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
#> 16 83 128 99 24
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
#> 0.29776 0.5901 0.6925 0.6861 0.8599
#> 0.53300 0.2135 0.5674 0.6894 0.8352
#> 0.52574 0.6920 0.5118 0.2915 0.8226
#> 0.50214 0.6039 0.2948 0.6201 0.8675
#> 0.06155 0.3297 0.6349 0.6697 0.7271
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.4745
#> τ2 0.5502
#> τ3 0.5710
#> τ4 0.5693
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.09773
#> 0001 0.10582
#> 0010 0.08946
#> 0011 0.01896
#> 0100 0.07938
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22586.41
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5188
#> M2: 0.49
#> total scores: 0.6139
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.29775749 0.5900971 0.6925137 0.6861163
#> [2,] 0.53299908 0.2134798 0.5674403 0.6894325
#> [3,] 0.52574237 0.6919573 0.5118377 0.2915179
#> [4,] 0.50214219 0.6038765 0.2948108 0.6200818
#> [5,] 0.06155305 0.3296737 0.6348960 0.6697372
#> [6,] 0.59803607 0.5290684 0.1659758 0.5963194(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9603115
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9068436
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8364286 0.8892857 0.9421429 0.9721429 0.9864286
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5057143 0.6314286 0.7971429 0.8914286 0.9457143a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 1995.091 NA 18037.56 1817.587 21850.23
#> D(theta_bar) 1941.895 NA 17382.04 1790.128 21114.06
#> DIC 2048.286 NA 18693.07 1845.047 22586.41
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.34 0.90 0.06 0.66 0.26
#> [2,] 0.98 0.60 0.62 0.66 0.68
#> [3,] 0.34 1.00 0.44 0.50 1.00
#> [4,] 0.80 0.96 0.74 0.50 0.34
#> [5,] 0.80 0.48 1.00 0.20 0.68
#> [6,] 0.76 0.28 0.84 0.78 0.20
head(a$PPP_item_means)
#> [1] 0.58 0.46 0.54 0.62 0.34 0.56
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.7 0.90 0.58 0.54 0.82 0.34 0.12 0.24 0.36 0.32 0.82 0.68 0.76
#> [2,] NA NA 0.78 0.94 0.72 0.76 0.98 0.62 0.46 0.88 0.28 0.50 0.44 0.88
#> [3,] NA NA NA 0.60 0.88 0.56 0.54 0.46 0.04 0.80 0.70 0.60 0.76 0.90
#> [4,] NA NA NA NA 0.88 0.52 0.68 0.70 0.14 0.86 0.52 0.40 0.74 0.66
#> [5,] NA NA NA NA NA 0.32 0.56 0.12 0.56 0.60 0.56 0.34 0.44 0.42
#> [6,] NA NA NA NA NA NA 0.62 0.24 0.50 0.62 0.86 0.26 0.10 0.76
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.38 0.22 0.58 0.20 0.36 0.46 0.62 0.58 0.08 0.42 0.92 0.72
#> [2,] 0.46 0.46 0.64 0.26 0.80 0.28 0.38 0.42 0.78 0.96 0.34 0.88
#> [3,] 0.42 0.72 0.68 0.70 0.14 0.54 0.42 0.26 0.92 0.96 0.70 0.72
#> [4,] 0.74 0.58 0.18 0.18 0.94 0.14 0.82 0.02 0.36 0.98 0.48 0.20
#> [5,] 0.60 0.10 0.86 0.36 0.70 0.28 0.46 0.78 0.94 0.56 1.00 0.80
#> [6,] 1.00 0.38 0.84 0.16 0.36 0.58 0.32 0.10 0.92 0.62 0.98 0.64
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.94 0.90 0.78 0.96 0.96 0.78 0.64 0.14 0.74 0.68 0.90 0.76
#> [2,] 0.84 0.70 0.56 0.36 0.28 0.92 0.22 0.02 0.04 0.98 0.64 0.26
#> [3,] 0.54 1.00 0.32 0.38 0.42 0.16 0.26 0.32 0.86 0.70 0.40 0.46
#> [4,] 0.00 0.84 0.72 0.20 0.74 1.00 0.66 0.72 0.66 0.28 0.42 0.56
#> [5,] 0.22 0.88 0.46 0.56 0.18 1.00 0.48 0.24 0.42 0.46 0.92 0.78
#> [6,] 0.74 0.36 0.64 0.26 0.96 0.88 0.92 0.10 0.68 0.50 0.60 0.74
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.30 0.60 0.60 0.20 0.54 0.90 0.66 0.94 0.36 0.76 0.66 0.90
#> [2,] 0.22 0.70 0.20 0.12 0.34 0.16 0.60 0.88 0.40 0.14 0.50 0.78
#> [3,] 0.48 0.62 0.30 0.92 0.18 0.12 0.76 0.30 0.16 0.22 0.22 0.52
#> [4,] 0.56 0.56 0.84 0.50 0.62 0.76 0.46 0.24 0.18 0.82 0.82 0.48
#> [5,] 0.30 0.70 0.08 0.74 0.26 0.64 0.28 0.66 0.76 0.56 0.66 0.62
#> [6,] 0.10 0.92 0.58 0.42 0.08 0.96 0.28 0.72 0.76 0.42 0.54 0.46