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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 
#>  35 107 126  68  14
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
#>  0.1819 0.2478
#>  0.2579 0.2439
#>  0.1818 0.1654
#>  0.2220 0.2238
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.3727
#> τ2   0.4323
#> τ3   0.2930
#> τ4   0.3812
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.12792
#> 0001 0.04752
#> 0010 0.06378
#> 0011 0.06141
#> 0100 0.07061
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23555.74 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4924
#> M2:  0.49
#> total scores:  0.6036
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1819058
#> [2,] 0.2578910
#> [3,] 0.1817671
#> [4,] 0.2220104

(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] 0.8728571 0.8971429 0.9292857 0.9621429 0.9678571

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 0.6485714 0.7314286 0.8628571 0.8800000

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2270.643            NA 18680.39 1866.094 22817.13
#> D(theta_bar)   2165.676            NA 18052.03 1860.802 22078.51
#> DIC            2375.610            NA 19308.74 1871.385 23555.74
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.94 0.74 0.90 0.74 0.42
#> [2,] 0.68 0.52 0.48 0.38 0.18
#> [3,] 1.00 0.56 0.52 0.50 0.34
#> [4,] 0.32 0.28 0.96 0.76 0.34
#> [5,] 0.50 0.44 0.26 0.68 0.88
#> [6,] 0.28 0.74 0.58 0.84 0.32
head(a$PPP_item_means)
#> [1] 0.90 0.78 0.64 0.14 0.26 0.28
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.14 0.04 0.60 0.54 0.72 0.74 0.36 0.90  0.50  0.12  0.22  0.00  0.94
#> [2,]   NA   NA 0.52 0.28 0.24 0.44 0.88 0.88 0.32  0.96  0.92  0.66  0.72  0.90
#> [3,]   NA   NA   NA 0.50 0.28 0.72 1.00 0.70 0.66  0.06  0.94  0.86  0.36  0.18
#> [4,]   NA   NA   NA   NA 0.06 0.88 0.66 0.70 0.68  0.72  0.44  0.54  0.48  0.20
#> [5,]   NA   NA   NA   NA   NA 0.28 0.76 0.00 0.22  0.12  0.46  0.48  0.16  0.94
#> [6,]   NA   NA   NA   NA   NA   NA 0.20 0.38 0.94  0.26  0.96  0.74  0.38  0.40
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.84  0.18  0.36  0.32  0.32  0.48  0.56  0.64  0.74  0.12  0.64  0.54
#> [2,]  0.54  0.64  1.00  0.48  0.14  0.80  0.60  0.18  0.76  0.78  0.58  0.10
#> [3,]  0.78  0.82  0.24  0.76  0.22  0.76  0.38  0.42  0.76  0.34  0.50  0.58
#> [4,]  0.56  0.50  0.14  0.82  0.68  0.76  0.30  0.76  0.62  0.86  0.56  0.28
#> [5,]  0.82  0.82  0.56  0.94  0.32  0.84  0.72  0.04  0.66  0.26  0.62  0.74
#> [6,]  0.26  0.12  0.62  0.38  0.88  0.54  0.04  0.40  0.78  0.42  0.56  0.48
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.00  0.14  0.86  0.66  0.84  0.32  0.64  0.44  0.88  0.20  0.84  0.52
#> [2,]  0.74  0.32  0.50  0.86  0.30  0.20  0.22  0.90  0.40  0.02  0.52  0.90
#> [3,]  0.68  0.28  0.02  0.04  0.92  0.84  0.42  0.82  0.36  0.60  0.84  0.30
#> [4,]  0.74  0.84  0.16  0.02  0.88  0.34  0.88  0.62  0.32  0.46  0.88  0.44
#> [5,]  0.32  0.28  0.74  0.44  0.90  0.70  0.38  0.08  0.52  0.22  0.38  0.96
#> [6,]  0.02  0.70  0.04  0.08  0.36  0.96  0.60  0.02  0.44  0.66  0.30  0.60
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.64  0.02  0.12  0.40  0.78  0.16  0.14  0.62  0.40  0.94  0.00  0.44
#> [2,]  0.12  0.60  0.90  0.22  0.12  0.66  1.00  0.34  0.06  0.64  1.00  0.78
#> [3,]  0.26  0.90  0.70  0.64  0.18  0.62  0.06  0.26  0.54  0.32  0.76  0.36
#> [4,]  0.70  0.56  0.18  0.62  0.58  0.42  0.22  0.00  0.64  1.00  0.18  0.48
#> [5,]  0.38  0.36  0.28  0.54  0.76  0.52  0.76  0.50  0.46  0.30  0.36  0.80
#> [6,]  0.20  0.04  0.42  0.88  0.04  0.22  0.96  0.30  0.70  0.14  0.24  0.40

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