ETAs <- ETAmat(K, J, Q_matrix)
class_0 <- sample(1:2^K, N, replace = L)
Alphas_0 <- matrix(0,N,K)
mu_thetatau = c(0,0)
Sig_thetatau = rbind(c(1.8^2,.4*.5*1.8),c(.4*.5*1.8,.25))
Z = matrix(rnorm(N*2),N,2)
thetatau_true = Z%*%chol(Sig_thetatau)
thetas_true = thetatau_true[,1]
taus_true = thetatau_true[,2]
G_version = 3
phi_true = 0.8
for(i in 1:N){
Alphas_0[i,] <- inv_bijectionvector(K,(class_0[i]-1))
}
lambdas_true <- c(-2, .4, .055) # empirical from Wang 2017
Alphas <- sim_alphas(model="HO_joint",
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
#> 72 51 96 108 23
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)
output_HMDCM_RT_joint = hmcdm(Y_sim,Q_matrix,"DINA_HO_RT_joint",Design_array,100,30,
Latency_array = L_sim, G_version = G_version,
theta_propose = 2,deltas_propose = c(.45,.25,.06))
#> 0
output_HMDCM_RT_joint
#>
#> Model: DINA_HO_RT_joint
#>
#> Sample Size: 350
#> Number of Items:
#> Number of Time Points:
#>
#> Chain Length: 100, burn-in: 50
summary(output_HMDCM_RT_joint)
#>
#> Model: DINA_HO_RT_joint
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.2551 0.12800
#> 0.1999 0.18830
#> 0.1917 0.01387
#> 0.1622 0.15506
#> 0.2550 0.15673
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.41186
#> λ1 0.29178
#> λ2 0.04296
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.08387
#> 0001 0.19689
#> 0010 0.18168
#> 0011 0.28340
#> 0100 0.18376
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 155613.2
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5188
#> M2: 0.49
#> total scores: 0.6258
a <- summary(output_HMDCM_RT_joint)
a
#>
#> Model: DINA_HO_RT_joint
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.2551 0.12800
#> 0.1999 0.18830
#> 0.1917 0.01387
#> 0.1622 0.15506
#> 0.2550 0.15673
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.41186
#> λ1 0.29178
#> λ2 0.04296
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.08387
#> 0001 0.19689
#> 0010 0.18168
#> 0011 0.28340
#> 0100 0.18376
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 155613.2
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5108
#> M2: 0.49
#> total scores: 0.624
a$ss_EAP
#> [,1]
#> [1,] 0.25505672
#> [2,] 0.19985722
#> [3,] 0.19169174
#> [4,] 0.16224993
#> [5,] 0.25497196
#> [6,] 0.09102966
#> [7,] 0.24307542
#> [8,] 0.13715636
#> [9,] 0.14387928
#> [10,] 0.12483618
#> [11,] 0.16091588
#> [12,] 0.19827579
#> [13,] 0.11923858
#> [14,] 0.11351582
#> [15,] 0.18465099
#> [16,] 0.14870709
#> [17,] 0.19106547
#> [18,] 0.14111011
#> [19,] 0.15048725
#> [20,] 0.19874950
#> [21,] 0.17552183
#> [22,] 0.18660104
#> [23,] 0.20654107
#> [24,] 0.15291209
#> [25,] 0.18325069
#> [26,] 0.27603382
#> [27,] 0.24133378
#> [28,] 0.19357756
#> [29,] 0.21090229
#> [30,] 0.27036582
#> [31,] 0.22032485
#> [32,] 0.20490594
#> [33,] 0.19267863
#> [34,] 0.18625162
#> [35,] 0.17280741
#> [36,] 0.21997863
#> [37,] 0.19870503
#> [38,] 0.13521872
#> [39,] 0.14932514
#> [40,] 0.11720520
#> [41,] 0.20218220
#> [42,] 0.25155947
#> [43,] 0.19971098
#> [44,] 0.21541873
#> [45,] 0.22580289
#> [46,] 0.07077954
#> [47,] 0.17635495
#> [48,] 0.06379298
#> [49,] 0.18848982
#> [50,] 0.18895834
head(a$ss_EAP)
#> [,1]
#> [1,] 0.25505672
#> [2,] 0.19985722
#> [3,] 0.19169174
#> [4,] 0.16224993
