NIDA_indept

library(hmcdm)

Load the spatial rotation data

N = dim(Design_array)[1]
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = dim(Design_array)[3]

(1) Simulate responses and response times based on the NIDA model

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 
#>  44 107 120  64  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)

(2) Run the MCMC to sample parameters from the posterior distribution

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
#>  0.1524 0.1171
#>  0.3015 0.2980
#>  0.1307 0.2297
#>  0.1879 0.2876
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.5516
#> τ2   0.3488
#> τ3   0.2500
#> τ4   0.2267
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.11889
#> 0001 0.04543
#> 0010 0.04398
#> 0011 0.05918
#> 0100 0.09293
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23294.03 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.498
#> M2:  0.49
#> total scores:  0.6036
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1524095
#> [2,] 0.3014561
#> [3,] 0.1307211
#> [4,] 0.1879393

(3) Check for parameter estimation accuracy

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8557143 0.8942857 0.9285714 0.9378571 0.9414286

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] 0.5142857 0.6257143 0.7485714 0.7742857 0.7800000

(4) Evaluate the fit of the model to the observed response

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2198.088            NA 18513.59 1866.924 22578.60
#> D(theta_bar)   2073.473            NA 17924.34 1865.358 21863.17
#> DIC            2322.702            NA 19102.84 1868.490 23294.03
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 0.24 0.24 0.34 0.56
#> [2,] 0.74 0.64 1.00 0.50 0.90
#> [3,] 0.40 0.62 0.66 1.00 0.76
#> [4,] 0.48 0.04 0.26 0.66 1.00
#> [5,] 0.74 0.34 0.68 0.22 0.44
#> [6,] 0.92 0.84 0.26 0.82 0.84
head(a$PPP_item_means)
#> [1] 0.84 0.70 0.46 0.58 0.80 0.14
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.14  0.6 0.30 0.28 0.80 0.36 0.50 0.00  0.52  0.18  0.82  0.18  0.66
#> [2,]   NA   NA  1.0 0.84 0.24 0.02 0.86 0.18 0.62  0.30  0.84  0.20  0.90  0.62
#> [3,]   NA   NA   NA 0.14 0.76 0.88 0.86 0.84 0.62  0.32  0.98  0.86  0.96  0.64
#> [4,]   NA   NA   NA   NA 0.14 0.74 0.76 0.58 0.06  0.82  0.34  0.62  0.40  0.86
#> [5,]   NA   NA   NA   NA   NA 0.56 0.26 0.90 0.40  0.58  0.14  0.90  0.66  0.08
#> [6,]   NA   NA   NA   NA   NA   NA 0.88 0.82 0.82  0.42  0.64  0.72  0.38  0.82
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.22  0.66  0.64  0.00  0.48  0.28  0.86  0.44  0.02  0.06  0.42  0.04
#> [2,]  0.26  0.18  0.70  0.20  0.36  0.92  0.72  0.78  0.02  0.68  0.64  0.32
#> [3,]  0.56  0.20  0.66  0.92  0.88  0.82  0.70  0.46  0.70  0.20  0.24  0.76
#> [4,]  0.26  0.62  0.10  0.02  0.12  0.24  0.48  0.66  0.62  0.70  0.90  0.22
#> [5,]  0.92  0.08  0.22  0.14  0.38  0.56  0.72  0.64  0.42  0.82  0.80  0.50
#> [6,]  0.88  0.80  0.74  0.12  0.38  0.68  0.40  0.56  0.48  0.66  0.28  0.50
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.16  0.04  0.58  0.48  0.76  0.02  0.04  0.42  0.24  0.18  0.18  0.28
#> [2,]  0.94  0.36  0.24  0.78  0.28  0.50  0.52  0.54  0.40  0.28  0.92  0.20
#> [3,]  0.20  0.36  0.14  0.22  0.80  0.50  0.96  0.50  0.18  0.44  0.88  0.80
#> [4,]  0.40  0.04  0.08  0.54  0.98  0.38  0.30  0.14  0.48  1.00  0.18  0.48
#> [5,]  0.82  0.48  0.60  0.68  1.00  0.72  0.64  0.98  0.22  0.82  0.56  0.24
#> [6,]  0.26  0.86  0.02  0.30  0.58  0.90  0.16  0.04  0.90  0.52  0.10  0.70
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.88  0.38  0.84  0.80  0.34  0.40  0.50  0.86  0.08  0.54  0.98  0.78
#> [2,]  0.00  0.82  0.44  0.72  0.10  0.06  0.66  0.20  0.04  0.16  0.42  0.92
#> [3,]  0.54  0.34  0.74  0.42  0.46  0.48  0.72  0.66  0.14  0.40  0.32  0.44
#> [4,]  0.08  0.98  0.48  0.30  0.62  0.66  0.62  0.22  0.64  0.72  0.88  0.64
#> [5,]  0.82  0.18  0.84  0.98  0.60  0.72  0.94  0.56  0.22  0.96  0.14  0.80
#> [6,]  0.40  0.64  0.70  0.82  0.74  0.68  0.42  0.26  0.96  0.70  0.82  0.58