DINA_HO_RT

library(hmcdm)

Load the spatial rotation data

N = length(Test_versions)
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = nrow(Test_order)

(1) Simulate responses and response times based on the HMDCM model with response times (no covariance between speed and learning ability)

class_0 <- sample(1:2^K, N, replace = L)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
  Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1))
}
thetas_true = rnorm(N,0,1)
tausd_true=0.5
taus_true = rnorm(N,0,tausd_true)
G_version = 3
phi_true = 0.8
lambdas_true <- c(-2, 1.6, .4, .055)       # empirical from Wang 2017
Alphas <- sim_alphas(model="HO_sep", 
                    lambdas=lambdas_true, 
                    thetas=thetas_true, 
                    Q_matrix=Q_matrix, 
                    Design_array=Design_array)
table(rowSums(Alphas[,,5]) - rowSums(Alphas[,,1])) # used to see how much transition has taken place
#> 
#>   0   1   2   3   4 
#>  68  50  80 121  31
itempars_true <- matrix(runif(J*2,.1,.2), ncol=2)
RT_itempars_true <- matrix(NA, nrow=J, ncol=2)
RT_itempars_true[,2] <- rnorm(J,3.45,.5)
RT_itempars_true[,1] <- runif(J,1.5,2)

Y_sim <- sim_hmcdm(model="DINA",Alphas,Q_matrix,Design_array,
                   itempars=itempars_true)
L_sim <- sim_RT(Alphas,Q_matrix,Design_array,RT_itempars_true,taus_true,phi_true,G_version)

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

output_HMDCM_RT_sep = hmcdm(Y_sim,Q_matrix,"DINA_HO_RT_sep",Design_array,
                            100, 30,
                            Latency_array = L_sim, G_version = G_version,
                            theta_propose = 2,deltas_propose = c(.45,.35,.25,.06))
#> 0
output_HMDCM_RT_sep
#> 
#> Model: DINA_HO_RT_sep 
#> 
#> Sample Size: 350
#> Number of Items: 
#> Number of Time Points: 
#> 
#> Chain Length: 100, burn-in: 50
summary(output_HMDCM_RT_sep)
#> 
#> Model: DINA_HO_RT_sep 
#> 
#> Item Parameters:
#>  ss_EAP  gs_EAP
#>  0.1721 0.13034
#>  0.1765 0.15182
#>  0.1635 0.03580
#>  0.2053 0.07863
#>  0.1712 0.15839
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0     -2.0677
#> λ1      1.9630
#> λ2      0.1649
#> λ3      0.1217
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1165
#> 0001  0.2040
#> 0010  0.1676
#> 0011  0.2438
#> 0100  0.2007
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 156282.7 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.512
#> M2:  0.49
#> total scores:  0.624
a <- summary(output_HMDCM_RT_sep)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1721326
#> [2,] 0.1764649
#> [3,] 0.1634737
#> [4,] 0.2052868
#> [5,] 0.1712385
#> [6,] 0.1284328

(3) Check for parameter estimation accuracy

(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#>           [,1]
#> [1,] 0.8112825
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#>          [,1]
#> [1,] 0.985651

(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#>          [,1]
#> [1,] 0.685453
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#>           [,1]
#> [1,] 0.6269805

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9185714 0.9128571 0.9392857 0.9435714 0.9478571

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] 0.7114286 0.7114286 0.7942857 0.8142857 0.8371429

(4) Evaluate the fit of the model to the observed response and response times data (here, Y_sim and R_sim)

