NIDA_indept

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NIDA_indept

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 
#>  27 109 123  71  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)

(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
#>  0.23889 0.2224
#>  0.16800 0.1611
#>  0.09922 0.2134
#>  0.16128 0.2410
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.3675
#> τ2   0.5436
#> τ3   0.4105
#> τ4   0.4078
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.07521
#> 0001 0.06104
#> 0010 0.05408
#> 0011 0.01081
#> 0100 0.06758
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 21653.93 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4844
#> M2:  0.49
#> total scores:  0.6075
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>            [,1]
#> [1,] 0.23888870
#> [2,] 0.16800476
#> [3,] 0.09922179
#> [4,] 0.16128011

(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] 0.8750000 0.9092857 0.9514286 0.9728571 0.9792857

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] 0.5914286 0.6942857 0.8342857 0.8914286 0.9200000

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          1972.354            NA 17195.46 1856.479 21024.29
#> D(theta_bar)   1887.976            NA 16664.74 1841.940 20394.66
#> DIC            2056.733            NA 17726.18 1871.017 21653.93
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.98 0.56 0.12 0.16 0.16
#> [2,] 0.24 0.94 0.84 0.98 0.20
#> [3,] 0.74 0.64 1.00 0.40 0.42
#> [4,] 0.90 0.34 0.30 0.82 0.96
#> [5,] 1.00 0.48 0.78 0.64 0.78
#> [6,] 0.90 0.42 0.20 0.50 0.72
head(a$PPP_item_means)
#> [1] 0.86 0.78 0.42 0.56 0.20 0.34
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA  0.9 0.88 0.52 1.00 0.78 0.64 0.98 0.92  0.06  0.06  0.44  0.46  0.34
#> [2,]   NA   NA 0.62 0.60 0.82 0.86 0.18 0.74 0.38  0.74  0.90  0.38  0.04  0.08
#> [3,]   NA   NA   NA 0.62 0.80 0.36 0.24 0.68 0.62  0.36  0.22  0.34  0.18  0.46
#> [4,]   NA   NA   NA   NA 0.72 0.70 0.72 0.96 0.74  0.86  0.72  0.72  0.06  0.74
#> [5,]   NA   NA   NA   NA   NA 0.72 0.06 0.16 0.64  0.18  0.06  0.06  0.64  0.16
#> [6,]   NA   NA   NA   NA   NA   NA 0.12 0.08 0.34  0.10  0.44  1.00  0.54  0.54
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.54  0.88  0.48  0.86  0.08  0.78  0.40  0.86  0.98  0.58  0.76  0.42
#> [2,]  0.68  0.82  0.20  0.26  0.14  0.50  0.38  0.16  0.70  0.32  0.10  0.88
#> [3,]  0.38  0.90  0.90  0.42  0.98  1.00  0.10  0.42  0.84  0.06  0.46  0.44
#> [4,]  0.72  0.66  0.32  0.46  0.44  0.38  0.16  0.40  0.56  0.26  0.30  0.22
#> [5,]  0.08  0.60  0.08  0.48  0.00  0.40  0.14  0.70  0.58  0.26  0.62  0.68
#> [6,]  0.86  0.42  0.22  0.06  0.36  0.62  0.40  0.96  0.42  0.60  0.26  0.04
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.82  0.68  0.00  0.88  0.72  0.54  0.20  0.76  0.52  0.44  0.16  0.54
#> [2,]  0.20  0.70  0.74  0.54  0.18  0.98  0.38  0.76  0.84  0.66  0.76  0.06
#> [3,]  0.14  0.18  0.14  0.88  0.24  0.14  0.14  0.70  0.34  0.58  0.16  0.18
#> [4,]  0.58  0.54  0.48  0.48  0.44  0.26  0.24  0.82  0.34  0.56  0.64  0.50
#> [5,]  0.68  0.00  0.72  0.78  0.38  1.00  0.22  0.76  0.62  0.74  0.46  0.08
#> [6,]  0.26  0.20  0.14  0.74  0.72  0.68  0.52  0.62  1.00  0.22  0.20  0.04
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.52  0.72  0.64  0.30  0.90  0.54  0.44  0.60  0.06  0.76  0.40  0.78
#> [2,]  0.38  0.60  0.28  0.94  0.82  0.42  0.82  0.46  0.56  0.66  0.02  0.56
#> [3,]  0.82  0.42  0.40  0.46  0.90  0.66  0.56  0.64  0.26  0.36  0.12  0.60
#> [4,]  0.36  0.72  0.54  0.74  0.98  0.56  0.50  0.78  0.58  0.44  0.72  0.90
#> [5,]  0.40  0.42  0.82  0.90  0.98  0.22  0.42  0.34  0.18  0.66  0.22  0.58
#> [6,]  0.04  0.28  0.74  0.98  0.98  0.64  0.88  0.76  0.76  0.46  0.32  0.50

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