library(hmcdm)N = length(Test_versions)
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = nrow(Test_order)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
#> 61 67 78 119 25
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
#> 0.1453 0.16476
#> 0.2235 0.18512
#> 0.2326 0.04447
#> 0.1232 0.15566
#> 0.1367 0.20499
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.87169
#> λ1 0.09275
#> λ2 0.12180
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1069
#> 0001 0.1718
#> 0010 0.1717
#> 0011 0.2851
#> 0100 0.1919
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 154397.3
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5024
#> M2: 0.49
#> total scores: 0.6229
a <- summary(output_HMDCM_RT_joint)
a
#>
#> Model: DINA_HO_RT_joint
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.1453 0.16476
#> 0.2235 0.18512
#> 0.2326 0.04447
#> 0.1232 0.15566
#> 0.1367 0.20499
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.87169
#> λ1 0.09275
#> λ2 0.12180
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1069
#> 0001 0.1718
#> 0010 0.1717
#> 0011 0.2851
#> 0100 0.1919
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 154397.3
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5208
#> M2: 0.49
#> total scores: 0.6268
a$ss_EAP
#> [,1]
#> [1,] 0.14527364
#> [2,] 0.22347089
#> [3,] 0.23264554
#> [4,] 0.12324120
#> [5,] 0.13671703
#> [6,] 0.15870662
#> [7,] 0.13474586
#> [8,] 0.16340068
#> [9,] 0.23955037
#> [10,] 0.09482755
#> [11,] 0.22594592
#> [12,] 0.21414600
#> [13,] 0.20544524
#> [14,] 0.16827695
#> [15,] 0.18610171
#> [16,] 0.24041734
#> [17,] 0.20221820
#> [18,] 0.19796050
#> [19,] 0.16214569
#> [20,] 0.16190172
#> [21,] 0.16581845
#> [22,] 0.15179118
#> [23,] 0.14965766
#> [24,] 0.22729361
#> [25,] 0.19476440
#> [26,] 0.23051407
#> [27,] 0.15559297
#> [28,] 0.18621418
#> [29,] 0.20944074
#> [30,] 0.10174868
#> [31,] 0.11808534
#> [32,] 0.14596304
#> [33,] 0.18828569
#> [34,] 0.14753469
#> [35,] 0.19077708
#> [36,] 0.23527372
#> [37,] 0.21634465
#> [38,] 0.18328075
#> [39,] 0.20804419
#> [40,] 0.20749658
#> [41,] 0.14474496
#> [42,] 0.25869170
#> [43,] 0.13241310
#> [44,] 0.12952914
#> [45,] 0.21678566
#> [46,] 0.11513858
#> [47,] 0.14294383
#> [48,] 0.23072136
#> [49,] 0.15857348
#> [50,] 0.15212187
head(a$ss_EAP)
#> [,1]
#> [1,] 0.1452736
#> [2,] 0.2234709
#> [3,] 0.2326455
#> [4,] 0.1232412
#> [5,] 0.1367170
#> [6,] 0.1587066(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#> [,1]
#> [1,] 0.8061758
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#> [,1]
#> [1,] 0.9879757
(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#> [,1]
#> [1,] 0.639022
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#> [,1]
#> [1,] 0.5692589
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9271429 0.9335714 0.9457143 0.9542857 0.9457143