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2185.065      134811.7 15117.94 3118.742 155233.5
#> D(theta_bar)   1881.710      134371.7 14826.58 3104.297 154184.3
#> DIC            2488.420      135251.8 15409.29 3133.188 156282.7
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.80 0.36 0.36 0.84 0.66
#> [2,] 0.96 0.88 0.92 0.32 0.52
#> [3,] 0.36 0.54 0.94 1.00 0.90
#> [4,] 0.74 0.44 0.70 0.56 0.96
#> [5,] 0.90 0.20 0.56 0.72 0.42
#> [6,] 0.94 0.88 0.68 0.86 0.48
head(a$PPP_item_means)
#> [1] 0.60 0.62 0.44 0.44 0.56 0.56
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.16 0.84  0.6 0.64 0.26 0.58 0.42 0.50  0.20  0.62  0.44  0.82  0.70
#> [2,]   NA   NA 0.94  0.7 0.50 0.52 0.58 0.82 0.66  0.38  0.56  0.26  0.84  0.90
#> [3,]   NA   NA   NA  0.8 0.44 0.72 0.88 0.82 0.86  0.92  0.60  0.94  0.66  0.84
#> [4,]   NA   NA   NA   NA 0.22 0.60 0.98 0.10 0.78  0.70  0.62  0.68  0.54  0.84
#> [5,]   NA   NA   NA   NA   NA 0.84 0.30 0.86 0.44  0.62  0.26  0.22  0.94  0.28
#> [6,]   NA   NA   NA   NA   NA   NA 0.42 0.40 0.84  0.62  0.56  0.38  0.94  0.20
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.08  0.40  0.82  0.06  0.50  0.84  0.10  0.88  0.28  0.58  0.24  0.62
#> [2,]  0.40  0.54  0.82  0.44  0.32  1.00  0.22  0.96  0.12  0.24  0.36  0.20
#> [3,]  0.90  0.62  0.98  0.38  0.84  0.58  0.60  0.48  0.10  0.62  0.06  0.26
#> [4,]  0.22  0.90  0.98  0.38  0.48  0.86  0.74  0.06  0.26  0.82  0.20  0.12
#> [5,]  0.80  0.52  0.86  0.42  0.90  0.76  0.22  0.54  0.06  0.92  0.38  0.66
#> [6,]  0.56  0.54  0.76  0.92  0.42  0.42  0.70  0.60  0.64  0.44  0.42  0.54
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.96  0.50  0.48  0.50  0.50  0.40  0.66  0.76  0.36  0.46  0.38  0.94
#> [2,]  0.86  0.76  0.14  0.52  0.38  0.88  0.90  0.80  0.24  0.46  0.38  0.84
#> [3,]  0.56  0.84  0.92  0.66  0.20  0.88  0.88  0.38  0.88  1.00  0.82  0.70
#> [4,]  0.56  0.10  0.66  1.00  0.78  0.96  0.64  0.32  0.96  0.78  0.64  0.94
#> [5,]  0.58  0.74  0.02  0.60  0.60  0.60  0.44  0.42  0.04  0.12  0.02  0.84
#> [6,]  0.66  0.06  0.24  0.34  0.24  0.00  0.76  0.52  0.00  0.10  0.00  0.22
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.82  0.24  0.56  0.94  0.42  0.82  0.82  0.38  0.30  0.72  0.54  0.56
#> [2,]  1.00  0.60  0.48  0.90  0.52  0.80  0.70  0.36  0.16  0.58  0.86  0.60
#> [3,]  0.42  0.72  0.38  0.94  0.92  1.00  0.98  0.56  0.30  0.68  0.54  0.76
#> [4,]  0.10  0.96  0.32  0.82  0.60  0.94  0.52  0.82  0.86  0.88  0.78  1.00
#> [5,]  0.70  0.42  0.28  0.62  0.52  0.80  0.24  0.46  0.18  0.86  0.66  0.88
#> [6,]  0.50  0.36  0.28  0.86  0.72  0.68  0.46  0.10  0.02  0.28  0.58  0.28
library(bayesplot)
#> This is bayesplot version 1.11.1
#> - Online documentation and vignettes at mc-stan.org/bayesplot
#> - bayesplot theme set to bayesplot::theme_default()
#>    * Does _not_ affect other ggplot2 plots
#>    * See ?bayesplot_theme_set for details on theme setting
pp_check(output_HMDCM_RT_sep, type="total_latency")