DINA_HO_RT_sep

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 
#>  40  73  95 110  32
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
#>  0.11573 0.1369
#>  0.15050 0.1028
#>  0.18653 0.1675
#>  0.18032 0.1421
#>  0.09694 0.1593
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0     -1.8414
#> λ1      1.7226
#> λ2      0.1516
#> λ3      0.1101
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1626
#> 0001  0.1878
#> 0010  0.2201
#> 0011  0.1570
#> 0100  0.1879
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 162808.8 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4928
#> M2:  0.49
#> total scores:  0.6243
a <- summary(output_HMDCM_RT_sep)
head(a$ss_EAP)
#>            [,1]
#> [1,] 0.11573008
#> [2,] 0.15050268
#> [3,] 0.18653017
#> [4,] 0.18031809
#> [5,] 0.09694252
#> [6,] 0.09862388

(3) Check for parameter estimation accuracy

(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#>           [,1]
#> [1,] 0.7794956
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#>           [,1]
#> [1,] 0.9859861

(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#>           [,1]
#> [1,] 0.6335389
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#>           [,1]
#> [1,] 0.7792111

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9357143 0.9335714 0.9478571 0.9535714 0.9514286

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] 0.7828571 0.7628571 0.8171429 0.8314286 0.8314286

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2408.026      141251.5 15053.72 3207.787 161921.1
#> D(theta_bar)   2142.419      140813.8 14870.89 3206.226 161033.3
#> DIC            2673.634      141689.3 15236.55 3209.349 162808.8
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.62 0.56 1.00 0.90 0.84
#> [2,] 0.36 0.78 0.76 0.20 0.76
#> [3,] 0.96 0.06 0.22 0.78 0.96
#> [4,] 0.98 0.64 0.52 0.42 0.58
#> [5,] 0.34 0.90 0.66 0.66 0.40
#> [6,] 0.98 0.48 0.28 1.00 0.92
head(a$PPP_item_means)
#> [1] 0.52 0.52 0.52 0.48 0.58 0.62
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA  0.5 0.98 0.74 0.66 0.72 0.84 0.72 0.78  0.42  0.84  1.00  0.96  0.68
#> [2,]   NA   NA 0.12 0.84 0.44 0.24 0.42 0.34 0.98  0.80  0.60  0.90  0.38  0.34
#> [3,]   NA   NA   NA 0.56 0.36 0.22 0.14 0.24 0.94  0.68  0.54  0.56  0.66  0.70
#> [4,]   NA   NA   NA   NA 0.64 0.78 0.62 0.86 0.58  0.68  0.50  0.46  0.60  0.38
#> [5,]   NA   NA   NA   NA   NA 0.22 0.62 0.86 0.46  0.12  0.16  1.00  0.92  0.68
#> [6,]   NA   NA   NA   NA   NA   NA 0.80 0.96 0.78  0.56  0.74  0.74  0.46  0.78
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.86  0.36  0.92  0.78  0.74  0.98  0.76  0.46  0.80  0.94  0.66  0.72
#> [2,]  0.16  0.28  0.64  0.20  0.32  0.28  0.70  0.44  0.62  0.34  0.14  0.88
#> [3,]  0.66  0.24  0.60  0.62  0.16  0.98  0.70  0.18  0.24  0.48  0.40  0.08
#> [4,]  0.64  0.12  0.90  0.74  0.38  0.54  0.40  0.26  0.50  0.66  0.28  0.32
#> [5,]  0.42  0.98  0.98  0.20  0.88  0.88  0.28  0.40  0.56  0.66  0.24  0.72
#> [6,]  0.32  0.24  0.94  0.60  0.26  0.80  0.36  0.38  0.86  0.96  0.66  0.54
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.30  0.36  0.38  0.66  0.96  0.62  0.62  0.90  0.22  1.00  0.62  0.82
#> [2,]  0.58  0.06  0.86  0.50  0.80  0.92  0.50  0.92  0.54  0.46  0.92  0.96
#> [3,]  0.36  0.56  0.26  0.30  0.96  0.58  0.54  0.96  0.62  0.80  0.70  0.18
#> [4,]  0.72  0.66  0.78  0.54  0.56  0.54  0.84  0.34  0.90  0.98  0.52  0.94
#> [5,]  0.88  0.46  0.64  0.64  0.62  0.70  0.30  0.30  0.10  0.34  0.54  0.54
#> [6,]  0.80  0.88  0.56  0.38  0.36  0.62  0.90  0.12  0.32  0.28  0.08  0.50
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.92  0.58  0.86  0.98  0.82  0.36  0.88  0.38  0.54  0.76  0.88  0.44
#> [2,]  0.46  0.00  0.66  0.80  0.90  0.94  0.80  0.72  0.12  0.62  0.88  0.46
#> [3,]  0.74  0.34  0.54  0.74  0.80  0.76  0.76  0.02  0.78  0.32  0.44  0.40
#> [4,]  0.78  0.56  0.70  0.40  0.98  0.58  0.72  0.40  0.92  0.26  0.26  0.72
#> [5,]  0.16  0.46  0.44  0.92  0.84  0.82  0.74  0.26  0.26  0.28  0.32  0.14
#> [6,]  0.22  0.12  0.70  0.82  0.26  0.30  0.84  0.64  0.34  0.06  0.22  0.18
library(bayesplot)
#> This is bayesplot version 1.9.0
#> - 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")