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 
#>  52  65  88 113  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
#>  0.1400 0.13213
#>  0.2031 0.08849
#>  0.1328 0.12207
#>  0.2102 0.07193
#>  0.2203 0.14342
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0    -1.52323
#> λ1     1.41001
#> λ2     0.25574
#> λ3     0.04317
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1431
#> 0001  0.1845
#> 0010  0.1878
#> 0011  0.2328
#> 0100  0.1852
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 156614.7 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.4996
#> M2:  0.49
#> total scores:  0.6217
a <- summary(output_HMDCM_RT_sep)
head(a$ss_EAP)
#>           [,1]
#> [1,] 0.1399525
#> [2,] 0.2030880
#> [3,] 0.1328132
#> [4,] 0.2101552
#> [5,] 0.2202825
#> [6,] 0.1843547

(3) Check for parameter estimation accuracy

(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#>           [,1]
#> [1,] 0.7820421
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#>           [,1]
#> [1,] 0.9878827

(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#>           [,1]
#> [1,] 0.6958719
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#>           [,1]
#> [1,] 0.7267447

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9342857 0.9342857 0.9428571 0.9550000 0.9657143

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] 0.7600000 0.7742857 0.8057143 0.8400000 0.8800000

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2405.175      135259.3 14972.49 3116.401 155753.4
#> D(theta_bar)   2166.328      134818.5 14842.73 3064.516 154892.1
#> DIC            2644.021      135700.2 15102.25 3168.286 156614.7
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.48 0.18 0.94 0.64 0.44
#> [2,] 0.86 0.86 1.00 0.74 0.42
#> [3,] 0.70 0.48 1.00 0.50 0.64
#> [4,] 0.62 0.56 0.86 0.82 0.88
#> [5,] 0.76 0.96 0.58 0.72 0.84
#> [6,] 0.56 0.74 0.80 0.92 0.32
head(a$PPP_item_means)
#> [1] 0.48 0.50 0.48 0.52 0.46 0.54
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.16 0.08 0.68 0.54 0.42 0.30 0.32 0.92  0.42  0.90  0.76  0.72  0.62
#> [2,]   NA   NA 0.42 0.34 0.50 0.18 0.60 0.68 0.22  0.14  0.30  0.64  0.98  0.00
#> [3,]   NA   NA   NA 0.92 0.74 0.64 0.84 0.88 1.00  0.74  0.22  0.44  0.36  0.30
#> [4,]   NA   NA   NA   NA 0.22 0.46 0.34 0.90 0.96  0.64  0.24  0.04  0.38  0.50
#> [5,]   NA   NA   NA   NA   NA 0.40 0.74 0.50 0.80  0.22  0.36  0.62  0.92  0.04
#> [6,]   NA   NA   NA   NA   NA   NA 0.32 0.52 0.84  0.18  0.22  0.72  0.88  0.04
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.74  0.32  0.54  0.18  0.90  0.54  0.48  0.80  0.22  0.44  0.22  0.52
#> [2,]  0.28  0.12  0.88  0.58  0.28  0.20  0.58  0.88  0.86  0.98  0.64  0.98
#> [3,]  0.92  0.56  0.66  0.58  0.36  0.30  0.54  0.04  0.36  0.90  0.60  0.56
#> [4,]  0.54  0.74  0.54  0.82  0.30  0.26  0.84  0.58  0.82  0.94  0.92  0.36
#> [5,]  0.92  0.22  0.56  0.90  0.26  0.22  0.58  0.98  0.44  1.00  0.46  0.94
#> [6,]  0.62  0.10  0.52  0.64  0.10  0.92  0.40  0.50  0.36  0.98  0.26  0.14
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.64  0.78  0.18  0.20  0.60  0.76  0.94  0.96  0.86  0.32  0.86  0.30
#> [2,]  1.00  0.72  0.74  0.68  0.92  0.64  0.70  0.98  0.36  0.28  0.26  0.60
#> [3,]  0.16  0.40  0.24  0.64  0.06  0.14  0.54  0.90  0.94  0.50  0.50  0.76
#> [4,]  0.88  0.60  0.82  0.50  0.42  0.34  0.98  0.98  0.66  0.84  0.62  0.56
#> [5,]  1.00  0.46  0.46  0.98  0.76  0.86  0.58  0.90  0.82  0.68  0.72  0.28
#> [6,]  0.16  0.84  0.16  0.50  0.96  0.88  0.48  0.46  0.22  1.00  0.20  0.58
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.66  0.92  0.84  0.74  0.74  0.66  0.52  0.30  0.16  0.46  0.56  0.58
#> [2,]  0.64  0.36  0.24  0.02  0.06  0.10  0.32  0.44  0.14  0.16  0.52  0.60
#> [3,]  0.44  0.04  0.48  0.96  0.36  0.18  0.42  0.66  0.78  0.66  0.78  0.04
#> [4,]  0.82  0.14  0.34  0.84  0.28  0.32  0.50  0.72  0.24  0.62  0.24  0.22
#> [5,]  0.40  0.68  0.42  0.18  0.64  0.40  0.54  0.84  0.50  0.56  0.48  0.34
#> [6,]  0.70  0.04  0.26  0.70  1.00  0.20  0.94  0.82  0.60  0.72  0.12  0.82
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")