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
#> 30 125 113 72 10
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
#> 0.1281 0.6022 0.6140 0.5372 0.7864
#> 0.6159 0.1664 0.5707 0.6832 0.8402
#> 0.5312 0.6961 0.6581 0.1755 0.7684
#> 0.5795 0.6583 0.2989 0.5328 0.8023
#> 0.3074 0.1266 0.6589 0.5704 0.7047
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.2907
#> τ2 0.5182
#> τ3 0.4751
#> τ4 0.2705
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.10465
#> 0001 0.03145
#> 0010 0.03940
#> 0011 0.05401
#> 0100 0.09308
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22844.89
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5032
#> M2: 0.49
#> total scores: 0.6134
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.1280841 0.6022223 0.6139969 0.5371909
#> [2,] 0.6159241 0.1663760 0.5707260 0.6831840
#> [3,] 0.5311502 0.6960942 0.6581206 0.1754828
#> [4,] 0.5795478 0.6583230 0.2989036 0.5327879
#> [5,] 0.3074269 0.1266272 0.6589252 0.5704463
#> [6,] 0.5237355 0.4366900 0.2256707 0.6139193
(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9549489
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9452464
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8707143 0.9021429 0.9357143 0.9492857 0.9585714
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5771429 0.6628571 0.7600000 0.8142857 0.8485714
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2116.166 NA 18144.13 1840.431 22100.73
#> D(theta_bar) 2025.948 NA 17513.28 1817.330 21356.56
#> DIC 2206.384 NA 18774.97 1863.532 22844.89
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.26 0.04 0.02 0.26 0.00
#> [2,] 0.52 0.70 0.46 0.66 0.44
#> [3,] 0.84 0.96 0.28 0.10 0.84
#> [4,] 0.62 0.06 0.62 0.62 0.84
#> [5,] 0.76 0.58 0.40 0.76 0.78
#> [6,] 0.70 0.26 0.84 0.54 0.58
head(a$PPP_item_means)
#> [1] 0.34 0.66 0.50 0.56 0.54 0.58
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.62 0.3 0.98 0.92 0.34 0.70 0.72 0.94 0.64 0.02 0.30 0.84 0.52
#> [2,] NA NA 1.0 0.42 0.68 0.60 0.46 0.90 0.40 0.52 0.06 0.96 0.06 0.98
#> [3,] NA NA NA 0.78 0.96 0.74 0.08 0.74 0.10 0.00 0.24 1.00 0.06 0.56
#> [4,] NA NA NA NA 0.22 0.36 0.08 0.80 0.76 0.30 0.20 0.04 0.86 0.42
#> [5,] NA NA NA NA NA 0.72 0.52 0.94 0.90 0.52 0.28 0.62 0.26 0.44
#> [6,] NA NA NA NA NA NA 0.16 0.94 0.80 0.24 0.90 0.34 0.02 0.02
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.92 0.26 0.28 0.12 0.74 0.48 0.56 0.06 0.82 0.50 0.56 0.02
#> [2,] 0.30 0.38 0.88 0.22 0.48 0.70 0.78 0.72 0.34 0.84 0.16 0.94
#> [3,] 0.70 0.22 0.76 0.66 0.76 0.62 0.92 0.66 0.22 0.06 0.30 0.24
#> [4,] 0.96 0.56 0.12 0.82 0.76 0.68 0.46 0.78 0.82 0.40 0.86 0.52
#> [5,] 0.72 0.28 0.36 0.14 0.84 0.06 0.88 0.62 0.62 0.46 0.48 0.74
#> [6,] 0.00 0.04 0.20 0.72 0.66 0.28 0.66 0.26 0.90 0.22 0.00 0.34
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.86 0.80 0.72 0.98 0.40 0.66 0.52 0.30 0.88 0.88 0.74 0.34
#> [2,] 0.64 0.62 0.74 0.96 0.86 0.84 0.70 0.32 0.68 0.72 0.92 0.74
#> [3,] 0.52 0.32 0.76 0.60 0.12 0.02 0.28 0.90 0.08 0.96 0.70 0.90
#> [4,] 1.00 0.74 0.16 0.68 0.52 0.82 0.60 0.94 0.34 0.06 0.98 0.54
#> [5,] 0.84 0.70 0.40 0.74 0.40 0.42 0.40 0.16 0.96 0.68 0.74 0.30
#> [6,] 0.20 0.44 0.60 0.08 0.22 0.38 0.88 0.28 0.72 0.74 0.20 0.46
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.64 0.40 0.52 0.56 0.72 0.84 0.74 0.90 0.82 0.72 0.40 0.86
#> [2,] 0.82 0.84 0.70 0.24 0.84 0.96 0.66 0.94 0.56 0.56 0.38 0.58
#> [3,] 0.78 0.12 0.44 0.04 0.30 1.00 0.32 0.18 0.82 0.42 0.46 0.54
#> [4,] 0.98 0.68 0.78 0.54 0.86 0.94 0.84 0.16 0.16 0.00 0.00 0.30
#> [5,] 0.84 0.92 0.50 0.72 0.84 0.32 0.74 0.48 0.96 0.78 1.00 0.60
#> [6,] 0.30 0.84 0.90 0.12 0.12 0.90 0.28 0.04 0.44 0.20 0.38 0.70