tau <- numeric(K)
for(k in 1:K){
tau[k] <- runif(1,.2,.6)
}
R = matrix(0,K,K)
# Initial alphas
p_mastery <- c(.5,.5,.4,.4)
Alphas_0 <- matrix(0,N,K)
for(i in 1:N){
for(k in 1:K){
prereqs <- which(R[k,]==1)
if(length(prereqs)==0){
Alphas_0[i,k] <- rbinom(1,1,p_mastery[k])
}
if(length(prereqs)>0){
Alphas_0[i,k] <- prod(Alphas_0[i,prereqs])*rbinom(1,1,p_mastery)
}
}
}
Alphas <- sim_alphas(model="indept",taus=tau,N=N,L=L,R=R,alpha0=Alphas_0)
table(rowSums(Alphas[,,5]) - rowSums(Alphas[,,1])) # used to see how much transition has taken place
#>
#> 0 1 2 3 4
#> 26 81 131 97 15
Smats <- matrix(runif(J*K,.1,.3),c(J,K))
Gmats <- matrix(runif(J*K,.1,.3),c(J,K))
# Simulate rRUM parameters
r_stars <- Gmats / (1-Smats)
pi_stars <- apply((1-Smats)^Q_matrix, 1, prod)
Y_sim <- sim_hmcdm(model="rRUM",Alphas,Q_matrix,Design_array,
r_stars=r_stars,pi_stars=pi_stars)output_rRUM_indept = hmcdm(Y_sim,Q_matrix,"rRUM_indept",Design_array,
100,30,R = R)
#> 0
output_rRUM_indept
#>
#> Model: rRUM_indept
#>
#> Sample Size: 350
#> Number of Items:
#> Number of Time Points:
#>
#> Chain Length: 100, burn-in: 50
summary(output_rRUM_indept)
#>
#> Model: rRUM_indept
#>
#> Item Parameters:
#> r_stars1_EAP r_stars2_EAP r_stars3_EAP r_stars4_EAP pi_stars_EAP
#> 0.3176 0.56935 0.6557 0.5686 0.7948
#> 0.5866 0.34038 0.6143 0.5746 0.7097
#> 0.6205 0.56921 0.5533 0.1699 0.9049
#> 0.5548 0.68518 0.3228 0.5565 0.6844
#> 0.3052 0.09051 0.6452 0.5397 0.5408
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.4811
#> τ2 0.3098
#> τ3 0.4789
#> τ4 0.5353
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.16409
#> 0001 0.05140
#> 0010 0.01208
#> 0011 0.05345
#> 0100 0.09501
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22492.79
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5244
#> M2: 0.49
#> total scores: 0.6171
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3176423 0.56935453 0.6556858 0.5685947
#> [2,] 0.5866180 0.34038099 0.6142510 0.5746406
#> [3,] 0.6204877 0.56921088 0.5532851 0.1698577
#> [4,] 0.5548152 0.68517833 0.3227724 0.5564594
#> [5,] 0.3051780 0.09050959 0.6451712 0.5396716
#> [6,] 0.5678409 0.17589919 0.3046964 0.5800936(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9528856
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9383346
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8571429 0.8878571 0.9328571 0.9700000 0.9785714
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5285714 0.6257143 0.7800000 0.8942857 0.9200000a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2229.594 NA 17716.58 1795.939 21742.11
#> D(theta_bar) 2169.645 NA 17038.69 1783.100 20991.44
#> DIC 2289.543 NA 18394.47 1808.778 22492.79
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.96 0.98 0.52 0.10 0.96
#> [2,] 0.94 0.18 0.32 0.60 0.04
#> [3,] 0.90 0.40 1.00 0.28 1.00
#> [4,] 0.86 0.26 0.02 1.00 0.22
#> [5,] 0.48 0.60 0.38 0.94 0.84
#> [6,] 0.62 0.62 1.00 1.00 0.98
head(a$PPP_item_means)
#> [1] 0.56 0.60 0.58 0.54 0.50 0.52
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] NA 0.2 0.76 0.90 0.56 0.98 0.8367347 0.54 0.46 0.10 0.06 0.90 0.52
#> [2,] NA NA 0.76 0.70 0.78 0.50 0.8571429 0.14 0.52 0.52 0.56 0.42 0.78
#> [3,] NA NA NA 0.64 0.44 0.56 0.8367347 0.40 0.40 0.14 0.48 0.26 0.68
#> [4,] NA NA NA NA 0.74 0.38 0.7551020 0.46 0.70 0.08 0.96 0.98 0.78
#> [5,] NA NA NA NA NA 0.90 0.8979592 0.06 0.44 0.42 0.84 0.58 0.92
#> [6,] NA NA NA NA NA NA 0.7551020 0.50 0.92 0.54 0.54 0.48 0.90
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0.26 0.38 0.52 0.60 0.86 0.94 0.06 0.76 0.80 0.28 0.44 0.08
#> [2,] 0.06 0.72 0.66 0.80 0.86 0.24 0.96 0.76 0.26 0.94 0.60 0.48
#> [3,] 0.78 0.70 0.36 0.42 0.86 0.44 0.18 0.56 0.54 0.08 0.22 0.36
#> [4,] 0.46 0.98 0.28 0.96 0.54 0.82 0.74 0.74 0.58 0.18 0.76 0.90
#> [5,] 0.18 0.98 0.94 0.88 0.90 0.84 0.82 0.36 0.68 0.38 0.36 0.68
#> [6,] 0.80 0.26 0.38 0.90 0.72 0.04 0.76 0.76 0.14 0.66 0.80 0.96
#> [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,] 0.34 0.32 0.46 0.76 0.64 0.48 0.82 0.98 0.64 0.88 0.82 0.54
#> [2,] 0.96 0.24 0.84 0.64 0.58 0.86 0.22 0.20 0.48 0.18 0.64 0.50
#> [3,] 0.36 0.52 0.64 0.74 0.28 0.38 0.14 0.94 0.82 0.46 0.88 0.20
#> [4,] 0.04 0.74 0.62 0.88 0.28 0.54 0.72 0.24 0.04 0.40 0.62 0.04
#> [5,] 0.74 0.38 0.42 0.18 0.82 0.94 0.60 0.84 0.14 0.84 0.74 0.56
#> [6,] 0.76 0.84 0.90 0.10 0.38 0.84 0.78 0.88 0.26 0.80 0.42 0.88
#> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.12 0.64 0.08 0.32 0.64 0.86 0.98 0.94 0.20 0.62 0.92 0.80
#> [2,] 0.36 0.84 0.08 0.86 0.20 0.58 0.52 0.76 0.24 0.32 0.38 0.24
#> [3,] 0.26 0.80 0.64 0.60 0.34 0.28 0.40 0.88 0.38 0.36 0.58 0.36
#> [4,] 0.50 0.58 0.54 0.22 0.26 0.82 0.56 0.92 0.42 0.56 0.78 0.24
#> [5,] 0.18 0.42 0.64 1.00 0.44 0.82 0.14 0.66 0.56 0.90 0.90 0.80
#> [6,] 0.24 0.34 0.20 0.34 0.82 0.50 0.44 0.54 0.38 0.34 0.90 0.74
#> [,50]
#> [1,] 0.3061224
#> [2,] 0.6938776
#> [3,] 0.2244898
#> [4,] 0.5306122
#> [5,] 0.4489796
#> [6,] 0.2857143