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 
#>  29  95 135  79  12
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
#>  0.1377 0.1447
#>  0.3171 0.1389
#>  0.1690 0.1767
#>  0.1208 0.1671
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.4531
#> τ2   0.3522
#> τ3   0.4789
#> τ4   0.3854
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.07330
#> 0001 0.03130
#> 0010 0.08204
#> 0011 0.06450
#> 0100 0.07737
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 21563.14 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5068
#> M2:  0.49
#> total scores:  0.6146
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1376827
#> [2,] 0.3171459
#> [3,] 0.1690285
#> [4,] 0.1207563

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8707143 0.9271429 0.9585714 0.9742857 0.9814286

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] 0.5828571 0.7371429 0.8485714 0.9057143 0.9257143

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2146.420            NA 16932.47 1894.838 20973.72
#> D(theta_bar)   2108.305            NA 16386.97 1889.036 20384.31
#> DIC            2184.534            NA 17477.96 1900.640 21563.14
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 0.14 0.82 0.76 0.58
#> [2,] 0.42 0.54 0.48 0.82 0.50
#> [3,] 0.84 0.78 0.44 0.56 0.94
#> [4,] 0.78 0.96 0.94 0.90 0.76
#> [5,] 0.48 0.46 0.52 0.90 0.94
#> [6,] 0.80 0.40 0.30 0.78 0.58
head(a$PPP_item_means)
#> [1] 0.34 0.30 0.18 0.02 0.72 0.24
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.08 0.42 0.82 0.54 0.02 0.30 0.30 0.88  0.74  0.78  0.38  0.48  0.72
#> [2,]   NA   NA 0.92 0.84 0.66 0.66 0.60 0.90 0.38  0.44  0.72  0.84  0.98  0.58
#> [3,]   NA   NA   NA 0.96 0.92 0.26 0.28 0.02 0.68  0.84  0.10  0.32  0.54  0.62
#> [4,]   NA   NA   NA   NA 0.50 0.28 0.18 0.76 0.48  0.72  0.32  0.36  0.10  0.28
#> [5,]   NA   NA   NA   NA   NA 0.18 0.84 0.72 0.00  0.50  0.40  0.36  0.78  0.48
#> [6,]   NA   NA   NA   NA   NA   NA 0.14 0.14 0.36  0.08  0.16  0.08  0.06  0.18
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.92  0.78  0.08  0.38  0.76  0.10  0.88  0.46  0.10  0.92  0.56  0.10
#> [2,]  0.22  0.84  0.32  0.92  0.90  0.64  0.74  0.64  0.96  0.38  0.34  0.92
#> [3,]  0.72  0.46  0.92  0.24  0.58  0.14  0.42  0.80  0.50  0.02  0.26  0.04
#> [4,]  0.36  0.60  0.68  0.78  0.90  0.82  0.22  0.42  0.12  1.00  0.66  0.42
#> [5,]  0.82  0.44  0.70  0.54  0.92  0.76  0.80  0.98  0.54  0.66  0.90  0.92
#> [6,]  0.46  0.10  0.96  0.24  0.24  0.04  0.92  0.36  0.56  0.80  0.10  0.84
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.76  0.08  0.44  0.70  0.88  0.88  0.40  0.54  0.00  0.86  0.56  0.02
#> [2,]  0.90  0.34  0.30  0.40  0.00  0.46  0.12  0.14  0.04  0.60  0.78  0.74
#> [3,]  0.78  0.20  0.14  0.44  0.42  0.48  0.30  0.34  0.14  0.14  0.34  0.82
#> [4,]  0.56  0.68  0.50  0.90  0.44  0.78  0.06  0.60  0.10  1.00  0.80  0.72
#> [5,]  0.60  0.70  0.58  0.20  0.22  0.54  0.20  0.32  0.16  0.16  0.48  0.82
#> [6,]  0.24  0.64  0.22  0.02  0.30  0.08  0.34  0.26  0.24  0.98  0.52  0.88
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.32  0.40  0.44  0.86  0.36  0.24  0.76  0.46  0.58  0.26  0.92  0.06
#> [2,]  0.00  0.36  0.62  0.22  0.02  0.82  0.10  0.26  0.12  0.54  0.30  0.06
#> [3,]  0.60  0.14  0.68  0.92  0.88  0.24  0.46  0.86  0.28  0.70  0.46  0.60
#> [4,]  0.04  0.68  0.22  0.88  0.90  0.84  0.20  0.92  0.70  0.38  0.54  0.90
#> [5,]  0.16  0.82  0.46  0.86  0.24  0.88  0.32  0.86  0.42  0.16  0.90  0.50
#> [6,]  0.54  0.24  0.24  0.12  0.34  0.86  0.40  0.66  0.84  0.72  1.00  0.44