#> [5,] 0.25497196
#> [6,] 0.09102966
(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#> [,1]
#> [1,] 0.8202868
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#> [,1]
#> [1,] 0.9886471
(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#> [,1]
#> [1,] 0.6356848
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#> [,1]
#> [1,] 0.711529
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9207143 0.9171429 0.9442857 0.9457143 0.9471429
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.7428571 0.7171429 0.8085714 0.8200000 0.8285714
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2109.751 134184.0 15140.07 3087.193 154521.0
#> D(theta_bar) 1870.746 133761.6 14884.48 2912.047 153428.9
#> DIC 2348.756 134606.5 15395.66 3262.339 155613.2
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.80 0.30 0.50 0.44 0.62
#> [2,] 0.44 0.50 0.94 1.00 0.32
#> [3,] 0.88 0.86 0.86 0.82 0.22
#> [4,] 0.94 0.76 0.78 0.62 0.68
#> [5,] 0.80 0.82 0.32 0.56 0.48
#> [6,] 0.96 0.82 0.32 0.90 0.82
head(a$PPP_total_RTs)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.08 0.26 0.80 0.24 0.74
#> [2,] 0.04 0.68 0.74 0.22 0.24
#> [3,] 0.80 0.26 0.64 0.16 0.40
#> [4,] 0.72 0.60 0.38 0.88 0.50
#> [5,] 0.78 0.46 0.54 0.32 0.46
#> [6,] 0.30 0.06 0.62 0.86 0.40
head(a$PPP_item_means)
#> [1] 0.46 0.52 0.44 0.60 0.48 0.46
head(a$PPP_item_mean_RTs)
#> [1] 0.76 0.76 0.32 0.34 0.46 0.76
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.42 0.62 0.24 0.44 0.62 0.14 0.42 0.98 0.76 0.14 0.98 0.54 0.30
#> [2,] NA NA 0.40 0.78 0.76 0.68 0.90 0.94 0.40 0.28 0.68 0.40 0.54 0.94
#> [3,] NA NA NA 0.60 0.46 0.78 0.84 0.72 0.50 0.88 0.30 0.96 0.86 0.70
#> [4,] NA NA NA NA 0.74 0.64 0.78 0.38 1.00 0.82 0.96 0.86 0.46 0.78
#> [5,] NA NA NA NA NA 0.16 0.60 0.38 0.26 0.30 0.68 0.54 0.72 0.66
#> [6,] NA NA NA NA NA NA 0.74 0.94 0.62 0.40 0.22 0.68 0.38 0.68
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.80 0.76 0.76 0.86 1.00 0.22 0.74 0.48 0.74 0.44 0.46 0.32
#> [2,] 0.40 0.68 0.58 0.96 0.26 0.66 0.60 0.80 0.96 0.98 1.00 0.74
#> [3,] 0.60 0.16 1.00 0.20 0.72 0.74 0.82 0.90 0.32 0.24 0.20 0.84
#> [4,] 0.62 0.64 0.74 0.68 0.84 0.20 0.94 0.96 0.58 0.82 0.72 0.86
#> [5,] 0.18 0.48 0.08 0.04 0.48 0.28 0.70 0.30 0.08 0.44 0.94 0.46
#> [6,] 0.94 0.84 0.62 0.46 0.90 0.50 0.88 0.88 0.30 0.46 0.22 0.36
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.40 0.04 0.06 0.46 0.70 0.54 0.36 0.98 0.72 0.68 0.44 0.98
#> [2,] 0.50 1.00 0.86 0.96 0.78 1.00 0.30 0.72 0.92 0.50 0.86 0.98
#> [3,] 0.64 0.56 0.40 0.00 0.80 0.24 0.70 0.76 0.54 0.08 0.68 0.78
#> [4,] 0.84 0.28 0.54 0.44 1.00 0.02 0.80 1.00 0.76 0.38 0.86 0.94
#> [5,] 0.40 0.42 0.34 0.84 0.86 0.88 0.86 0.16 0.70 0.96 0.60 0.48
#> [6,] 0.64 0.40 0.30 0.28 0.18 0.30 0.36 0.88 0.34 0.12 0.10 0.72
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.78 0.88 0.92 0.90 0.48 0.62 0.76 0.84 0.16 0.54 0.60 0.36
#> [2,] 0.16 1.00 0.36 0.10 0.86 0.50 0.60 0.44 0.72 0.70 0.54 0.64
#> [3,] 0.42 0.06 0.58 0.96 0.98 1.00 0.88 0.42 0.84 0.74 0.64 0.84
#> [4,] 0.84 0.12 0.98 0.52 0.28 0.70 0.90 0.74 0.76 0.42 1.00 0.92
#> [5,] 0.16 0.80 0.50 0.36 0.44 0.94 0.76 0.84 0.94 0.72 0.48 0.40
#> [6,] 0.34 0.08 0.90 0.86 0.38 0.24 0.94 0.22 0.50 0.18 0.42 0.24