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
#> 30 125 113 72 10
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
#> 0.2668 0.1996
#> 0.2557 0.2735
#> 0.1736 0.2767
#> 0.2789 0.1968
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.2643
#> τ2 0.5262
#> τ3 0.4935
#> τ4 0.2852
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.09039
#> 0001 0.05052
#> 0010 0.03148
#> 0011 0.07752
#> 0100 0.07745
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 24138.91
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.4888
#> M2: 0.49
#> total scores: 0.5993
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#> [,1]
#> [1,] 0.2667624
#> [2,] 0.2557295
#> [3,] 0.1736389
#> [4,] 0.2789057
AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8121429 0.8557143 0.9142857 0.9292857 0.9457143
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.4571429 0.5400000 0.7028571 0.7485714 0.8057143
a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2070.571 NA 19460.89 1833.956 23365.41
#> D(theta_bar) 1914.972 NA 18872.14 1804.813 22591.92
#> DIC 2226.170 NA 20049.64 1863.098 24138.91
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 0.14 0.42 0.60 0.40
#> [2,] 0.90 0.86 0.66 0.44 1.00
#> [3,] 0.10 0.76 0.68 0.56 0.54
#> [4,] 0.66 0.42 0.18 0.44 0.78
#> [5,] 0.58 0.24 0.38 0.76 0.80
#> [6,] 0.72 0.54 0.66 0.80 0.76
head(a$PPP_item_means)
#> [1] 0.86 0.28 0.36 1.00 0.18 0.12
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.96 0.80 0.68 0.58 0.50 0.72 0.84 0.68 0.50 0.18 0.16 0.78 0.84
#> [2,] NA NA 0.86 0.46 0.72 0.34 0.04 0.40 0.92 0.24 0.52 0.28 0.84 0.22
#> [3,] NA NA NA 0.14 0.38 0.30 0.10 0.44 0.60 0.96 0.58 0.80 0.42 0.18
#> [4,] NA NA NA NA 0.80 0.84 0.72 0.56 1.00 0.50 0.18 0.92 0.66 0.70
#> [5,] NA NA NA NA NA 0.14 0.34 0.12 0.90 0.62 0.16 0.96 1.00 0.82
#> [6,] NA NA NA NA NA NA 0.32 0.54 0.72 0.44 0.14 0.00 0.26 0.00
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.20 0.54 0.82 0.00 0.48 0.78 0.76 1.00 0.02 0.32 0.60 0.08
#> [2,] 0.12 0.54 0.46 0.62 0.44 0.46 0.68 0.74 0.42 0.42 0.80 0.64
#> [3,] 0.66 0.30 0.48 0.58 0.92 0.38 0.50 0.76 0.62 0.66 0.08 0.18
#> [4,] 0.34 0.62 0.34 0.76 0.92 0.34 0.20 0.76 0.82 0.02 0.12 0.94
#> [5,] 0.62 1.00 0.66 0.36 0.22 0.94 0.66 0.64 0.60 0.80 0.86 0.84
#> [6,] 0.14 0.04 0.02 0.12 0.38 0.00 0.28 0.90 0.24 0.02 0.24 0.86
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.96 0.18 0.92 0.58 0.60 0.04 0.34 0.00 0.00 0.24 0.68 0.32
#> [2,] 0.84 0.00 0.38 0.60 0.20 0.50 0.16 0.70 0.20 0.12 0.14 0.78
#> [3,] 0.56 0.30 0.08 0.44 0.34 0.22 0.14 0.50 0.50 0.18 0.32 0.46
#> [4,] 0.34 0.12 0.86 0.42 0.82 0.28 0.80 0.56 0.06 0.26 0.46 0.86
#> [5,] 0.60 0.48 0.44 0.58 0.92 0.92 0.16 0.24 0.14 0.10 0.74 0.20
#> [6,] 0.38 0.04 0.38 0.84 0.90 0.30 0.50 0.60 0.02 0.42 0.84 0.70
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.76 0.20 0.62 0.34 0.12 0.58 0.76 0.52 0.62 0.12 0.94 0.22
#> [2,] 0.94 0.06 0.12 0.84 0.70 1.00 0.18 0.28 0.30 0.22 0.44 0.14
#> [3,] 0.40 0.78 0.96 0.20 0.22 0.46 0.04 0.84 0.36 0.74 0.92 1.00
#> [4,] 0.82 0.20 0.40 0.14 0.84 0.16 0.08 0.38 0.96 0.72 0.86 0.24
#> [5,] 0.56 0.66 0.78 0.22 0.76 0.70 0.44 0.62 0.88 0.38 0.20 0.70
#> [6,] 0.54 0.72 0.22 0.14 0.04 0.44 0.30 0.08 0.50 0.52 0.24 0.04