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
#> 37 106 118 72 17
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
#> 0.2989 0.5341 0.5993 0.6475 0.8725
#> 0.6758 0.3190 0.6093 0.5328 0.7884
#> 0.5138 0.5329 0.6858 0.2400 0.6886
#> 0.5473 0.5956 0.1320 0.5432 0.8603
#> 0.2891 0.3269 0.5103 0.6944 0.6696
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.3364
#> τ2 0.4608
#> τ3 0.2979
#> τ4 0.3786
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.14686
#> 0001 0.04497
#> 0010 0.04501
#> 0011 0.04183
#> 0100 0.04043
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22668.23
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.5172
#> M2: 0.49
#> total scores: 0.6144
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2988551 0.5340914 0.5992655 0.6474611
#> [2,] 0.6758219 0.3190238 0.6093436 0.5328129
#> [3,] 0.5138256 0.5329382 0.6858376 0.2399989
#> [4,] 0.5472993 0.5955933 0.1320301 0.5432113
#> [5,] 0.2891097 0.3268992 0.5103029 0.6943803
#> [6,] 0.6568055 0.3739598 0.3769342 0.6470811(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9407145
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9357966
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8592857 0.8978571 0.9357143 0.9571429 0.9642857
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5228571 0.6257143 0.7657143 0.8428571 0.8657143a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2250.124 NA 17841.71 1853.633 21945.46
#> D(theta_bar) 2166.459 NA 17206.19 1850.046 21222.70
#> DIC 2333.788 NA 18477.22 1857.221 22668.23
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.08 0.60 0.78 0.88 0.80
#> [2,] 0.70 0.58 0.72 0.16 0.22
#> [3,] 0.36 0.50 0.44 0.40 0.88
#> [4,] 0.48 0.92 0.96 0.62 0.26
#> [5,] 0.20 0.80 0.28 0.86 0.50
#> [6,] 0.26 0.06 0.70 1.00 1.00
head(a$PPP_item_means)
#> [1] 0.58 0.50 0.52 0.40 0.58 0.56
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] NA 0.4 1.00 0.50 0.24 0.20 0.86 0.60 0.58 0.9183673 0.48 0.02 0.00
#> [2,] NA NA 0.82 0.26 0.64 0.96 0.52 0.56 0.02 0.6122449 0.20 0.92 0.76
#> [3,] NA NA NA 0.04 0.86 0.62 0.88 0.64 0.04 0.6938776 0.30 0.22 0.24
#> [4,] NA NA NA NA 0.56 0.28 0.98 0.42 0.66 0.5510204 0.54 0.42 0.50
#> [5,] NA NA NA NA NA 0.24 0.66 0.46 0.60 0.5918367 0.20 0.46 0.12
#> [6,] NA NA NA NA NA NA 0.98 0.28 0.68 0.4897959 0.70 0.10 0.94
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] 0.74 0.58 0.50 0.38 0.20 0.50 0.58 0.42 0.30 0.00 0.06 0.90
#> [2,] 0.60 0.54 0.58 0.24 0.30 0.36 0.10 0.44 0.98 0.28 0.06 0.90
#> [3,] 0.68 0.38 0.72 0.18 0.44 0.26 0.40 0.48 0.58 0.30 0.20 0.84
#> [4,] 0.26 0.70 0.80 0.50 0.54 0.30 0.38 0.68 0.28 0.24 0.82 0.58
#> [5,] 0.96 0.80 0.86 0.96 0.72 0.78 0.42 0.76 0.74 0.10 0.76 0.40
#> [6,] 0.84 0.64 0.94 0.18 0.44 0.34 0.34 0.42 0.54 0.60 0.76 0.30
#> [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,] 0.38 0.40 0.72 0.14 0.72 0.04 0.62 0.36 0.18 0.94 0.04 0.86
#> [2,] 0.42 0.40 0.40 0.30 0.92 0.86 0.82 0.88 0.98 0.66 0.24 0.74
#> [3,] 0.34 0.70 0.42 0.30 0.70 0.66 0.50 0.10 0.24 0.82 0.02 0.56
#> [4,] 0.80 0.40 0.56 0.72 0.98 0.74 0.64 0.16 0.90 0.64 0.68 0.22
#> [5,] 0.70 0.84 0.54 0.54 0.38 0.76 0.64 0.48 0.06 0.26 0.38 0.58
#> [6,] 0.30 0.32 0.20 0.02 0.52 0.40 0.14 0.30 0.96 0.06 0.62 0.18
#> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.20 0.80 0.98 0.28 0.56 1.00 0.98 0.54 0.22 0.84 1.00 0.86
#> [2,] 0.66 0.54 0.52 0.08 0.02 1.00 0.84 0.72 0.50 0.84 0.52 0.94
#> [3,] 0.42 0.84 0.86 0.48 0.02 1.00 0.88 0.24 0.14 0.36 0.70 0.58
#> [4,] 1.00 0.58 0.66 0.42 0.78 0.80 0.76 0.88 0.74 1.00 0.90 0.82
#> [5,] 0.84 0.10 0.52 0.10 0.36 0.74 0.70 0.80 0.42 0.98 0.82 0.84
#> [6,] 0.16 0.78 0.46 0.42 0.28 0.92 0.20 0.80 0.60 0.72 0.68 0.48
#> [,50]
#> [1,] 0.2857143
#> [2,] 0.6122449
#> [3,] 0.3061224
#> [4,] 0.6122449
#> [5,] 0.1020408
#> [6,] 0.4489796