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
#> 38 98 137 68 9
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
#> 0.1420 0.5674 0.5659 0.5809 0.8576
#> 0.6138 0.1482 0.6094 0.5620 0.9023
#> 0.5903 0.5263 0.5929 0.3732 0.6638
#> 0.6775 0.5657 0.2399 0.5278 0.8380
#> 0.1947 0.3000 0.6021 0.6130 0.6492
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.3164
#> τ2 0.4639
#> τ3 0.5673
#> τ4 0.2454
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.04978
#> 0001 0.05058
#> 0010 0.09310
#> 0011 0.05643
#> 0100 0.09097
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22073.03
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5232
#> M2: 0.49
#> total scores: 0.614
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.1419869 0.5673534 0.5659281 0.5809410
#> [2,] 0.6137632 0.1482431 0.6094120 0.5620024
#> [3,] 0.5902780 0.5263124 0.5929408 0.3731520
#> [4,] 0.6775224 0.5657326 0.2399112 0.5277968
#> [5,] 0.1946883 0.2999615 0.6021230 0.6130080
#> [6,] 0.5237672 0.2974212 0.1273147 0.5874604(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9264962
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9075435
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8492857 0.9107143 0.9421429 0.9585714 0.9600000
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5200000 0.6971429 0.7942857 0.8485714 0.8542857a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2078.810 NA 17440.30 1876.274 21395.38
#> D(theta_bar) 2025.526 NA 16852.92 1839.292 20717.73
#> DIC 2132.095 NA 18027.68 1913.256 22073.03
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.00 0.10 0.26 0.94 0.96
#> [2,] 0.32 0.66 0.62 0.90 0.24
#> [3,] 0.48 0.72 0.48 0.82 0.20
#> [4,] 0.96 0.72 0.04 0.70 0.32
#> [5,] 0.96 0.82 0.98 0.76 0.60
#> [6,] 0.52 0.64 0.92 0.50 0.50
head(a$PPP_item_means)
#> [1] 0.48 0.54 0.50 0.48 0.48 0.46
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.84 0.96 0.90 0.32 0.52 0.84 0.78 0.64 0.28 0.84 0.92 0.54 0.72
#> [2,] NA NA 0.98 0.72 0.84 0.58 0.20 0.22 0.58 0.32 0.24 0.54 0.24 0.46
#> [3,] NA NA NA 0.66 0.98 0.78 0.92 0.86 0.80 0.56 0.66 0.32 0.86 0.44
#> [4,] NA NA NA NA 0.90 0.84 1.00 0.78 0.40 0.96 0.26 0.34 0.84 0.64
#> [5,] NA NA NA NA NA 0.38 0.54 0.84 0.94 0.50 0.98 0.42 0.74 0.26
#> [6,] NA NA NA NA NA NA 0.46 0.48 0.40 0.46 0.26 1.00 0.78 0.42
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.88 0.10 0.24 0.78 0.46 1.00 0.84 0.18 0.34 0.26 0.94 0.46
#> [2,] 0.40 0.34 0.70 0.72 0.20 0.80 0.96 0.58 0.70 0.58 0.04 0.66
#> [3,] 0.24 0.28 0.78 0.82 0.26 0.68 0.62 0.30 0.30 0.96 0.98 0.12
#> [4,] 0.84 0.52 0.76 0.30 0.12 0.66 0.04 0.46 0.96 0.24 0.56 0.70
#> [5,] 0.72 0.68 0.92 0.54 0.12 0.44 0.48 0.16 0.80 0.40 0.12 0.60
#> [6,] 0.38 0.42 0.72 0.44 0.32 0.68 0.32 0.34 0.96 0.64 0.22 0.98
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.60 0.46 0.56 0.20 0.64 0.76 0.80 1.00 0.74 0.74 0.74 0.84
#> [2,] 0.98 0.60 0.28 0.42 0.58 0.08 0.84 0.70 0.86 0.76 0.72 0.32
#> [3,] 0.60 0.94 0.90 0.68 0.48 0.54 0.10 0.10 0.72 0.66 0.38 1.00
#> [4,] 0.46 0.98 0.24 0.42 0.52 0.82 0.16 0.92 0.48 0.46 0.78 0.72
#> [5,] 0.76 0.86 0.12 0.12 0.76 0.84 0.70 0.38 0.92 0.30 0.08 0.16
#> [6,] 0.96 0.72 0.26 0.28 0.98 0.82 0.74 0.66 0.56 0.34 0.10 0.86
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.84 0.14 0.52 0.50 0.48 0.12 0.98 0.50 0.06 0.52 0.68 0.48
#> [2,] 0.54 0.26 0.92 0.88 0.02 0.88 0.94 0.38 0.04 0.44 0.56 0.24
#> [3,] 0.54 0.70 0.86 0.94 0.42 0.74 0.76 0.00 0.18 0.82 0.28 0.38
#> [4,] 0.88 0.28 0.44 0.34 0.98 0.90 0.24 0.94 0.98 1.00 0.88 0.38
#> [5,] 0.24 0.20 0.54 1.00 0.26 0.32 0.88 0.50 0.76 0.90 0.88 0.70
#> [6,] 0.80 0.66 0.26 0.84 0.38 0.40 0.92 0.98 0.38 0.36 0.80 0.70