30  0.22  0.42  0.24
#> [6,]  0.06  0.90  0.24  1.00  0.70  0.26  0.94  0.18  0.88  0.24  0.84  0.16
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.64  0.64  0.32  0.88  0.34  0.52  0.20  0.54  0.96  0.92  0.52  1.00
#> [2,]  0.16  0.84  0.32  0.36  0.24  0.80  0.72  0.54  0.98  0.86  0.90  0.00
#> [3,]  0.66  0.34  0.26  0.76  0.02  0.38  0.30  0.00  0.18  0.44  0.10  0.84
#> [4,]  0.78  0.08  0.38  0.14  0.78  0.34  0.34  0.48  0.82  0.20  0.92  0.30
#> [5,]  0.02  0.14  0.42  0.88  0.00  0.78  0.84  0.06  0.52  0.08  0.06  0.30
#> [6,]  0.96  0.80  0.62  0.36  0.80  0.98  0.88  0.50  0.82  0.74  0.28  0.62