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
#> 44 107 120 64 15
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
#> 0.1524 0.1171
#> 0.3015 0.2980
#> 0.1307 0.2297
#> 0.1879 0.2876
#>
#> Transition Parameters:
#> taus_EAP
#> τ1 0.5516
#> τ2 0.3488
#> τ3 0.2500
#> τ4 0.2267
#>
#> Class Probabilities:
#> pis_EAP
#> 0000 0.11889
#> 0001 0.04543
#> 0010 0.04398
#> 0011 0.05918
#> 0100 0.09293
#> ... 11 more classes
#>
#> Deviance Information Criterion (DIC): 23294.03
#>
#> Posterior Predictive P-value (PPP):
#> M1: 0.498
#> M2: 0.49
#> total scores: 0.6036
a <- summary(output_NIDA_indept)
head(a$ss_EAP)
#> [,1]
#> [1,] 0.1524095
#> [2,] 0.3014561
#> [3,] 0.1307211
#> [4,] 0.1879393AAR_vec <- numeric(L)
for(t in 1:L){
AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8557143 0.8942857 0.9285714 0.9378571 0.9414286
PAR_vec <- numeric(L)
for(t in 1:L){
PAR_vec[t] <- mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5142857 0.6257143 0.7485714 0.7742857 0.7800000a$DIC
#> Transition Response_Time Response Joint Total
#> D_bar 2198.088 NA 18513.59 1866.924 22578.60
#> D(theta_bar) 2073.473 NA 17924.34 1865.358 21863.17
#> DIC 2322.702 NA 19102.84 1868.490 23294.03
head(a$PPP_total_scores)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 0.24 0.24 0.34 0.56
#> [2,] 0.74 0.64 1.00 0.50 0.90
#> [3,] 0.40 0.62 0.66 1.00 0.76
#> [4,] 0.48 0.04 0.26 0.66 1.00
#> [5,] 0.74 0.34 0.68 0.22 0.44
#> [6,] 0.92 0.84 0.26 0.82 0.84
head(a$PPP_item_means)
#> [1] 0.84 0.70 0.46 0.58 0.80 0.14
head(a$PPP_item_ORs)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] NA 0.14 0.6 0.30 0.28 0.80 0.36 0.50 0.00 0.52 0.18 0.82 0.18 0.66
#> [2,] NA NA 1.0 0.84 0.24 0.02 0.86 0.18 0.62 0.30 0.84 0.20 0.90 0.62
#> [3,] NA NA NA 0.14 0.76 0.88 0.86 0.84 0.62 0.32 0.98 0.86 0.96 0.64
#> [4,] NA NA NA NA 0.14 0.74 0.76 0.58 0.06 0.82 0.34 0.62 0.40 0.86
#> [5,] NA NA NA NA NA 0.56 0.26 0.90 0.40 0.58 0.14 0.90 0.66 0.08
#> [6,] NA NA NA NA NA NA 0.88 0.82 0.82 0.42 0.64 0.72 0.38 0.82
#> [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.22 0.66 0.64 0.00 0.48 0.28 0.86 0.44 0.02 0.06 0.42 0.04
#> [2,] 0.26 0.18 0.70 0.20 0.36 0.92 0.72 0.78 0.02 0.68 0.64 0.32
#> [3,] 0.56 0.20 0.66 0.92 0.88 0.82 0.70 0.46 0.70 0.20 0.24 0.76
#> [4,] 0.26 0.62 0.10 0.02 0.12 0.24 0.48 0.66 0.62 0.70 0.90 0.22
#> [5,] 0.92 0.08 0.22 0.14 0.38 0.56 0.72 0.64 0.42 0.82 0.80 0.50
#> [6,] 0.88 0.80 0.74 0.12 0.38 0.68 0.40 0.56 0.48 0.66 0.28 0.50
#> [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.16 0.04 0.58 0.48 0.76 0.02 0.04 0.42 0.24 0.18 0.18 0.28
#> [2,] 0.94 0.36 0.24 0.78 0.28 0.50 0.52 0.54 0.40 0.28 0.92 0.20
#> [3,] 0.20 0.36 0.14 0.22 0.80 0.50 0.96 0.50 0.18 0.44 0.88 0.80
#> [4,] 0.40 0.04 0.08 0.54 0.98 0.38 0.30 0.14 0.48 1.00 0.18 0.48
#> [5,] 0.82 0.48 0.60 0.68 1.00 0.72 0.64 0.98 0.22 0.82 0.56 0.24
#> [6,] 0.26 0.86 0.02 0.30 0.58 0.90 0.16 0.04 0.90 0.52 0.10 0.70
#> [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.88 0.38 0.84 0.80 0.34 0.40 0.50 0.86 0.08 0.54 0.98 0.78
#> [2,] 0.00 0.82 0.44 0.72 0.10 0.06 0.66 0.20 0.04 0.16 0.42 0.92
#> [3,] 0.54 0.34 0.74 0.42 0.46 0.48 0.72 0.66 0.14 0.40 0.32 0.44
#> [4,] 0.08 0.98 0.48 0.30 0.62 0.66 0.62 0.22 0.64 0.72 0.88 0.64
#> [5,] 0.82 0.18 0.84 0.98 0.60 0.72 0.94 0.56 0.22 0.96 0.14 0.80
#> [6,] 0.40 0.64 0.70 0.82 0.74 0.68 0.42 0.26 0.96 0.70 0.82 0.58