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 
#>  28  77 130  87  28
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
#>  0.1913 0.1435
#>  0.2620 0.1841
#>  0.2223 0.1323
#>  0.2686 0.2360
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.4732
#> τ2   0.4485
#> τ3   0.4685
#> τ4   0.4047
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.09973
#> 0001 0.07230
#> 0010 0.03874
#> 0011 0.06317
#> 0100 0.05590
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23550.72 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5096
#> M2:  0.49
#> total scores:  0.6035
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1913028
#> [2,] 0.2620098
#> [3,] 0.2222702
#> [4,] 0.2685795

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8521429 0.8985714 0.9300000 0.9650000 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] 0.5285714 0.6571429 0.7542857 0.8742857 0.9000000

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2082.824            NA 18838.25 1890.781 22811.85
#> D(theta_bar)   2022.810            NA 18153.09 1897.087 22072.99
#> DIC            2142.838            NA 19523.41 1884.475 23550.72
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.02 0.06 0.04 0.68 0.34
#> [2,] 0.26 0.74 0.82 0.76 0.64
#> [3,] 0.86 0.16 0.54 0.88 0.76
#> [4,] 0.32 0.94 0.02 0.58 0.96
#> [5,] 0.66 0.68 0.42 0.64 0.58
#> [6,] 0.72 0.88 0.12 0.48 0.46
head(a$PPP_item_means)
#> [1] 0.58 0.58 0.54 0.20 0.96 0.20
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.76 0.64 0.40 0.82 0.30 0.66 0.62 0.56  0.46  0.88  0.40  0.76  0.52
#> [2,]   NA   NA 0.58 0.44 0.44 0.80 0.32 0.66 0.74  0.94  0.68  0.52  0.88  0.16
#> [3,]   NA   NA   NA 0.10 0.08 0.44 0.74 0.74 0.74  0.78  0.72  0.14  0.08  0.40
#> [4,]   NA   NA   NA   NA 0.86 0.18 0.36 0.58 0.88  0.56  0.62  0.52  0.78  0.54
#> [5,]   NA   NA   NA   NA   NA 0.72 0.00 0.60 0.58  0.96  0.80  0.24  0.12  0.98
#> [6,]   NA   NA   NA   NA   NA   NA 0.46 0.98 0.60  0.12  0.52  1.00  0.52  0.70
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.88  0.72  0.76  0.48  0.52  0.02  0.90  0.90  0.94  0.84  0.08  0.70
#> [2,]  0.52  0.72  0.82  0.68  0.58  0.24  0.44  0.48  0.60  0.20  0.96  0.72
#> [3,]  0.58  0.40  0.48  1.00  0.58  0.62  0.04  0.86  0.86  0.22  0.48  0.84
#> [4,]  0.48  0.54  0.42  0.38  0.92  0.74  0.76  0.52  0.88  0.66  0.90  1.00
#> [5,]  0.72  0.62  0.52  0.32  0.78  0.28  0.08  0.84  0.56  0.14  0.68  0.48
#> [6,]  0.58  0.94  0.18  0.84  0.96  0.10  0.84  0.28  0.68  0.36  0.62  0.56
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.86  0.34  0.64  0.90  0.94  0.24  0.74  0.72  0.48  0.46  0.60  0.80
#> [2,]  0.34  0.74  0.96  0.40  0.86  0.14  0.88  0.58  0.86  0.64  0.50  0.60
#> [3,]  0.76  0.52  0.62  0.98  0.42  0.48  0.38  0.94  0.98  0.46  0.58  0.28
#> [4,]  0.16  0.68  0.42  0.18  0.74  0.36  0.72  0.26  0.98  0.70  0.80  0.94
#> [5,]  0.82  1.00  0.72  0.20  0.70  0.10  0.52  0.34  0.04  0.90  0.78  0.68
#> [6,]  0.32  0.44  0.58  0.56  0.68  0.06  0.48  0.16  0.60  0.82  0.22  0.50
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.62  0.38  0.80  1.00  0.58  0.18  0.46  0.10  0.74  0.02  0.32  0.68
#> [2,]  0.28  0.32  0.86  0.24  0.10  0.48  0.86  0.78  0.76  0.84  0.92  0.72
#> [3,]  0.60  0.00  0.50  0.62  0.54  0.14  0.08  0.06  0.10  0.10  0.08  0.42
#> [4,]  0.74  0.30  0.94  0.44  0.14  0.58  0.76  0.62  0.26  0.04  0.80  0.38
#> [5,]  0.36  0.14  0.82  0.96  0.44  0.44  0.34  0.42  0.10  0.12  0.16  0.20
#> [6,]  0.36  0.74  0.34  0.94  0.02  0.08  0.24  0.00  0.28  0.50  0.40  0.14