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
#> 33 104 142 56 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
#> 0.1090 0.6497 0.6664 0.5431 0.7346
#> 0.5105 0.1389 0.6202 0.6858 0.9074
#> 0.5665 0.6455 0.6599 0.2906 0.7193
#> 0.5811 0.6295 0.1843 0.6234 0.7037
#> 0.1642 0.3118 0.5275 0.6264 0.6543
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.5237
#> τ2 0.3333
#> τ3 0.3879
#> τ4 0.2244
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.10047
#> 0001 0.08954
#> 0010 0.05301
#> 0011 0.05931
#> 0100 0.05846
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22157.27
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5124
#> M2: 0.49
#> total scores: 0.6161
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.1089692 0.6496760 0.6663546 0.5430807
#> [2,] 0.5105329 0.1389175 0.6201826 0.6858008
#> [3,] 0.5665165 0.6455004 0.6598620 0.2905530
#> [4,] 0.5810751 0.6294537 0.1843273 0.6234479
#> [5,] 0.1641884 0.3117803 0.5275295 0.6264469
#> [6,] 0.5695720 0.2016084 0.5605426 0.5370223(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9496857
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9156414
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8607143 0.9050000 0.9378571 0.9478571 0.9578571
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5457143 0.6714286 0.7800000 0.8200000 0.8514286a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2215.355 NA 17330.91 1883.356 21429.62
#> D(theta_bar) 2123.356 NA 16693.08 1885.537 20701.97
#> DIC 2307.355 NA 17968.74 1881.175 22157.27
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.56 0.64 0.02 0.02 0.30
#> [2,] 0.68 0.76 0.14 0.46 0.36
#> [3,] 0.62 0.82 0.30 0.22 0.64
#> [4,] 0.86 0.52 0.64 0.98 0.80
#> [5,] 0.26 0.94 0.62 0.74 0.74
#> [6,] 0.74 0.72 0.66 0.92 0.00
head(a$PPP_item_means)
#> [1] 0.54 0.80 0.42 0.38 0.52 0.52
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.12 0.54 0.20 0.34 0.20 0.14 0.80 0.92 0.32 0.58 0.28 0.92 0.06
#> [2,] NA NA 0.56 0.84 0.62 0.86 0.28 0.42 0.74 0.86 0.12 0.50 0.94 0.36
#> [3,] NA NA NA 0.36 0.08 0.16 0.36 0.30 0.32 0.70 0.28 0.18 0.48 0.18
#> [4,] NA NA NA NA 0.20 0.78 0.48 0.40 0.22 0.32 0.18 0.14 0.96 0.68
#> [5,] NA NA NA NA NA 0.22 0.84 0.10 0.32 0.10 0.16 0.16 0.28 0.30
#> [6,] NA NA NA NA NA NA 0.12 0.64 0.58 0.70 0.54 0.72 0.90 0.38
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 1.00 0.18 0.08 0.92 0.22 0.92 0.02 0.58 0.42 0.26 0.78 0.04
#> [2,] 0.66 0.54 0.34 0.00 0.38 0.52 0.76 0.48 0.44 0.36 0.42 0.04
#> [3,] 0.32 0.64 0.20 0.14 0.16 0.36 0.42 0.86 0.70 0.22 0.40 0.62
#> [4,] 0.14 0.76 0.52 0.92 0.66 0.72 0.48 1.00 0.38 0.32 0.84 0.84
#> [5,] 0.70 0.76 0.26 0.54 0.84 0.20 0.16 0.76 0.20 0.18 0.34 0.02
#> [6,] 0.10 0.72 0.74 0.18 0.38 0.18 0.10 0.66 0.60 0.16 0.02 0.40
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.68 0.24 0.28 0.16 0.16 0.08 0.90 0.60 0.02 0.12 0.22 0.18
#> [2,] 0.72 0.82 0.74 0.88 0.76 0.68 1.00 0.72 0.34 0.16 0.98 0.88
#> [3,] 0.40 0.70 0.44 0.98 0.48 0.72 0.94 0.56 0.30 0.30 0.92 0.78
#> [4,] 1.00 0.06 0.98 0.84 0.92 0.56 0.80 0.88 1.00 0.72 0.12 0.68
#> [5,] 0.00 0.12 0.34 0.20 0.36 0.04 0.52 0.42 0.48 0.26 0.66 0.64
#> [6,] 0.22 0.12 0.22 0.44 0.38 0.30 0.92 0.82 0.80 0.28 0.72 0.68
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.46 0.14 0.50 0.20 0.76 0.22 0.32 0.72 0.88 0.04 0.10 0.32
#> [2,] 0.42 0.44 0.20 0.62 0.20 0.66 0.84 0.26 0.66 0.30 0.64 0.60
#> [3,] 0.74 0.70 0.84 0.32 0.72 0.28 0.92 0.74 0.84 0.70 0.50 0.32
#> [4,] 0.74 0.10 1.00 0.46 0.94 0.98 0.42 0.58 0.60 0.84 0.38 0.80
#> [5,] 0.00 0.50 0.30 0.44 0.86 0.48 0.74 0.30 0.32 0.18 0.40 0.44
#> [6,] 0.62 0.32 0.78 0.72 0.34 0.70 0.82 0.40 0.76 0.80 0.00 0.42