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
#> 23 99 136 80 12
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
#> 0.4890 0.6650 0.55971 0.6216 0.6968
#> 0.5658 0.2544 0.58988 0.5436 0.8849
#> 0.5416 0.6930 0.59358 0.2736 0.8774
#> 0.6121 0.5087 0.08738 0.6412 0.9056
#> 0.2606 0.3813 0.60446 0.5671 0.7057
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.4126
#> τ2 0.3796
#> τ3 0.4450
#> τ4 0.3198
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.03897
#> 0001 0.05010
#> 0010 0.10378
#> 0011 0.03177
#> 0100 0.14896
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22661.85
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4984
#> M2: 0.49
#> total scores: 0.612
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.4889528 0.6650032 0.55970922 0.6215847
#> [2,] 0.5658196 0.2543981 0.58987838 0.5436222
#> [3,] 0.5415788 0.6930347 0.59358192 0.2736228
#> [4,] 0.6121427 0.5087013 0.08737577 0.6411849
#> [5,] 0.2606450 0.3812726 0.60445549 0.5670881
#> [6,] 0.5947591 0.2192572 0.20598793 0.5736394(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9574978
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.923862
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8407143 0.8814286 0.9400000 0.9557143 0.9657143
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5085714 0.6085714 0.7800000 0.8371429 0.8714286a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2247.450 NA 17845.96 1845.382 21938.79
#> D(theta_bar) 2182.441 NA 17195.18 1838.104 21215.73
#> DIC 2312.460 NA 18496.73 1852.660 22661.85
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.10 0.58 0.28 0.08 0.06
#> [2,] 0.42 0.86 0.82 0.74 0.46
#> [3,] 0.78 0.80 0.86 0.96 0.84
#> [4,] 0.84 0.60 0.82 0.48 0.92
#> [5,] 0.70 0.30 0.98 1.00 0.36
#> [6,] 0.78 0.88 0.54 0.96 0.92
head(a$PPP_item_means)
#> [1] 0.58 0.38 0.34 0.46 0.60 0.44
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.18 0.68 0.76 0.86 0.64 0.24 0.86 0.02 0.36 0.06 0.38 0.82 0.12
#> [2,] NA NA 0.10 0.56 0.84 0.94 0.82 0.84 0.42 0.36 0.72 0.68 0.34 0.92
#> [3,] NA NA NA 0.50 0.66 0.42 0.38 0.78 0.62 0.96 0.98 0.08 0.90 0.70
#> [4,] NA NA NA NA 0.28 0.58 0.18 0.78 0.30 0.74 0.80 0.34 0.90 0.94
#> [5,] NA NA NA NA NA 0.92 0.10 0.94 0.58 0.80 0.44 0.88 0.86 0.96
#> [6,] NA NA NA NA NA NA 0.76 0.56 0.42 0.54 0.42 0.98 0.14 0.76
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.20 0.62 0.04 0.76 0.66 0.24 0.76 0.30 0.26 0.44 0.64 0.30
#> [2,] 0.68 0.96 0.72 0.96 1.00 0.62 0.82 0.66 0.92 0.80 0.66 0.76
#> [3,] 0.68 0.54 0.48 0.94 0.76 0.60 0.38 0.80 0.52 0.26 0.78 0.54
#> [4,] 0.34 0.20 0.60 0.98 0.44 0.68 0.42 0.92 0.36 0.46 0.54 0.76
#> [5,] 0.94 0.36 0.32 0.86 0.96 0.24 0.54 1.00 0.90 0.08 0.64 0.70
#> [6,] 0.56 0.18 0.32 0.94 0.36 0.66 0.40 0.94 0.58 0.74 0.38 0.92
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.44 0.96 0.30 0.88 0.18 0.98 0.50 0.70 0.74 0.80 0.74 0.16
#> [2,] 0.86 0.86 0.38 0.22 1.00 0.80 0.80 0.82 0.92 0.14 0.52 0.78
#> [3,] 0.70 0.44 0.22 0.08 0.22 0.98 0.52 0.58 0.12 0.10 0.40 0.04
#> [4,] 0.44 0.76 0.62 0.60 0.92 0.92 0.76 0.72 0.70 0.52 0.52 0.24
#> [5,] 0.94 0.98 0.52 0.64 0.70 0.70 0.56 0.32 0.66 0.02 0.58 0.66
#> [6,] 0.50 0.54 0.36 0.44 0.94 0.96 0.86 0.70 0.94 0.18 0.76 0.42
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.10 0.70 0.58 0.46 0.36 0.82 0.32 0.44 0.54 0.30 0.32 0.60
#> [2,] 0.16 0.64 0.62 0.56 0.18 0.76 0.66 0.54 0.60 0.48 0.50 0.48
#> [3,] 0.84 0.26 0.08 0.22 0.56 0.94 0.26 0.04 0.92 0.66 0.02 0.48
#> [4,] 0.66 0.36 0.50 0.40 0.44 0.62 0.20 0.96 0.86 0.20 0.68 0.38
#> [5,] 0.54 0.80 0.46 0.66 0.16 0.84 0.68 0.04 0.46 0.02 0.32 0.26
#> [6,] 0.64 0.38 0.80 0.58 0.94 0.88 0.60 0.90 0.52 0.30 0.74 0.50