library(hmcdm)N = dim(Design_array)[1]
J = nrow(Q_matrix)
K = ncol(Q_matrix)
L = dim(Design_array)[3]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
#> 40 113 108 73 16
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
#> 0.2201 0.63916 0.5136 0.6006 0.8725
#> 0.6384 0.26734 0.5350 0.6329 0.9119
#> 0.5041 0.51642 0.5014 0.2379 0.7484
#> 0.5130 0.54455 0.2144 0.6876 0.7460
#> 0.1747 0.08728 0.5567 0.5889 0.6286
#> ... 45 more items
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.4278
#> τ2 0.3184
#> τ3 0.2943
#> τ4 0.3873
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.10548
#> 0001 0.07632
#> 0010 0.03664
#> 0011 0.02147
#> 0100 0.04348
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 22466.89
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4872
#> M2: 0.49
#> total scores: 0.6101
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2200505 0.63915789 0.5135897 0.6005675
#> [2,] 0.6383718 0.26733970 0.5350295 0.6329117
#> [3,] 0.5041279 0.51641669 0.5014147 0.2379158
#> [4,] 0.5130058 0.54455479 0.2144217 0.6876169
#> [5,] 0.1746550 0.08728403 0.5566902 0.5889067
#> [6,] 0.5617911 0.42562100 0.2734040 0.5995232(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.968261
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9453268
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8857143 0.9171429 0.9335714 0.9478571 0.9557143
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5971429 0.7057143 0.7657143 0.8085714 0.8428571a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2348.935 NA 17561.43 1828.865 21739.23
#> D(theta_bar) 2291.026 NA 16906.92 1813.628 21011.57
#> DIC 2406.844 NA 18215.94 1844.102 22466.89
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.98 0.90 0.38 0.52 0.06
#> [2,] 0.62 0.30 1.00 0.94 0.98
#> [3,] 0.66 0.58 0.38 1.00 0.32
#> [4,] 0.98 0.82 0.46 0.86 0.48
#> [5,] 0.90 0.86 0.50 0.70 0.76
#> [6,] 0.94 0.94 0.92 0.78 0.82
head(a$PPP_item_means)
#> [1] 0.52 0.54 0.48 0.46 0.46 0.56
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.82 0.24 0.48 0.90 0.84 0.68 0.46 0.58 0.20 0.88 0.88 0.50 0.82
#> [2,] NA NA 0.42 0.58 0.70 0.60 0.72 0.98 0.80 0.98 0.18 0.88 0.42 0.78
#> [3,] NA NA NA 0.70 0.02 0.00 0.12 0.44 0.92 0.88 0.76 0.52 0.92 0.38
#> [4,] NA NA NA NA 0.68 0.92 0.56 0.88 0.24 0.96 0.60 0.06 0.16 0.16
#> [5,] NA NA NA NA NA 0.86 0.38 0.92 0.82 0.28 0.48 0.98 0.92 0.10
#> [6,] NA NA NA NA NA NA 0.58 0.88 0.28 0.74 0.20 0.30 0.72 1.00
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.16 0.34 0.40 0.22 0.14 0.08 0.26 0.22 0.14 0.74 0.64 0.40
#> [2,] 0.14 0.64 0.38 0.38 0.54 0.30 0.94 0.32 0.10 0.84 0.98 0.48
#> [3,] 0.52 0.50 0.62 0.28 0.56 0.56 0.64 0.60 0.76 0.10 0.14 0.90
#> [4,] 0.90 0.04 0.24 1.00 0.66 0.98 0.78 0.60 0.78 0.90 0.70 0.28
#> [5,] 0.12 0.46 0.86 0.40 0.54 0.34 0.62 0.82 0.06 0.84 0.76 0.44
#> [6,] 0.42 0.34 0.84 0.80 0.98 0.72 0.74 0.24 0.54 0.38 0.80 0.98
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,] 0.62 0.94 0.56 0.24 0.10 0.82 0.16 0.06 0.7346939 0.84 0.34
#> [2,] 0.38 0.94 0.14 0.78 0.62 0.52 0.98 0.00 0.6530612 0.96 0.06
#> [3,] 1.00 0.72 0.12 0.92 0.36 0.22 0.36 0.80 0.7346939 0.58 0.98
#> [4,] 0.08 0.14 0.80 0.88 0.16 0.28 0.78 0.60 0.7551020 0.60 0.12
#> [5,] 0.16 0.96 0.82 0.16 0.94 0.98 0.60 0.40 0.7755102 0.36 0.38
#> [6,] 0.04 0.78 0.12 0.70 0.20 0.80 0.52 0.00 0.7959184 0.60 0.40
#> [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,] 0.16 0.38 0.70 0.10 0.50 1.00 0.24 0.38 0.34 0.72 0.34 0.46
#> [2,] 0.88 0.30 0.86 0.70 0.78 0.64 0.96 0.68 0.20 1.00 0.38 0.78
#> [3,] 0.64 1.00 0.26 0.30 0.98 0.36 0.64 0.52 0.60 0.84 0.06 0.22
#> [4,] 0.98 0.22 0.20 0.62 0.82 0.84 0.86 0.94 0.54 0.96 0.46 0.78
#> [5,] 0.26 0.06 0.90 0.42 0.38 0.52 0.72 0.52 0.18 0.50 0.72 0.36
#> [6,] 0.96 0.00 0.52 0.14 0.70 0.20 0.36 0.44 0.16 0.50 0.44 0.46
#> [,50]
#> [1,] 0.74
#> [2,] 0.80
#> [3,] 0.68
#> [4,] 0.76
#> [5,] 0.94
#> [6,] 0.74