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
#> 27 82 127 90 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
#> 0.3081 0.5385 0.6212 0.5782 0.7310
#> 0.5001 0.3482 0.5509 0.5863 0.8390
#> 0.6712 0.6390 0.6901 0.2140 0.9042
#> 0.6484 0.5420 0.1269 0.6512 0.7376
#> 0.4346 0.2727 0.5536 0.6695 0.6713
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.5358
#> τ2 0.3648
#> τ3 0.5138
#> τ4 0.3337
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.12053
#> 0001 0.08251
#> 0010 0.03308
#> 0011 0.04807
#> 0100 0.12996
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22482.6
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4992
#> M2: 0.49
#> total scores: 0.6108
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.3081118 0.5384539 0.6211834 0.5782396
#> [2,] 0.5001011 0.3481962 0.5508894 0.5863365
#> [3,] 0.6712041 0.6389907 0.6900689 0.2139740
#> [4,] 0.6484342 0.5419983 0.1268692 0.6512053
#> [5,] 0.4345869 0.2727459 0.5536478 0.6695411
#> [6,] 0.5818555 0.1747877 0.2873324 0.5116342(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9637261
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9183922
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8650000 0.9057143 0.9414286 0.9578571 0.9671429
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5542857 0.6685714 0.7914286 0.8428571 0.8771429a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2201.124 NA 17685.82 1842.071 21729.02
#> D(theta_bar) 2159.336 NA 16996.81 1819.292 20975.44
#> DIC 2242.913 NA 18374.84 1864.850 22482.60
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.96 1.00 0.72 0.52 0.50
#> [2,] 0.42 0.38 0.40 0.44 0.36
#> [3,] 0.76 0.46 0.32 0.40 0.60
#> [4,] 0.92 0.44 0.38 0.70 0.30
#> [5,] 0.28 0.86 0.30 0.38 0.94
#> [6,] 0.64 0.68 0.08 0.30 0.56
head(a$PPP_item_means)
#> [1] 0.52 0.54 0.48 0.46 0.54 0.56
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.72 0.76 0.96 0.82 0.04 0.66 0.46 0.24 0.04 0.90 0.44 0.46 0.48
#> [2,] NA NA 0.56 0.68 0.86 0.66 0.08 0.10 0.72 0.66 0.48 0.44 0.62 0.56
#> [3,] NA NA NA 0.24 0.80 0.94 0.02 0.82 0.42 0.74 0.76 0.54 0.82 0.42
#> [4,] NA NA NA NA 0.10 0.48 0.82 0.84 0.78 0.46 0.84 0.74 0.66 0.20
#> [5,] NA NA NA NA NA 0.80 0.62 0.10 0.62 0.46 0.32 0.60 0.36 0.50
#> [6,] NA NA NA NA NA NA 0.44 0.36 0.92 0.38 0.90 0.88 0.74 0.50
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.66 0.30 0.80 0.82 0.22 0.62 0.70 0.44 0.12 0.34 0.02 0.12
#> [2,] 0.80 0.64 0.64 0.08 0.62 0.46 0.66 0.12 0.00 0.24 0.26 0.22
#> [3,] 0.24 0.96 0.26 0.02 0.92 0.26 0.60 0.46 0.52 0.74 0.90 0.60
#> [4,] 0.80 0.80 0.32 0.96 0.64 0.58 0.38 0.56 0.86 0.68 0.28 0.82
#> [5,] 0.06 0.48 0.48 0.30 0.68 0.06 0.90 0.66 0.14 0.36 0.20 0.42
#> [6,] 0.10 0.76 0.72 0.74 0.60 0.38 1.00 0.80 0.98 0.94 0.50 0.94
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.28 0.48 0.72 0.14 0.18 0.30 0.68 0.82 0.84 0.32 0.56 0.62
#> [2,] 0.28 0.82 0.48 0.14 0.60 0.68 0.24 0.20 0.54 0.46 0.14 0.38
#> [3,] 0.24 0.62 0.80 0.22 0.34 0.72 0.70 0.84 0.92 0.52 0.54 0.88
#> [4,] 0.80 0.64 0.24 0.50 0.48 0.06 0.14 1.00 0.94 0.84 0.38 1.00
#> [5,] 0.50 0.68 0.40 0.82 0.44 0.82 0.12 0.56 0.60 0.76 0.58 0.72
#> [6,] 0.50 0.04 0.82 0.64 0.56 0.00 0.46 0.36 0.46 0.28 0.02 0.66
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.78 0.42 0.46 0.16 0.14 0.08 0.54 0.46 0.34 0.08 0.06 0.20
#> [2,] 0.16 0.14 0.76 0.76 0.76 0.52 0.48 0.32 0.30 0.78 0.50 0.14
#> [3,] 0.82 0.86 0.82 0.12 0.08 0.60 0.82 0.34 0.06 0.88 0.66 0.62
#> [4,] 0.20 0.30 0.50 0.88 0.92 0.72 0.70 0.64 0.98 0.42 0.56 0.28
#> [5,] 0.44 0.32 0.60 0.26 0.54 0.62 0.06 0.10 0.76 0.10 0.38 0.30
#> [6,] 0.92 0.88 0.24 0.78 0.48 0.38 0.26 0.02 0.44 0.52 0.40 0.12