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 
#>  20  96 156  65  13
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
#>  0.2655 0.2242
#>  0.2151 0.2383
#>  0.1901 0.2788
#>  0.1296 0.3105
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.4003
#> τ2   0.3330
#> τ3   0.5419
#> τ4   0.4910
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.07875
#> 0001 0.11993
#> 0010 0.06023
#> 0011 0.01711
#> 0100 0.06114
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 23468.5 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.478
#> M2:  0.49
#> total scores:  0.6039
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.2655415
#> [2,] 0.2151101
#> [3,] 0.1900912
#> [4,] 0.1295927

(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] 0.8178571 0.8892857 0.9257143 0.9535714 0.9628571

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] 0.4657143 0.6371429 0.7400000 0.8314286 0.8628571

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2148.809            NA 18730.15 1826.258 22705.21
#> D(theta_bar)   2065.348            NA 18071.92 1804.659 21941.93
#> DIC            2232.271            NA 19388.37 1847.857 23468.50
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 0.72 0.02 0.48 0.64
#> [2,] 0.86 0.72 0.56 0.96 0.12
#> [3,] 0.98 0.42 0.56 0.40 0.40
#> [4,] 0.52 0.44 0.50 0.88 0.04
#> [5,] 0.92 0.54 0.56 0.70 0.60
#> [6,] 0.56 0.84 0.48 1.00 0.66
head(a$PPP_item_means)
#> [1] 0.72 0.70 0.46 0.62 0.52 0.54
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.42 0.82 0.66 0.64 0.10 0.92 0.94 0.18  0.36  0.52  0.44  0.32  0.74
#> [2,]   NA   NA 0.20 0.24 0.72 0.64 0.40 0.84 0.36  0.10  0.74  0.68  0.98  0.70
#> [3,]   NA   NA   NA 0.26 0.14 0.26 0.36 0.82 0.20  0.36  0.22  0.68  0.92  0.18
#> [4,]   NA   NA   NA   NA 0.58 0.64 0.56 0.48 0.54  0.26  0.16  0.40  0.74  0.06
#> [5,]   NA   NA   NA   NA   NA 0.32 0.26 0.26 0.86  0.40  0.66  0.22  0.46  0.44
#> [6,]   NA   NA   NA   NA   NA   NA 0.06 0.06 0.64  0.12  0.24  0.30  0.52  0.62
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.28  0.18  0.18  0.86  0.60  0.70  0.12  0.16  0.74  0.90  0.44  0.48
#> [2,]  0.96  0.50  0.78  0.20  0.36  0.96  0.34  0.52  0.32  0.72  0.50  0.20
#> [3,]  0.30  0.22  0.08  0.96  0.62  0.54  0.74  0.34  0.92  0.72  0.14  0.42
#> [4,]  0.70  0.34  0.08  0.92  0.40  0.14  0.06  0.62  0.98  0.92  0.88  0.40
#> [5,]  0.62  0.18  0.94  0.02  0.98  0.84  0.46  0.58  0.56  0.80  0.90  0.62
#> [6,]  0.84  0.60  0.30  0.86  0.98  0.22  0.82  0.94  0.82  0.80  0.74  0.92
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.90  0.58  0.12  0.24  0.36  0.74  0.12  0.76  0.38  0.00  1.00  0.42
#> [2,]  0.74  0.58  0.30  0.58  0.36  0.74  0.80  1.00  0.00  0.54  0.94  0.50
#> [3,]  0.38  0.46  0.32  0.96  0.02  0.76  0.48  0.84  0.58  0.50  0.20  0.42
#> [4,]  0.56  0.18  0.90  0.02  0.00  0.98  0.78  0.42  0.70  0.18  0.98  0.36
#> [5,]  0.20  1.00  0.80  0.90  1.00  0.40  0.04  0.98  0.52  0.90  0.88  0.26
#> [6,]  0.72  0.50  0.46  0.36  0.14  0.78  0.06  0.76  0.70  0.62  0.54  0.14
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  1.00  0.70  0.24  0.32  0.94  0.90  0.20  0.94  0.36  0.88  0.94  0.68
#> [2,]  0.88  0.34  0.92  0.42  0.54  0.26  0.84  0.96  0.48  0.62  0.20  0.78
#> [3,]  0.42  0.86  0.88  0.82  0.84  0.46  0.78  0.34  0.06  0.68  0.36  0.64
#> [4,]  0.76  0.50  0.22  0.94  0.96  0.34  0.90  0.20  0.78  1.00  1.00  0.68
#> [5,]  0.88  0.40  0.88  0.42  0.34  0.40  0.72  0.32  0.96  0.30  0.60  0.54
#> [6,]  0.02  0.18  0.98  0.30  0.02  0.04  0.72  0.86  0.48  0.82  0.26  0.82

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