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 
#>  53 123 118  50   6
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
#>  0.1641 0.2279
#>  0.2060 0.2207
#>  0.2881 0.2089
#>  0.3470 0.1773
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.3205
#> τ2   0.3092
#> τ3   0.3197
#> τ4   0.2328
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.04004
#> 0001 0.07464
#> 0010 0.04591
#> 0011 0.04867
#> 0100 0.03776
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23690.22 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5012
#> M2:  0.49
#> total scores:  0.6052
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1641021
#> [2,] 0.2060292
#> [3,] 0.2881147
#> [4,] 0.3469760

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8042857 0.8642857 0.8985714 0.9185714 0.9350000

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] 0.4285714 0.5600000 0.6514286 0.7114286 0.7628571

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2094.117            NA 19017.34 1883.369 22994.83
#> D(theta_bar)   1970.954            NA 18451.64 1876.841 22299.44
#> DIC            2217.281            NA 19583.04 1889.898 23690.22
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.96 1.00 0.90 0.50 0.26
#> [2,] 0.90 0.70 0.40 0.26 0.88
#> [3,] 0.60 0.88 0.86 0.96 0.52
#> [4,] 0.40 0.20 0.96 0.18 0.56
#> [5,] 0.74 0.98 0.50 0.20 0.22
#> [6,] 0.48 0.82 0.66 0.40 0.60
head(a$PPP_item_means)
#> [1] 0.48 0.34 0.02 0.84 0.84 0.08
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.96 0.02 0.30 0.28 0.36 1.00 0.88 0.88  0.84  0.14  0.64  0.28  0.04
#> [2,]   NA   NA 0.48 0.48 0.64 0.18 1.00 0.38 1.00  0.74  0.54  0.44  0.66  0.30
#> [3,]   NA   NA   NA 0.56 0.86 0.58 0.80 0.66 0.32  0.88  0.24  0.90  0.78  0.26
#> [4,]   NA   NA   NA   NA 0.26 0.00 0.46 0.06 0.74  0.48  0.36  0.76  0.80  0.08
#> [5,]   NA   NA   NA   NA   NA 0.10 0.54 0.06 0.10  0.56  0.22  0.76  0.68  0.44
#> [6,]   NA   NA   NA   NA   NA   NA 0.36 0.48 0.20  0.72  0.06  0.12  0.88  0.00
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.34  0.84  0.62  1.00  0.70  0.84  0.24  0.30  0.42  1.00  0.82  0.48
#> [2,]  0.12  0.40  0.50  0.48  0.62  0.86  0.56  0.32  0.30  0.96  1.00  0.20
#> [3,]  0.70  0.80  0.82  0.80  0.98  0.60  0.32  0.56  0.88  0.08  0.82  0.12
#> [4,]  0.90  0.02  0.70  0.56  0.30  0.72  0.74  0.26  0.72  0.46  0.50  0.68
#> [5,]  0.44  0.64  1.00  0.34  0.62  0.68  0.34  0.62  0.54  0.84  0.82  0.38
#> [6,]  0.36  0.18  0.26  0.28  0.06  0.72  0.66  0.24  0.18  0.42  0.60  0.70
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.60  1.00  0.54  1.00  0.58  0.82  0.34  0.66  0.98  0.90  0.54  0.92
#> [2,]  0.54  0.82  0.78  0.86  0.66  0.68  0.16  0.06  0.56  0.86  0.94  0.88
#> [3,]  0.82  0.50  0.22  0.84  0.72  0.26  0.90  0.92  0.72  0.46  0.20  0.62
#> [4,]  0.74  0.90  0.94  0.14  0.46  0.28  0.58  0.04  0.22  0.46  0.48  0.44
#> [5,]  0.90  0.84  0.98  1.00  0.32  0.52  0.42  0.30  0.36  0.76  0.68  0.38
#> [6,]  0.98  0.50  0.56  0.62  0.16  0.00  0.46  1.00  0.48  0.14  0.36  0.26
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.30  0.76  0.94  0.50  0.76  1.00  0.20  0.98  0.72  1.00  0.58  0.62
#> [2,]  0.06  0.58  0.08  1.00  0.54  0.42  0.76  1.00  0.32  0.80  0.70  0.14
#> [3,]  1.00  0.44  0.36  0.52  0.00  0.12  0.20  0.38  0.30  0.86  0.28  0.88
#> [4,]  0.40  0.32  0.24  0.78  0.22  0.16  0.02  0.02  0.40  0.02  0.12  0.56
#> [5,]  0.16  0.38  0.12  0.90  0.24  0.14  0.54  0.34  0.68  0.64  0.82  0.64
#> [6,]  0.58  0.30  0.54  0.72  0.78  0.58  0.88  0.24  0.24  0.40  0.52  0.94