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
#> 49 105 130 57 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
#> 0.3152 0.6401 0.5718 0.52759 0.8298
#> 0.6602 0.1320 0.5197 0.68390 0.6972
#> 0.6553 0.6323 0.6044 0.08386 0.8361
#> 0.5103 0.6475 0.1057 0.58763 0.7809
#> 0.6201 0.1982 0.6997 0.59279 0.5620
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.4261
#> τ2 0.2763
#> τ3 0.2844
#> τ4 0.2768
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.08742
#> 0001 0.09844
#> 0010 0.09890
#> 0011 0.03801
#> 0100 0.03575
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22425.17
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5236
#> M2: 0.49
#> total scores: 0.6169
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3152164 0.6400939 0.5718395 0.5275947
#> [2,] 0.6602373 0.1319738 0.5197494 0.6838979
#> [3,] 0.6552615 0.6323201 0.6044435 0.0838628
#> [4,] 0.5102571 0.6475082 0.1057078 0.5876288
#> [5,] 0.6201470 0.1982244 0.6996860 0.5927894
#> [6,] 0.6951720 0.2651339 0.1744787 0.6982831(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9421469
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9145602
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8607143 0.9035714 0.9364286 0.9407143 0.9507143
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5228571 0.6800000 0.7771429 0.7971429 0.8228571a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2171.287 NA 17732.90 1871.069 21775.26
#> D(theta_bar) 2107.351 NA 17161.53 1856.469 21125.34
#> DIC 2235.224 NA 18304.28 1885.669 22425.17
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.50 1.00 0.30 0.82 0.22
#> [2,] 0.46 0.42 0.62 0.58 0.80
#> [3,] 0.86 0.06 0.48 0.68 0.82
#> [4,] 0.66 0.76 0.72 0.78 0.26
#> [5,] 0.68 0.50 0.28 0.60 0.80
#> [6,] 0.30 0.66 0.90 0.96 0.84
head(a$PPP_item_means)
#> [1] 0.60 0.40 0.46 0.40 0.64 0.50
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.32 0.40 0.68 0.46 0.20 0.30 0.38 0.30 0.46 0.72 0.12 0.74 0.68
#> [2,] NA NA 0.78 0.46 0.14 0.50 0.38 0.22 0.84 0.28 0.18 0.42 0.98 0.74
#> [3,] NA NA NA 0.94 0.34 0.70 0.92 0.84 0.98 0.72 1.00 0.16 0.24 0.12
#> [4,] NA NA NA NA 0.04 0.70 0.28 0.82 0.72 0.50 0.88 0.10 0.88 0.28
#> [5,] NA NA NA NA NA 0.46 0.58 0.92 0.36 0.60 0.14 0.66 0.80 0.82
#> [6,] NA NA NA NA NA NA 0.50 0.46 0.32 0.68 0.96 0.56 0.44 0.50
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.22 0.80 0.64 1.00 0.16 0.48 0.36 0.02 0.86 0.86 0.44 0.94
#> [2,] 0.66 0.50 0.58 0.64 1.00 0.58 0.54 0.98 0.38 0.84 0.22 0.36
#> [3,] 0.96 0.86 0.32 0.76 0.18 0.14 0.62 0.12 0.90 0.14 0.96 0.78
#> [4,] 0.54 0.18 0.18 0.88 0.26 0.46 0.18 0.56 0.58 0.02 0.92 0.38
#> [5,] 0.90 0.78 0.62 0.14 0.84 0.52 1.00 0.20 0.00 0.32 0.68 0.98
#> [6,] 0.30 0.82 0.90 1.00 0.98 0.66 0.78 0.24 0.50 0.06 0.42 0.32
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.04 0.26 0.42 0.48 0.18 0.82 0.26 0.02 0.30 0.18 0.20 0.14
#> [2,] 0.60 0.38 0.22 0.90 0.38 0.00 0.16 0.66 0.06 0.90 0.40 0.64
#> [3,] 0.62 0.84 0.26 0.36 0.44 0.36 0.38 0.34 0.86 0.62 0.86 0.68
#> [4,] 0.40 0.72 0.02 0.12 0.56 0.66 0.10 0.32 0.54 0.76 0.46 0.20
#> [5,] 0.44 0.98 0.84 1.00 0.92 0.68 0.44 0.38 0.98 0.94 0.82 0.56
#> [6,] 0.22 0.82 0.30 0.42 0.16 0.52 0.72 0.12 0.74 0.38 0.38 0.86
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.16 0.30 0.26 0.38 0.80 0.94 0.16 0.22 0.58 0.84 0.10 0.44
#> [2,] 0.64 0.52 0.90 0.96 0.32 1.00 0.42 0.28 0.88 0.46 0.82 0.08
#> [3,] 0.46 0.12 0.16 0.52 0.82 0.30 0.20 0.44 0.36 0.34 0.06 0.26
#> [4,] 0.30 0.08 0.98 0.92 0.90 0.22 0.60 0.80 0.98 0.50 0.30 0.22
#> [5,] 0.96 0.90 0.76 0.50 0.68 0.84 0.98 0.80 0.80 0.74 0.82 0.92
#> [6,] 0.38 0.46 0.58 0.80 0.68 0.20 0.44 1.00 0.80 0.66 0.90 0.08