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
#> 34 107 135 60 14
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
#> 0.2639 0.6337 0.5053 0.6014 0.7882
#> 0.5614 0.1759 0.6107 0.6420 0.6912
#> 0.5691 0.6889 0.5826 0.2728 0.8570
#> 0.6423 0.5356 0.2754 0.6794 0.7189
#> 0.1017 0.3603 0.5540 0.5713 0.5796
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.1525
#> τ2 0.3176
#> τ3 0.4911
#> τ4 0.5699
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.156438
#> 0001 0.009126
#> 0010 0.055847
#> 0011 0.031968
#> 0100 0.086305
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22744.8
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5052
#> M2: 0.49
#> total scores: 0.6124
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2639004 0.6337238 0.5053409 0.6014084
#> [2,] 0.5614006 0.1759072 0.6106623 0.6419966
#> [3,] 0.5691449 0.6888898 0.5825672 0.2728218
#> [4,] 0.6422957 0.5356001 0.2753518 0.6793860
#> [5,] 0.1017327 0.3603076 0.5539542 0.5713264
#> [6,] 0.6760022 0.3345030 0.2083058 0.5790801(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9731244
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9545279
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8521429 0.9100000 0.9414286 0.9535714 0.9600000
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5228571 0.7085714 0.8142857 0.8342857 0.8600000a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2109.496 NA 18065.46 1803.162 21978.12
#> D(theta_bar) 1984.572 NA 17422.40 1804.459 21211.43
#> DIC 2234.421 NA 18708.51 1801.866 22744.80
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.66 0.10 0.68 0.42 0.16
#> [2,] 0.58 0.72 0.98 0.06 0.80
#> [3,] 0.72 0.64 0.54 1.00 0.26
#> [4,] 0.54 0.14 0.60 0.06 0.80
#> [5,] 0.24 0.32 0.70 0.70 0.34
#> [6,] 0.44 0.32 0.40 0.68 0.42
head(a$PPP_item_means)
#> [1] 0.38 0.50 0.52 0.48 0.28 0.68
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.76 0.06 0.68 0.74 0.58 0.72 0.32 0.36 0.52 0.34 0.02 0.28 0.60
#> [2,] NA NA 0.24 0.94 0.78 0.38 0.80 0.66 0.40 0.90 0.16 0.94 0.18 0.82
#> [3,] NA NA NA 0.50 0.10 0.20 0.24 0.62 0.52 0.46 0.46 0.42 0.44 0.58
#> [4,] NA NA NA NA 0.10 0.76 0.74 0.38 0.68 0.94 0.20 0.64 0.52 0.12
#> [5,] NA NA NA NA NA 0.60 0.84 0.26 0.22 0.48 0.64 0.82 0.06 0.82
#> [6,] NA NA NA NA NA NA 0.86 0.26 0.90 0.56 0.88 0.38 0.94 0.52
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.82 0.72 0.06 0.32 0.26 0.64 0.22 0.02 0.00 0.42 0.48 0.36
#> [2,] 0.36 0.42 0.10 0.00 0.38 0.10 0.66 0.48 0.58 0.74 0.22 1.00
#> [3,] 0.18 0.36 0.76 0.02 0.06 0.12 0.94 0.66 0.38 0.26 0.64 0.74
#> [4,] 0.94 0.88 0.96 0.62 0.98 0.80 0.50 0.80 0.80 0.56 0.84 0.16
#> [5,] 0.80 0.76 0.76 0.34 0.28 0.94 0.70 0.74 0.56 1.00 0.18 0.94
#> [6,] 0.66 0.52 0.44 0.72 0.66 0.62 0.60 0.14 0.56 0.74 0.64 0.78
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.28 0.22 0.10 0.76 0.16 0.48 0.02 0.04 0.52 0.08 0.50 0.48
#> [2,] 0.28 0.20 0.16 0.26 0.30 0.26 0.58 0.52 0.96 0.60 0.50 0.70
#> [3,] 0.64 0.48 0.28 0.74 0.98 0.16 0.24 0.68 0.96 0.28 0.60 0.48
#> [4,] 0.76 0.14 0.90 0.48 0.84 0.14 0.40 0.48 0.94 0.08 0.42 0.48
#> [5,] 0.40 0.90 0.20 0.24 0.28 0.72 0.48 0.58 0.78 0.02 0.60 0.44
#> [6,] 0.38 0.70 0.36 0.26 0.74 0.78 0.88 0.64 0.84 0.66 0.88 0.72
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.16 0.44 0.20 1.00 0.62 0.38 0.72 0.98 0.38 0.78 0.06 0.32
#> [2,] 0.48 0.30 0.80 0.68 0.50 0.86 1.00 0.96 0.78 0.66 0.54 0.12
#> [3,] 0.24 0.02 0.52 0.94 0.56 0.42 0.44 0.36 0.18 0.66 0.58 0.66
#> [4,] 0.42 0.68 0.22 0.48 0.48 0.94 0.58 0.12 0.86 0.94 0.60 0.30
#> [5,] 0.38 0.50 0.38 0.16 0.54 0.48 0.80 0.82 0.12 0.92 0.78 0.42
#> [6,] 0.84 0.84 0.68 0.98 0.70 0.88 0.76 0.98 0.72 0.94 0.54 0.24