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
#> 41 110 115 70 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
#> 0.1302 0.6825 0.6183 0.5339 0.7409
#> 0.5213 0.5079 0.5291 0.6317 0.6683
#> 0.6874 0.5009 0.6341 0.2334 0.8266
#> 0.5534 0.6193 0.4453 0.5151 0.7284
#> 0.2005 0.4101 0.5383 0.6939 0.5980
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.2967
#> τ2 0.3594
#> τ3 0.3295
#> τ4 0.4809
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.09130
#> 0001 0.07124
#> 0010 0.09372
#> 0011 0.05630
#> 0100 0.05379
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 23159.75
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5192
#> M2: 0.49
#> total scores: 0.6151
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.1302459 0.6825197 0.6182755 0.5338955
#> [2,] 0.5213094 0.5078983 0.5290785 0.6316690
#> [3,] 0.6873631 0.5009308 0.6340834 0.2333791
#> [4,] 0.5534394 0.6193282 0.4452943 0.5150836
#> [5,] 0.2004698 0.4101382 0.5382574 0.6938787
#> [6,] 0.5791486 0.2274723 0.1505156 0.6274593(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9386292
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9222922
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8485714 0.8885714 0.9235714 0.9514286 0.9521429
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5257143 0.6342857 0.7314286 0.8200000 0.8171429a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2239.317 NA 18333.99 1849.711 22423.01
#> D(theta_bar) 2168.087 NA 17688.93 1829.258 21686.28
#> DIC 2310.548 NA 18979.04 1870.164 23159.75
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.98 1.00 0.26 0.42 0.92
#> [2,] 0.86 0.82 0.74 0.60 0.76
#> [3,] 0.10 0.64 0.82 0.48 0.98
#> [4,] 0.82 0.48 0.26 0.12 0.48
#> [5,] 0.74 0.44 0.48 0.72 0.84
#> [6,] 0.96 0.72 0.78 0.86 0.52
head(a$PPP_item_means)
#> [1] 0.54 0.40 0.26 0.56 0.50 0.54
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.88 0.12 0.74 0.42 0.84 0.52 0.94 0.92 0.32 0.24 0.12 0.36 0.88
#> [2,] NA NA 0.00 0.54 0.68 0.72 0.76 0.18 0.48 0.50 0.36 0.96 0.76 0.50
#> [3,] NA NA NA 0.08 0.96 0.36 0.04 0.58 0.02 0.14 0.26 0.98 0.10 0.54
#> [4,] NA NA NA NA 0.98 0.46 0.94 0.70 0.10 0.86 0.80 0.74 0.64 0.44
#> [5,] NA NA NA NA NA 0.72 0.72 0.58 0.74 0.60 0.70 0.18 0.40 0.66
#> [6,] NA NA NA NA NA NA 0.86 0.78 0.94 0.24 0.12 0.44 0.08 0.30
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.66 0.32 0.26 0.76 0.62 0.50 0.52 0.26 1.00 0.60 0.64 0.04
#> [2,] 0.58 0.68 0.90 0.26 0.76 0.32 0.56 0.22 0.06 0.34 0.32 0.40
#> [3,] 0.10 0.20 0.82 0.16 0.72 0.80 0.58 0.44 0.30 0.20 0.10 0.22
#> [4,] 0.22 0.40 0.32 0.30 0.28 0.06 0.86 0.62 0.72 0.62 0.14 0.34
#> [5,] 0.80 0.78 0.36 0.34 0.52 0.88 0.86 0.72 0.86 0.16 0.20 0.14
#> [6,] 0.12 0.96 0.14 0.86 0.58 0.10 0.98 0.56 0.40 0.60 0.40 0.88
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.62 0.04 0.26 0.08 0.36 1.00 0.78 0.44 0.68 0.52 0.80 0.34
#> [2,] 0.68 0.18 0.72 0.78 0.54 0.20 0.32 0.24 0.72 0.16 0.80 0.44
#> [3,] 0.94 0.66 0.52 0.58 0.58 0.38 0.28 0.42 0.52 0.04 0.32 0.96
#> [4,] 0.32 0.92 0.10 0.66 0.92 0.92 0.74 0.04 0.96 0.62 0.34 0.02
#> [5,] 0.90 0.42 0.82 0.96 0.22 0.38 0.64 0.48 0.70 0.70 0.94 0.62
#> [6,] 0.10 0.72 0.44 0.36 0.58 0.74 0.96 0.48 0.60 0.94 0.16 0.02
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.52 0.26 0.48 0.98 0.76 0.30 0.38 0.22 0.12 0.36 0.66 0.72
#> [2,] 0.68 0.38 0.26 0.50 1.00 0.42 0.14 0.96 0.68 0.98 0.58 0.32
#> [3,] 0.08 0.36 0.62 0.28 0.46 0.36 0.62 0.32 0.12 0.60 0.50 0.90
#> [4,] 0.40 1.00 0.02 0.54 0.92 0.26 0.06 0.68 0.32 0.82 0.96 0.96
#> [5,] 0.94 0.46 0.48 0.96 0.56 0.62 0.90 0.46 0.10 0.14 0.10 0.70
#> [6,] 0.08 0.38 0.48 0.88 0.98 0.42 0.16 0.02 0.56 0.14 0.56 0.62