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 
#>  20  83 142  84  21
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
#>        0.1345       0.5643       0.6930       0.5490       0.7087
#>        0.6633       0.2065       0.6031       0.5260       0.7942
#>        0.5607       0.5467       0.6871       0.2240       0.8623
#>        0.6092       0.5071       0.2707       0.5366       0.8333
#>        0.2328       0.2660       0.6640       0.5080       0.7193
#>    ... 45 more items
#> 
#> Transition Parameters:
#>    taus_EAP
#> τ1   0.4279
#> τ2   0.4181
#> τ3   0.5759
#> τ4   0.5375
#> 
#> Class Probabilities:
#>      pis_EAP
#> 0000 0.08429
#> 0001 0.08398
#> 0010 0.04602
#> 0011 0.01500
#> 0100 0.13739
#>    ... 11 more classes
#> 
#> Deviance Information Criterion (DIC): 22929.56 
#> 
#> Posterior Predictive P-value (PPP):
#> M1:   0.5
#> M2:  0.49
#> total scores:  0.6105
a <- summary(output_rRUM_indept)
head(a$r_stars_EAP)
#>           [,1]      [,2]      [,3]      [,4]
#> [1,] 0.1344617 0.5643205 0.6929589 0.5490303
#> [2,] 0.6633021 0.2064912 0.6030876 0.5260488
#> [3,] 0.5606544 0.5467405 0.6871179 0.2240308
#> [4,] 0.6092055 0.5070976 0.2707032 0.5365697
#> [5,] 0.2328241 0.2660043 0.6640119 0.5080245
#> [6,] 0.5585330 0.3077579 0.3372768 0.5225505

(cor_pistars <- cor(as.vector(pi_stars),as.vector(a$pi_stars_EAP)))
#> [1] 0.9200365
(cor_rstars <- cor(as.vector(r_stars*Q_matrix),as.vector(a$r_stars_EAP*Q_matrix)))
#> [1] 0.9128301

AAR_vec <- numeric(L)
for(t in 1:L){
  AAR_vec[t] <- mean(Alphas[,,t]==a$Alphas_est[,,t])
}
AAR_vec
#> [1] 0.8478571 0.9007143 0.9357143 0.9642857 0.9735714

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] 0.5257143 0.6714286 0.7828571 0.8685714 0.8971429

a$DIC
#>              Transition Response_Time Response    Joint    Total
#> D_bar          2090.404            NA 18302.17 1783.206 22175.78
#> D(theta_bar)   2037.153            NA 17630.88 1753.971 21422.00
#> DIC            2143.655            NA 18973.47 1812.440 22929.56
head(a$PPP_total_scores)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.00 0.92 1.00 0.90 1.00
#> [2,] 0.58 0.46 0.54 0.52 0.46
#> [3,] 0.64 0.58 0.54 0.76 1.00
#> [4,] 0.36 0.60 0.78 0.86 0.48
#> [5,] 0.44 0.56 0.48 0.66 0.60
#> [6,] 0.44 0.72 0.84 0.72 0.52
head(a$PPP_item_means)
#> [1] 0.42 0.54 0.42 0.50 0.50 0.54
head(a$PPP_item_ORs)
#>      [,1] [,2] [,3] [,4] [,5] [,6]      [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,]   NA 0.36 0.46 0.38 0.74 0.82 0.8979592 0.34 0.70  0.34  0.52  0.34  0.80
#> [2,]   NA   NA 0.80 0.20 0.64 0.46 0.6734694 0.32 0.16  0.12  0.90  0.32  0.48
#> [3,]   NA   NA   NA 0.68 0.88 0.76 0.4285714 0.62 0.92  0.54  0.06  0.50  0.44
#> [4,]   NA   NA   NA   NA 0.04 0.52 0.5102041 0.54 0.38  0.92  0.72  0.88  0.42
#> [5,]   NA   NA   NA   NA   NA 0.50 0.2040816 0.48 0.32  0.60  0.06  0.58  0.44
#> [6,]   NA   NA   NA   NA   NA   NA 0.7755102 0.96 0.80  0.72  0.50  0.80  0.24
#>      [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,]  0.42  0.12  0.44  0.20  0.84  0.74  0.60  0.72  0.28  0.12  0.24  0.76
#> [2,]  0.38  0.34  0.62  0.48  0.42  0.52  0.70  0.32  1.00  0.92  0.92  1.00
#> [3,]  0.56  0.34  0.08  0.28  0.00  0.02  0.66  0.26  0.24  0.12  0.42  0.56
#> [4,]  0.60  0.04  0.08  0.76  0.06  0.48  0.86  0.16  0.26  0.86  0.48  0.06
#> [5,]  0.06  0.22  0.42  0.16  0.56  0.16  0.90  0.80  0.22  0.54  0.88  0.90
#> [6,]  0.78  0.38  0.40  0.74  0.16  0.38  0.32  0.14  0.50  0.28  0.02  0.20
#>      [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
#> [1,]  0.04  0.44  0.22  0.44  0.84  0.14  0.82  0.58  0.80  0.44  0.40  0.38
#> [2,]  0.12  0.50  0.72  0.40  0.68  0.92  0.94  1.00  0.42  0.10  0.70  0.16
#> [3,]  0.12  0.52  0.76  0.74  0.26  0.76  0.54  0.22  0.64  0.90  0.84  0.18
#> [4,]  0.30  0.02  0.42  0.20  0.32  0.66  0.06  0.46  0.22  0.00  0.08  0.08
#> [5,]  0.16  0.30  0.22  0.70  0.60  0.50  0.96  0.32  0.38  0.74  0.92  0.04
#> [6,]  0.62  0.04  0.12  0.10  0.02  0.82  0.20  0.04  0.08  0.34  0.26  0.08
#>      [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
#> [1,]  0.06  0.38  0.36  0.72  0.32  0.54  0.74  0.08  0.54  0.84  0.40  0.10
#> [2,]  0.34  0.56  0.48  0.86  0.44  0.48  0.74  0.72  0.16  0.84  0.66  0.18
#> [3,]  0.46  0.54  0.72  0.10  0.50  0.78  0.98  0.52  0.84  0.94  0.84  0.74
#> [4,]  0.22  0.86  0.12  0.36  0.88  0.60  0.26  0.32  0.18  0.38  0.04  0.52
#> [5,]  0.08  0.30  0.86  0.94  0.62  0.80  0.88  0.18  0.52  0.62  1.00  0.36
#> [6,]  0.22  0.26  0.68  0.56  0.94  0.96  0.76  0.48  0.64  0.92  0.54  0.98
#>      [,50]
#> [1,]  0.64
#> [2,]  0.10
#> [3,]  0.46
#> [4,]  0.56
#> [5,]  0.28
#> [6,]  0.96