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.7428571 0.7685714 0.8085714 0.8314286 0.8228571a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 1990.836 133126.8 15066.03 3277.902 153461.6
#> D(theta_bar) 1723.832 132699.9 14961.74 3140.410 152525.9
#> DIC 2257.839 133553.8 15170.31 3415.393 154397.3
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.46 0.10 0.30 0.82 0.62
#> [2,] 0.84 0.00 0.24 0.24 0.06
#> [3,] 0.40 0.32 0.28 0.44 0.06
#> [4,] 0.88 0.92 0.84 0.24 0.98
#> [5,] 0.74 0.88 0.46 0.52 0.04
#> [6,] 0.42 0.80 0.24 0.50 0.88
head(a$PPP_total_RTs)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.38 0.14 0.22 0.96 0.72
#> [2,] 0.04 0.96 0.56 0.96 0.32
#> [3,] 0.80 0.40 0.40 0.32 0.50
#> [4,] 0.96 0.08 0.84 0.72 0.12
#> [5,] 0.36 0.54 0.98 0.22 0.84
#> [6,] 0.42 0.24 0.74 0.32 0.86
head(a$PPP_item_means)
#> [1] 0.64 0.44 0.52 0.50 0.46 0.56
head(a$PPP_item_mean_RTs)
#> [1] 0.42 0.72 0.52 0.66 0.62 0.48
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.86 0.58 0.40 0.44 0.60 0.60 0.74 0.08 0.74 0.36 0.94 0.78 0.76
#> [2,] NA NA 0.98 0.88 0.80 0.48 0.82 0.88 0.64 0.62 0.78 0.80 0.80 0.46
#> [3,] NA NA NA 0.84 1.00 0.98 0.98 0.76 0.80 0.92 0.02 0.54 0.42 0.56
#> [4,] NA NA NA NA 0.96 0.94 0.82 0.94 0.80 0.96 0.94 0.82 0.90 0.96
#> [5,] NA NA NA NA NA 0.78 0.50 0.30 0.12 0.36 0.56 0.08 0.96 0.32
#> [6,] NA NA NA NA NA NA 0.84 0.74 0.74 0.82 0.40 0.94 1.00 0.26
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.62 0.14 0.62 0.56 0.56 0.28 0.40 0.22 0.48 0.16 0.94 0.14
#> [2,] 0.16 0.60 0.28 0.24 0.38 0.72 0.76 0.92 0.96 0.84 0.58 0.74
#> [3,] 0.88 0.18 0.58 0.74 0.88 0.44 0.90 0.58 0.62 0.96 0.44 0.32
#> [4,] 0.68 0.70 0.66 0.82 0.80 0.80 0.82 0.98 0.54 0.88 0.80 0.90
#> [5,] 0.10 0.14 0.02 0.30 0.44 0.20 0.34 0.92 0.44 0.16 0.88 0.20
#> [6,] 0.48 0.06 0.12 0.36 0.84 0.14 0.64 0.98 0.38 0.16 0.54 0.56
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.32 0.86 0.82 0.68 1.00 0.92 0.04 0.60 1.00 0.64 0.90 0.82
#> [2,] 0.70 0.90 0.62 0.98 0.68 0.78 0.86 0.64 0.94 0.44 0.98 0.76
#> [3,] 0.90 0.48 0.38 0.88 0.64 0.84 1.00 0.74 0.66 0.60 1.00 0.74
#> [4,] 0.74 0.84 0.92 0.42 0.60 0.74 0.50 0.82 0.94 0.38 0.72 1.00
#> [5,] 0.72 0.30 0.44 0.70 0.26 0.72 0.88 0.98 0.90 0.44 0.96 0.14
#> [6,] 0.88 0.62 0.64 0.56 0.90 0.16 0.56 0.80 0.82 0.14 0.72 0.40
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.00 0.42 0.44 0.74 0.10 0.96 0.04 0.14 0.30 0.18 0.96 0.76
#> [2,] 0.68 0.78 0.58 1.00 0.40 0.42 0.82 0.34 0.10 0.64 0.42 0.82
#> [3,] 0.50 0.86 0.68 1.00 1.00 0.78 0.82 0.92 0.98 1.00 1.00 0.96
#> [4,] 0.56 0.92 0.76 0.52 1.00 0.96 0.38 0.94 0.70 0.84 0.38 0.50
#> [5,] 0.62 0.38 0.96 0.68 0.66 0.54 0.66 0.80 0.36 0.84 0.52 0.80
#> [6,] 0.26 0.78 0.90 0.94 0.92 0.84 0.82 0.46 0.50 0.82 0.48 1.00