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 
#>  14 100 122  85  29
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
#>  0.2243 0.1115
#>  0.2815 0.3103
#>  0.1645 0.1346
#>  0.1144 0.2201
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.5241
#> τ2   0.5006
#> τ3   0.5352
#> τ4   0.5309
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.13848
#> 0001 0.06974
#> 0010 0.03330
#> 0011 0.04563
#> 0100 0.04256
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 22656.33 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4832
#> M2:  0.49
#> total scores:  0.6061
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.2243114
#> [2,] 0.2814553
#> [3,] 0.1645379
#> [4,] 0.1144351

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8564286 0.9007143 0.9414286 0.9735714 0.9842857

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] 0.5342857 0.6685714 0.8000000 0.9057143 0.9371429

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          1912.231            NA 18194.23 1856.032 21962.49
#> D(theta_bar)   1860.056            NA 17569.12 1839.469 21268.65
#> DIC            1964.406            NA 18819.33 1872.594 22656.33
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.24 0.28 0.56 0.58 0.50
#> [2,] 0.82 0.34 0.62 0.36 0.64
#> [3,] 0.60 0.84 0.82 0.52 0.98
#> [4,] 0.28 0.24 0.80 0.18 0.80
#> [5,] 0.48 0.52 0.50 0.92 0.10
#> [6,] 0.96 0.26 0.00 0.82 0.66
head(a$PPP_item_means)
#> [1] 0.26 0.14 0.34 0.28 0.44 0.34
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.36 0.56 0.42 0.44 0.50 0.14 0.36 0.46  0.30  0.56  0.64  0.66  0.76
#> [2,]   NA   NA 0.94 0.40 0.54 0.50 0.86 0.72 0.06  0.84  0.08  0.78  0.82  0.62
#> [3,]   NA   NA   NA 0.58 0.90 0.88 0.46 0.70 0.98  0.88  0.84  0.26  0.98  0.96
#> [4,]   NA   NA   NA   NA 0.86 0.40 0.24 0.66 0.14  0.20  0.74  0.24  0.80  0.98
#> [5,]   NA   NA   NA   NA   NA 0.92 0.54 0.68 0.26  0.02  0.96  0.66  0.96  0.80
#> [6,]   NA   NA   NA   NA   NA   NA 0.26 0.52 0.98  0.78  0.72  0.02  0.96  0.94
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.76  0.04  0.62  0.64  0.42  0.72  0.84  0.26  0.96  0.00  0.70  0.26
#> [2,]  0.00  0.30  0.08  0.12  0.88  0.34  0.26  0.50  0.08  0.34  0.74  0.66
#> [3,]  0.40  0.44  0.34  0.40  0.84  0.84  0.74  0.70  0.94  0.78  0.68  0.38
#> [4,]  0.12  0.92  0.28  0.86  0.42  0.40  0.22  0.70  0.14  0.80  0.26  0.28
#> [5,]  0.34  0.30  0.66  0.56  0.68  0.82  0.24  0.70  0.38  0.08  0.50  0.12
#> [6,]  0.22  0.90  0.84  0.84  0.78  0.62  0.20  0.74  0.56  0.82  0.64  0.30
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.22  0.30  0.18  0.34  0.70  0.18  0.86  0.30  0.42  0.92  0.84  0.18
#> [2,]  0.74  0.92  0.80  0.76  0.02  0.70  0.42  0.42  0.54  0.76  0.76  0.94
#> [3,]  0.16  0.10  0.54  0.08  0.54  1.00  0.36  0.22  0.98  0.44  0.80  0.90
#> [4,]  0.50  0.10  0.12  0.52  0.78  0.98  0.58  0.98  0.08  0.84  0.70  0.80
#> [5,]  0.36  0.02  0.92  0.70  0.64  0.58  0.96  0.70  0.14  0.92  0.20  0.54
#> [6,]  0.24  0.86  0.48  0.80  0.72  0.18  0.24  0.24  0.88  0.20  0.16  0.94
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.74  0.00  0.96  0.62  0.56  0.52  0.94  0.54  0.58  0.98  0.54  0.96
#> [2,]  0.40  0.04  0.46  0.76  0.96  0.72  0.68  0.56  0.78  0.66  0.88  0.48
#> [3,]  0.24  0.96  0.54  0.44  0.26  0.12  0.32  0.20  0.06  0.58  0.60  0.28
#> [4,]  1.00  0.16  0.74  0.44  0.26  0.28  0.98  0.12  0.26  0.74  0.88  0.62
#> [5,]  0.98  0.08  0.58  0.18  0.48  0.48  0.84  0.18  0.00  0.36  0.06  0.78
#> [6,]  0.24  0.74  0.62  0.36  0.40  0.90  0.18  0.38  0.18  0.72  0.58  0.60