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
#> 77 56 72 112 33
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
#> 0.13496 0.12365
#> 0.09031 0.08922
#> 0.12600 0.08207
#> 0.16039 0.08965
#> 0.19121 0.12032
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.8148
#> λ1 0.1533
#> λ2 0.1272
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1309
#> 0001 0.1672
#> 0010 0.1950
#> 0011 0.2144
#> 0100 0.1915
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 155440.4
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5324
#> M2: 0.49
#> total scores: 0.6298
a <- summary(output_HMDCM_RT_joint)
a
#>
#> Model: DINA_HO_RT_joint
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.13496 0.12365
#> 0.09031 0.08922
#> 0.12600 0.08207
#> 0.16039 0.08965
#> 0.19121 0.12032
#> ... 45 more items
#>
#> Transition Parameters:
#> lambdas_EAP
#> λ0 -1.8148
#> λ1 0.1533
#> λ2 0.1272
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.1309
#> 0001 0.1672
#> 0010 0.1950
#> 0011 0.2144
#> 0100 0.1915
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 155440.4
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.518
#> M2: 0.49
#> total scores: 0.6299
a$ss_EAP
#> [,1]
#> [1,] 0.13495948
#> [2,] 0.09030975
#> [3,] 0.12599924
#> [4,] 0.16038546
#> [5,] 0.19120580
#> [6,] 0.17824807
#> [7,] 0.20688173
#> [8,] 0.18225436
#> [9,] 0.15951738
#> [10,] 0.16122713
#> [11,] 0.20206295
#> [12,] 0.20600604
#> [13,] 0.16809303
#> [14,] 0.28606135
#> [15,] 0.20753438
#> [16,] 0.13856575
#> [17,] 0.12575606
#> [18,] 0.14944526
#> [19,] 0.20659179
#> [20,] 0.24171264
#> [21,] 0.16623863
#> [22,] 0.10601124
#> [23,] 0.14695381
#> [24,] 0.09722359
#> [25,] 0.19436406
#> [26,] 0.14416242
#> [27,] 0.22145273
#> [28,] 0.16390729
#> [29,] 0.13252240
#> [30,] 0.16266288
#> [31,] 0.19818887
#> [32,] 0.23402195
#> [33,] 0.16493216
#> [34,] 0.13881787
#> [35,] 0.19426245
#> [36,] 0.12993108
#> [37,] 0.11382120
#> [38,] 0.15541963
#> [39,] 0.17862068
#> [40,] 0.11508894
#> [41,] 0.14846873
#> [42,] 0.19731941
#> [43,] 0.26293574
#> [44,] 0.10400561
#> [45,] 0.13566321
#> [46,] 0.17931902
#> [47,] 0.18787786
#> [48,] 0.20761956
#> [49,] 0.18265152
#> [50,] 0.22874902
head(a$ss_EAP)
#> [,1]
#> [1,] 0.13495948
#> [2,] 0.09030975
#> [3,] 0.12599924
#> [4,] 0.16038546
#> [5,] 0.19120580
#> [6,] 0.17824807
(cor_thetas <- cor(thetas_true,a$thetas_EAP))
#> [,1]
#> [1,] 0.8365949
(cor_taus <- cor(taus_true,a$response_times_coefficients$taus_EAP))
#> [,1]
#> [1,] 0.9869377
(cor_ss <- cor(as.vector(itempars_true[,1]),a$ss_EAP))
#> [,1]
#> [1,] 0.7443532
(cor_gs <- cor(as.vector(itempars_true[,2]),a$gs_EAP))
#> [,1]
#> [1,] 0.6600402
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.9292857 0.9450000 0.9578571 0.9600000 0.9521429
