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 
#>  57  64  95 107  27
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
#>  0.32818 0.18818
#>  0.15063 0.11961
#>  0.13383 0.14289
#>  0.26966 0.08958
#>  0.08136 0.14174
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0     -1.6866
#> λ1      1.6346
#> λ2      0.2300
#> λ3      0.0632
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1833
#> 0001  0.1232
#> 0010  0.1807
#> 0011  0.2540
#> 0100  0.1670
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 150552.3 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.518
#> M2:  0.49
#> total scores:  0.6232
a <- summary(output_HMDCM_RT_sep)
head(a$ss_EAP)
#>            [,1]
#> [1,] 0.32817986
#> [2,] 0.15062843
#> [3,] 0.13382623
#> [4,] 0.26966091
#> [5,] 0.08136275
#> [6,] 0.16000673

(3) Check for parameter estimation accuracy

(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#>           [,1]
#> [1,] 0.7477372
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#>           [,1]
#> [1,] 0.9874821

(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#>           [,1]
#> [1,] 0.6340749
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#>           [,1]
#> [1,] 0.6238132

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9257143 0.9271429 0.9564286 0.9621429 0.9571429

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] 0.7457143 0.7457143 0.8428571 0.8571429 0.8514286

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2267.166      129193.5 15188.24 3086.174 149735.0
#> D(theta_bar)   1957.394      128751.5 15167.99 3040.827 148917.7
#> DIC            2576.939      129635.4 15208.49 3131.522 150552.3
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.32 0.50 0.04 0.90 0.80
#> [2,] 0.50 0.22 0.26 0.90 0.86
#> [3,] 0.82 0.32 0.56 0.80 0.98
#> [4,] 0.72 0.54 0.62 0.98 0.84
#> [5,] 0.84 0.32 0.92 1.00 0.86
#> [6,] 0.64 0.48 0.90 1.00 0.78
head(a$PPP_item_means)
#> [1] 0.50 0.52 0.64 0.44 0.76 0.54
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.28 0.18 0.46 0.72 0.20 0.30 0.80 0.88  0.42  0.46  0.86  0.58  0.38
#> [2,]   NA   NA 0.64 0.50 0.76 0.42 0.56 0.90 0.46  0.60  0.94  0.48  1.00  0.36
#> [3,]   NA   NA   NA 0.88 0.24 0.42 0.36 0.52 0.34  0.74  0.06  0.56  0.50  0.60
#> [4,]   NA   NA   NA   NA 0.58 0.48 0.60 0.86 0.54  0.96  0.48  0.60  0.36  0.02
#> [5,]   NA   NA   NA   NA   NA 0.36 0.84 0.70 0.96  0.86  0.94  0.98  0.94  0.60
#> [6,]   NA   NA   NA   NA   NA   NA 0.38 0.72 0.60  0.60  0.76  0.84  0.38  0.92
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.64  0.42  0.98  0.60  0.98  0.54  0.74  0.46  0.24  0.98  0.94  0.84
#> [2,]  0.70  0.66  0.26  0.66  0.58  0.96  0.30  1.00  0.86  0.78  0.80  0.78
#> [3,]  0.84  0.48  0.22  0.76  0.42  0.14  0.70  0.74  0.24  0.20  0.34  0.48
#> [4,]  0.04  0.58  0.90  0.88  0.54  0.10  0.18  0.60  0.74  0.54  0.08  0.34
#> [5,]  0.44  0.58  0.06  0.92  0.74  0.40  0.70  0.78  0.78  0.26  0.42  0.44
#> [6,]  0.80  0.34  0.10  0.28  0.68  0.68  0.02  0.68  0.38  0.44  0.20  0.40
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  0.32  0.76  0.98  0.62  0.46  0.12  0.58  0.94  0.60  0.54  0.80  0.62
#> [2,]  0.92  0.60  0.16  0.94  0.54  0.90  0.42  0.92  1.00  0.26  0.90  0.44
#> [3,]  0.40  0.64  0.58  0.44  0.70  0.62  0.34  0.70  0.86  0.92  0.70  0.76
#> [4,]  0.32  0.50  0.06  0.96  0.44  0.10  0.28  0.48  0.06  0.74  0.62  0.18
#> [5,]  0.70  0.30  0.84  0.56  0.54  0.44  0.56  0.68  0.38  0.20  0.74  0.32
#> [6,]  0.58  0.18  0.26  0.44  0.26  0.80  0.50  0.36  0.56  0.12  0.62  0.30
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.48  0.68  0.26  0.18  0.34  0.70  0.88  0.34  0.00  0.40  0.36  0.46
#> [2,]  0.60  0.12  0.82  0.18  0.82  0.68  0.90  0.34  0.94  0.90  0.72  0.86
#> [3,]  0.72  0.62  0.76  0.60  0.74  0.88  0.58  0.22  0.48  0.90  0.58  0.50
#> [4,]  0.58  0.04  0.84  0.44  0.86  0.62  0.84  0.76  0.70  1.00  0.76  0.72
#> [5,]  0.16  0.02  0.66  0.14  0.84  0.74  0.74  0.02  0.58  0.60  0.82  0.46
#> [6,]  0.04  0.54  0.74  0.52  0.10  0.80  0.94  0.08  0.26  0.18  0.90  0.38
library(bayesplot)
#> This is bayesplot version 1.16.0
#> - 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")