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 
#>  30 102 123  75  20
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
#>  0.1147 0.1272
#>  0.2177 0.1937
#>  0.2294 0.3208
#>  0.2565 0.1566
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.5897
#> τ2   0.2786
#> τ3   0.3148
#> τ4   0.5204
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.09741
#> 0001 0.06567
#> 0010 0.02443
#> 0011 0.04231
#> 0100 0.04114
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 22751.76 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4936
#> M2:  0.49
#> total scores:  0.6078
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1146640
#> [2,] 0.2177339
#> [3,] 0.2294356
#> [4,] 0.2564578

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8264286 0.8985714 0.9371429 0.9514286 0.9621429

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] 0.4771429 0.6485714 0.7828571 0.8257143 0.8600000

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2097.379            NA 18163.73 1833.662 22094.77
#> D(theta_bar)   2020.574            NA 17599.31 1817.907 21437.79
#> DIC            2174.184            NA 18728.15 1849.417 22751.76
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.00 0.78 0.72 0.18 0.26
#> [2,] 0.68 0.76 0.74 0.58 0.46
#> [3,] 0.48 0.64 0.22 0.86 0.94
#> [4,] 0.80 0.42 0.22 1.00 1.00
#> [5,] 0.78 0.36 0.82 0.84 0.36
#> [6,] 0.96 0.30 1.00 0.86 0.72
head(a$PPP_item_means)
#> [1] 0.94 0.28 0.18 0.06 0.62 0.94
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.66 0.70 0.16 0.28 0.86 0.88 0.22 0.82  0.86  0.48  0.20  0.12  0.38
#> [2,]   NA   NA 0.38 0.14 0.14 0.38 0.10 0.78 0.08  0.14  0.22  0.64  0.92  0.00
#> [3,]   NA   NA   NA 0.50 0.26 0.72 0.30 0.12 0.48  0.18  0.88  0.06  0.38  0.72
#> [4,]   NA   NA   NA   NA 0.24 0.94 0.04 0.56 0.18  0.92  0.84  0.66  0.92  0.56
#> [5,]   NA   NA   NA   NA   NA 0.12 0.22 0.72 0.42  0.34  0.80  0.20  0.20  0.26
#> [6,]   NA   NA   NA   NA   NA   NA 0.72 0.94 0.72  0.76  0.54  0.64  0.78  0.98
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.78  0.82  0.64  0.26  0.74  0.70  0.32  0.48  0.00  0.86  0.12  0.08
#> [2,]  0.30  0.10  0.38  0.44  0.02  0.82  0.90  0.18  0.38  0.74  0.02  0.92
#> [3,]  0.18  0.12  0.10  0.34  0.16  0.76  0.94  0.98  0.68  0.26  0.50  0.70
#> [4,]  0.38  0.94  0.96  0.06  0.98  0.40  0.54  1.00  0.40  1.00  0.84  0.50
#> [5,]  0.02  0.78  0.18  0.90  0.00  0.42  0.64  0.96  0.16  0.44  0.04  0.60
#> [6,]  0.30  0.90  0.74  0.34  0.96  0.16  0.86  0.96  0.46  0.28  0.68  0.18
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.98  0.04  0.92  0.12  1.00  0.16  0.14  0.64  0.90  0.70  0.52  0.88
#> [2,]  1.00  0.04  0.44  0.68  0.02  0.00  0.22  0.90  0.30  0.10  0.22  0.04
#> [3,]  0.96  0.70  0.84  0.74  0.70  0.16  0.94  0.24  0.92  0.62  0.88  0.36
#> [4,]  0.26  0.68  0.90  1.00  0.98  0.34  0.88  0.78  0.98  0.52  0.90  0.42
#> [5,]  0.62  0.18  0.62  0.32  0.06  0.16  0.78  0.56  0.82  0.70  0.16  0.14
#> [6,]  0.36  0.36  0.38  0.48  0.14  0.00  0.40  0.76  0.74  0.08  0.10  0.34
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.14  0.42  0.74  0.90  0.56  0.64  0.16  0.42  0.76  0.84  0.92  0.76
#> [2,]  0.02  0.10  1.00  0.52  0.06  0.70  0.96  0.48  0.36  0.20  0.46  1.00
#> [3,]  0.86  0.42  0.18  0.54  0.22  0.40  0.12  0.44  0.50  0.70  0.62  0.70
#> [4,]  0.88  0.80  0.62  0.48  0.18  0.36  0.04  0.46  0.20  0.74  0.26  0.66
#> [5,]  0.88  0.48  0.36  0.38  0.24  0.02  0.20  0.44  0.30  0.74  0.04  0.74
#> [6,]  0.02  0.52  0.64  0.10  0.42  0.32  0.08  0.04  0.22  0.16  0.70  0.40