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.7457143 0.8000000 0.8485714 0.8685714 0.8457143
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 1855.302 134285.2 14793.10 3506.829 154440.5
#> D(theta_bar) 1589.299 133855.3 14618.38 3377.556 153440.5
#> DIC 2121.305 134715.2 14967.81 3636.101 155440.4
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.68 0.50 0.24 0.64 0.80
#> [2,] 0.00 0.98 0.84 0.72 0.50
#> [3,] 0.40 0.80 0.76 0.70 0.14
#> [4,] 0.90 0.66 0.52 0.54 0.12
#> [5,] 0.94 0.94 0.86 0.40 0.58
#> [6,] 0.54 0.38 0.02 0.82 0.96
head(a$PPP_total_RTs)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.70 0.44 0.90 0.66 0.06
#> [2,] 0.94 0.62 0.14 0.22 0.36
#> [3,] 0.66 0.68 0.02 0.82 0.56
#> [4,] 0.52 0.70 0.64 0.74 0.24
#> [5,] 0.34 0.10 0.88 0.18 0.74
#> [6,] 0.42 0.54 0.62 0.04 0.22
head(a$PPP_item_means)
#> [1] 0.64 0.58 0.44 0.58 0.50 0.58
head(a$PPP_item_mean_RTs)
#> [1] 0.38 0.34 0.34 0.28 0.56 0.50
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.8 0.68 0.90 0.58 0.66 0.92 0.84 0.98 0.98 0.52 0.08 0.72 0.38
#> [2,] NA NA 0.86 0.42 0.56 0.26 0.30 0.64 0.02 0.54 0.22 0.44 0.86 0.44
#> [3,] NA NA NA 0.82 0.16 0.72 0.80 0.80 0.84 0.36 0.74 0.68 0.24 0.70
#> [4,] NA NA NA NA 0.56 0.12 0.78 0.40 0.96 0.94 0.72 0.48 0.34 0.62
#> [5,] NA NA NA NA NA 0.66 0.40 0.78 0.44 0.54 0.58 0.20 0.02 0.12
#> [6,] NA NA NA NA NA NA 0.12 0.54 0.50 0.34 0.74 0.56 0.70 0.74
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.56 0.30 0.34 0.94 0.86 0.92 0.52 0.78 0.90 0.50 0.72 0.52
#> [2,] 0.80 0.22 0.16 0.78 0.90 0.88 0.78 0.90 0.92 0.14 0.86 0.76
#> [3,] 1.00 0.50 0.98 0.28 0.96 0.84 0.32 0.32 0.96 0.70 0.40 0.98
#> [4,] 0.42 0.36 0.68 0.58 0.52 0.70 0.84 0.10 0.78 0.44 0.62 0.32
#> [5,] 0.42 0.00 0.12 0.06 0.38 0.04 0.32 0.00 0.56 0.32 0.84 0.00
#> [6,] 0.34 0.34 0.56 0.46 0.76 0.94 0.90 0.98 0.38 0.92 0.96 0.66
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.96 0.66 0.44 0.88 0.52 0.56 0.52 1.00 0.56 0.76 0.26 0.92
#> [2,] 1.00 0.48 0.82 0.90 0.30 0.74 0.72 0.96 0.60 0.68 0.28 0.56
#> [3,] 0.72 0.64 0.52 0.78 0.34 0.10 0.32 0.86 0.40 0.94 0.38 0.88
#> [4,] 0.26 0.82 0.98 0.80 0.56 0.74 0.94 0.94 0.78 0.82 0.84 0.76
#> [5,] 0.92 0.14 0.66 0.20 0.88 0.28 0.60 0.10 0.20 0.94 0.10 0.88
#> [6,] 0.88 0.58 0.76 0.86 0.40 0.38 0.38 0.94 0.12 0.54 0.60 0.98
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.98 0.82 0.56 0.94 0.36 0.90 0.50 0.86 0.74 0.72 0.92 0.28
#> [2,] 0.78 0.96 0.62 0.78 0.50 0.88 0.98 0.68 0.44 0.92 0.70 0.06
#> [3,] 0.74 0.70 0.42 0.28 0.82 0.90 0.64 0.52 0.78 0.80 0.92 0.62
#> [4,] 0.48 0.74 0.34 0.88 0.42 0.86 0.12 0.30 0.40 0.60 0.90 0.92
#> [5,] 0.28 0.68 0.48 0.36 0.78 0.98 0.22 0.98 0.62 0.76 0.50 0.50
#> [6,] 0.50 0.02 0.94 0.06 0.06 0.74 0.60 0.10 0.30 0.74 0.06 0.32