rRUM_indept

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 
#>  33  89 139  79  10
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
#>        0.2781       0.6792       0.6201       0.6436       0.8204
#>        0.5422       0.1011       0.6665       0.6236       0.8176
#>        0.6219       0.6512       0.5843       0.2000       0.8191
#>        0.6711       0.5022       0.1893       0.5535       0.7830
#>        0.1142       0.2764       0.5600       0.6678       0.6988
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.6025
#> τ2   0.2616
#> τ3   0.3540
#> τ4   0.4458
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.07538
#> 0001 0.10249
#> 0010 0.04019
#> 0011 0.05713
#> 0100 0.13001
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 22366.34 
#> 
#> Posterior Predictive P-value (PPP):
#> M1: 0.494
#> M2:  0.49
#> total scores:  0.6145
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#>           [,1]      [,2]      [,3]      [,4]
#> [1,] 0.2781204 0.6791891 0.6201037 0.6435526
#> [2,] 0.5421509 0.1010740 0.6664536 0.6235942
#> [3,] 0.6218539 0.6512051 0.5842794 0.2000476
#> [4,] 0.6710642 0.5021942 0.1893288 0.5534743
#> [5,] 0.1141753 0.2763554 0.5600443 0.6678219
#> [6,] 0.5029857 0.3006291 0.2997223 0.5265600

(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.963348
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9309798

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8457143 0.9042857 0.9285714 0.9521429 0.9664286

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] 0.5200000 0.6857143 0.7600000 0.8400000 0.8828571

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2103.685            NA 17736.25 1876.355 21716.29
#> D(theta_bar)   2032.666            NA 17178.03 1855.554 21066.25
#> DIC            2174.703            NA 18294.48 1897.156 22366.34
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.00 0.84 0.02 0.14 0.16
#> [2,] 0.46 0.74 0.74 0.40 1.00
#> [3,] 0.40 0.48 0.96 0.84 0.78
#> [4,] 0.90 0.90 0.60 0.90 0.98
#> [5,] 0.58 0.34 0.86 0.46 0.68
#> [6,] 0.90 0.58 0.78 0.38 0.78
head(a$PPP_item_means)
#> [1] 0.38 0.56 0.56 0.54 0.60 0.66
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,]   NA 0.62 0.72 0.26 0.52 0.70 0.84 0.58 0.14  0.62  0.66  0.84  0.68  0.10
#> [2,]   NA   NA 0.66 0.76 0.98 0.56 0.76 0.08 0.38  0.82  0.18  0.76  0.20  0.78
#> [3,]   NA   NA   NA 1.00 0.48 0.98 0.50 0.92 0.64  0.86  0.88  0.76  0.70  0.78
#> [4,]   NA   NA   NA   NA 0.26 0.46 0.56 0.62 0.50  0.26  0.38  0.84  0.22  0.02
#> [5,]   NA   NA   NA   NA   NA 0.40 0.94 0.32 0.00  0.98  0.16  0.68  0.20  0.14
#> [6,]   NA   NA   NA   NA   NA   NA 0.52 0.92 0.50  0.62  0.84  0.74  0.66  0.38
#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,]  0.22  0.54  0.14  0.32  0.32  0.28  0.52  0.16  0.86  0.64  0.80  0.20
#> [2,]  0.70  0.98  0.92  0.70  0.60  0.56  0.42  0.26  0.28  0.94  0.46  0.44
#> [3,]  0.92  0.98  0.32  0.76  0.82  0.94  0.28  0.50  0.70  0.94  0.28  0.82
#> [4,]  0.38  0.30  0.26  0.18  0.60  0.88  0.98  0.66  0.30  0.62  0.72  0.50
#> [5,]  0.10  0.18  0.40  0.52  0.12  0.16  0.74  0.38  0.46  0.80  0.54  0.38
#> [6,]  0.10  0.10  0.92  0.34  0.54  0.82  0.92  0.70  0.32  0.64  0.60  0.46
#>      [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35]     [,36] [,37]
#> [1,]  0.00  0.14  0.02  0.14  0.54  0.20  0.62  0.36  0.46 0.2448980  0.72
#> [2,]  0.62  0.26  0.22  0.78  0.10  0.62  0.90  0.12  0.40 0.9387755  0.28
#> [3,]  0.66  0.08  0.76  0.70  0.62  1.00  0.68  0.32  0.84 1.0000000  0.80
#> [4,]  0.88  0.12  0.98  0.24  0.86  0.44  0.24  0.00  0.62 0.5102041  1.00
#> [5,]  0.54  0.78  0.62  0.60  0.34  0.82  0.36  0.02  0.36 0.5714286  0.80
#> [6,]  0.22  0.82  0.28  0.68  0.56  0.80  0.36  0.26  0.78 0.4081633  0.82
#>      [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,]  0.48  0.78  0.50  0.94  0.42  0.70  0.72  0.72  0.34  0.28  0.46  0.02
#> [2,]  0.80  0.08  0.46  0.50  0.74  0.10  0.14  0.16  0.64  0.74  0.94  0.52
#> [3,]  0.90  0.56  0.88  0.42  0.96  0.28  0.76  0.36  0.86  0.34  0.10  0.50
#> [4,]  0.48  0.68  0.98  0.86  0.32  0.74  0.60  0.98  0.82  0.56  0.36  0.62
#> [5,]  0.44  0.44  0.96  0.34  0.42  0.36  0.16  0.58  0.56  0.14  0.84  0.86
#> [6,]  0.74  0.54  0.86  0.64  0.10  0.44  0.68  0.98  0.12  0.36  0.78  0.96
#>      [,50]
#> [1,]  0.84
#> [2,]  0.18
#> [3,]  0.46
#> [4,]  0.24
#> [5,]  0.54
#> [6,]  0.38