DINA_HO_RT

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DINA_HO_RT_sep

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 
#>  66  52  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
#>  0.16149 0.19939
#>  0.09851 0.08643
#>  0.21014 0.17458
#>  0.18473 0.23380
#>  0.11463 0.20836
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    lambdas_EAP
#> λ0    -1.85612
#> λ1     1.80213
#> λ2     0.23449
#> λ3     0.08619
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000  0.1441
#> 0001  0.1981
#> 0010  0.1769
#> 0011  0.2421
#> 0100  0.1737
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 157110.6 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.5172
#> M2:  0.49
#> total scores:  0.6265
a <- summary(output_HMDCM_RT_sep)
head(a$ss_EAP)
#>            [,1]
#> [1,] 0.16149025
#> [2,] 0.09850913
#> [3,] 0.21013584
#> [4,] 0.18473048
#> [5,] 0.11463297
#> [6,] 0.12763509

(3) Check for parameter estimation accuracy

(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#>           [,1]
#> [1,] 0.8073238
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#>           [,1]
#> [1,] 0.9869721

(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#>           [,1]
#> [1,] 0.5477734
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#>           [,1]
#> [1,] 0.7695372

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9221429 0.9435714 0.9592857 0.9685714 0.9614286

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] 0.7485714 0.8085714 0.8514286 0.8857143 0.8628571

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

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2205.921      135843.4 15042.20 3067.784 156159.4
#> D(theta_bar)   1905.363      135402.1 14870.05 3030.558 155208.1
#> DIC            2506.479      136284.8 15214.35 3105.011 157110.6
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.82 0.16 0.08 0.94 1.00
#> [2,] 0.54 0.78 0.10 0.96 0.78
#> [3,] 0.76 0.42 0.38 0.58 0.86
#> [4,] 0.48 0.76 0.08 1.00 1.00
#> [5,] 0.66 0.74 0.68 0.78 0.96
#> [6,] 0.50 0.70 0.80 0.98 0.12
head(a$PPP_item_means)
#> [1] 0.50 0.38 0.56 0.46 0.42 0.32
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.22 0.96 0.94 0.48 0.26 0.36 0.38 0.82  0.36  0.14  0.18  0.68  0.20
#> [2,]   NA   NA 0.60 0.82 0.24 0.64 0.18 0.72 0.82  0.44  0.44  0.68  1.00  0.58
#> [3,]   NA   NA   NA 0.64 0.82 0.92 0.72 0.94 0.78  0.22  0.70  0.02  0.64  0.86
#> [4,]   NA   NA   NA   NA 1.00 0.46 0.66 0.90 0.78  0.92  0.66  0.60  0.84  0.68
#> [5,]   NA   NA   NA   NA   NA 0.12 0.40 0.62 0.84  0.68  0.96  0.28  1.00  0.12
#> [6,]   NA   NA   NA   NA   NA   NA 0.50 0.86 0.74  0.60  0.58  0.32  0.86  0.80
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.08  0.06  0.16  0.42  0.16  0.72  0.10  0.64  0.42  0.48  0.68  0.30
#> [2,]  0.80  0.54  0.46  0.54  0.72  0.84  0.62  0.76  0.82  0.54  0.44  0.24
#> [3,]  0.50  0.16  0.16  0.56  0.46  0.90  0.22  0.94  0.48  0.70  0.56  0.42
#> [4,]  0.78  0.64  0.22  0.32  0.52  0.56  0.92  0.82  0.78  0.62  0.96  0.00
#> [5,]  0.40  0.24  0.16  0.36  0.76  0.78  0.72  0.40  0.08  0.98  0.90  0.62
#> [6,]  0.22  0.62  0.02  0.86  0.78  0.78  0.76  0.60  0.94  0.16  0.94  0.84
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,]  1.00  0.04  0.02  0.34  0.12  0.00  0.40  0.50  0.12  0.20  0.16  0.18
#> [2,]  0.36  0.54  0.68  0.16  0.96  0.42  0.70  0.34  0.44  0.04  0.48  0.68
#> [3,]  0.74  0.48  0.54  0.68  0.38  0.48  0.50  0.80  0.98  0.58  0.98  0.40
#> [4,]  0.58  0.18  0.82  0.76  0.48  0.56  0.38  0.24  0.10  0.54  0.96  0.58
#> [5,]  0.56  0.48  0.14  0.76  0.98  0.78  0.56  0.46  0.82  0.86  0.66  0.96
#> [6,]  0.64  0.92  0.66  0.64  0.42  0.16  0.54  0.62  0.14  0.04  0.68  0.64
#>      [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,]  0.48  0.10  0.26  1.00  0.72  0.10  0.26  0.24  0.54  0.44  0.84  0.12
#> [2,]  0.72  0.50  0.76  0.62  0.12  0.80  0.76  0.86  0.24  0.92  0.50  0.54
#> [3,]  0.76  0.28  0.78  0.86  0.96  0.20  0.68  0.96  0.12  0.38  0.80  0.84
#> [4,]  0.22  0.70  0.60  0.66  0.78  0.96  0.68  0.54  0.56  0.22  0.66  0.48
#> [5,]  0.26  0.62  0.98  0.90  0.44  0.66  0.68  0.42  0.36  0.62  0.80  0.48
#> [6,]  0.64  0.22  0.82  0.56  0.26  0.36  0.90  0.70  0.32  0.04  0.64  0.68
library(bayesplot)
#> This is bayesplot version 1.14.0
#> - 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")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.