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 
#>  36 103 137  59  15
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
#>  0.1982 0.1482
#>  0.2198 0.2354
#>  0.1114 0.1410
#>  0.1483 0.2462
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.2847
#> τ2   0.2027
#> τ3   0.4877
#> τ4   0.3626
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.09799
#> 0001 0.05034
#> 0010 0.09505
#> 0011 0.03719
#> 0100 0.09565
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 21502.37 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5264
#> M2:  0.49
#> total scores:  0.6145
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1982011
#> [2,] 0.2197755
#> [3,] 0.1113549
#> [4,] 0.1482584

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8878571 0.9207143 0.9478571 0.9592857 0.9650000

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] 0.6514286 0.7428571 0.8114286 0.8485714 0.8685714

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2284.979            NA 16748.83 1860.040 20893.85
#> D(theta_bar)   2195.809            NA 16248.04 1841.468 20285.32
#> DIC            2374.149            NA 17249.61 1878.613 21502.37
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.92 0.98 1.00 0.90 0.64
#> [2,] 0.66 0.54 0.18 1.00 0.34
#> [3,] 0.54 0.62 0.98 0.38 0.92
#> [4,] 0.56 0.36 0.20 0.40 0.82
#> [5,] 0.58 0.74 0.88 0.24 0.90
#> [6,] 0.42 0.50 0.62 0.66 0.84
head(a$PPP_item_means)
#> [1] 0.64 0.48 0.56 1.00 0.62 0.76
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.86 0.86 1.00 0.20 0.70 0.32 0.80 0.34  0.32  0.86  0.96  0.90  0.74
#> [2,]   NA   NA 0.82 0.94 0.12 0.86 0.32 0.78 0.88  0.62  0.38  0.30  0.48  0.18
#> [3,]   NA   NA   NA 0.74 0.72 0.32 0.26 0.26 0.48  0.70  0.36  0.32  0.48  0.90
#> [4,]   NA   NA   NA   NA 0.40 1.00 0.46 0.96 0.42  0.98  0.68  0.88  0.40  1.00
#> [5,]   NA   NA   NA   NA   NA 0.42 1.00 0.86 0.36  0.36  0.14  0.44  0.60  0.70
#> [6,]   NA   NA   NA   NA   NA   NA 0.68 0.92 1.00  0.92  0.50  0.86  0.04  0.44
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.24  0.86  0.96  0.00  0.22  0.94  0.98  0.52  0.24  0.16  0.46  0.24
#> [2,]  0.78  0.88  0.26  0.30  0.80  0.48  0.58  0.62  0.72  0.64  0.10  0.48
#> [3,]  0.48  0.86  0.78  0.04  0.62  0.12  0.98  0.06  0.22  0.14  0.92  0.82
#> [4,]  0.66  0.94  0.34  0.36  0.90  0.96  0.94  0.04  0.20  0.70  0.66  0.58
#> [5,]  0.28  0.70  0.32  0.00  0.44  0.46  0.48  0.40  0.82  0.14  0.94  0.82
#> [6,]  0.14  0.96  0.28  0.18  0.24  0.86  0.90  0.78  0.54  0.48  0.52  0.96
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.88  0.40  0.06  0.54  0.74  0.52  0.74  0.54  0.14  0.52  0.46  0.66
#> [2,]  0.42  0.16  0.84  0.50  0.04  0.38  0.50  0.78  0.68  0.86  0.78  0.88
#> [3,]  0.88  0.96  0.48  0.10  0.92  0.66  0.38  0.34  0.42  0.46  0.68  0.46
#> [4,]  0.32  0.82  0.18  0.62  0.60  0.90  0.54  0.18  0.86  0.84  0.44  0.96
#> [5,]  0.88  0.26  0.38  0.82  0.42  0.92  0.62  0.88  0.20  0.16  0.72  0.26
#> [6,]  0.12  0.24  0.26  0.86  0.20  0.32  0.78  0.02  0.50  0.06  0.00  0.62
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.32  0.66  0.12  0.30  0.20  0.76  0.50  0.72  0.86  0.82  0.24  0.20
#> [2,]  0.64  0.72  0.02  0.62  0.10  0.66  0.22  0.84  0.40  0.60  0.36  0.44
#> [3,]  0.12  0.86  0.52  0.28  0.34  0.38  0.90  0.42  0.28  0.74  0.44  0.20
#> [4,]  0.48  0.64  0.18  0.66  0.92  0.36  0.64  0.64  0.86  0.92  0.60  0.80
#> [5,]  0.12  0.28  0.16  0.72  0.94  0.88  0.98  0.76  0.22  0.84  0.48  1.00
#> [6,]  0.06  0.58  0.14  0.18  0.96  0.42  0.78  0.90  0.54  0.94  0.82  0.58