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
#> 27 109 123 71 20
Svec <- runif(K,.1,.3)
Gvec <- runif(K,.1,.3)
Y_sim <- sim_hmcdm(model="NIDA",Alphas,Q_matrix,Design_array,
Svec=Svec,Gvec=Gvec)output_NIDA_indept = hmcdm(Y_sim, Q_matrix, "NIDA_indept", Design_array,
100, 30, R = R)
#> 0
output_NIDA_indept
#>
#> Model: NIDA_indept
#>
#> Sample Size: 350
#> Number of Items:
#> Number of Time Points:
#>
#> Chain Length: 100, burn-in: 50
summary(output_NIDA_indept)
#>
#> Model: NIDA_indept
#>
#> Item Parameters:
#> ss_EAP gs_EAP
#> 0.23889 0.2224
#> 0.16800 0.1611
#> 0.09922 0.2134
#> 0.16128 0.2410
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.3675
#> τ2 0.5436
#> τ3 0.4105
#> τ4 0.4078
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.07521
#> 0001 0.06104
#> 0010 0.05408
#> 0011 0.01081
#> 0100 0.06758
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 21653.93
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4844
#> M2: 0.49
#> total scores: 0.6075
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#> [,1]
#> [1,] 0.23888870
#> [2,] 0.16800476
#> [3,] 0.09922179
#> [4,] 0.16128011AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8750000 0.9092857 0.9514286 0.9728571 0.9792857
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5914286 0.6942857 0.8342857 0.8914286 0.9200000a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 1972.354 NA 17195.46 1856.479 21024.29
#> D(theta_bar) 1887.976 NA 16664.74 1841.940 20394.66
#> DIC 2056.733 NA 17726.18 1871.017 21653.93
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.98 0.56 0.12 0.16 0.16
#> [2,] 0.24 0.94 0.84 0.98 0.20
#> [3,] 0.74 0.64 1.00 0.40 0.42
#> [4,] 0.90 0.34 0.30 0.82 0.96
#> [5,] 1.00 0.48 0.78 0.64 0.78
#> [6,] 0.90 0.42 0.20 0.50 0.72
head(a$PPP_item_means)
#> [1] 0.86 0.78 0.42 0.56 0.20 0.34
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.9 0.88 0.52 1.00 0.78 0.64 0.98 0.92 0.06 0.06 0.44 0.46 0.34
#> [2,] NA NA 0.62 0.60 0.82 0.86 0.18 0.74 0.38 0.74 0.90 0.38 0.04 0.08
#> [3,] NA NA NA 0.62 0.80 0.36 0.24 0.68 0.62 0.36 0.22 0.34 0.18 0.46
#> [4,] NA NA NA NA 0.72 0.70 0.72 0.96 0.74 0.86 0.72 0.72 0.06 0.74
#> [5,] NA NA NA NA NA 0.72 0.06 0.16 0.64 0.18 0.06 0.06 0.64 0.16
#> [6,] NA NA NA NA NA NA 0.12 0.08 0.34 0.10 0.44 1.00 0.54 0.54
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.54 0.88 0.48 0.86 0.08 0.78 0.40 0.86 0.98 0.58 0.76 0.42
#> [2,] 0.68 0.82 0.20 0.26 0.14 0.50 0.38 0.16 0.70 0.32 0.10 0.88
#> [3,] 0.38 0.90 0.90 0.42 0.98 1.00 0.10 0.42 0.84 0.06 0.46 0.44
#> [4,] 0.72 0.66 0.32 0.46 0.44 0.38 0.16 0.40 0.56 0.26 0.30 0.22
#> [5,] 0.08 0.60 0.08 0.48 0.00 0.40 0.14 0.70 0.58 0.26 0.62 0.68
#> [6,] 0.86 0.42 0.22 0.06 0.36 0.62 0.40 0.96 0.42 0.60 0.26 0.04
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.82 0.68 0.00 0.88 0.72 0.54 0.20 0.76 0.52 0.44 0.16 0.54
#> [2,] 0.20 0.70 0.74 0.54 0.18 0.98 0.38 0.76 0.84 0.66 0.76 0.06
#> [3,] 0.14 0.18 0.14 0.88 0.24 0.14 0.14 0.70 0.34 0.58 0.16 0.18
#> [4,] 0.58 0.54 0.48 0.48 0.44 0.26 0.24 0.82 0.34 0.56 0.64 0.50
#> [5,] 0.68 0.00 0.72 0.78 0.38 1.00 0.22 0.76 0.62 0.74 0.46 0.08
#> [6,] 0.26 0.20 0.14 0.74 0.72 0.68 0.52 0.62 1.00 0.22 0.20 0.04
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.52 0.72 0.64 0.30 0.90 0.54 0.44 0.60 0.06 0.76 0.40 0.78
#> [2,] 0.38 0.60 0.28 0.94 0.82 0.42 0.82 0.46 0.56 0.66 0.02 0.56
#> [3,] 0.82 0.42 0.40 0.46 0.90 0.66 0.56 0.64 0.26 0.36 0.12 0.60
#> [4,] 0.36 0.72 0.54 0.74 0.98 0.56 0.50 0.78 0.58 0.44 0.72 0.90
#> [5,] 0.40 0.42 0.82 0.90 0.98 0.22 0.42 0.34 0.18 0.66 0.22 0.58
#> [6,] 0.04 0.28 0.74 0.98 0.98 0.64 0.88 0.76 0.76 0.46 0.32 0.50