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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$Alphas_est[,,t])^2)==0)
}
PAR_vec
#> [1] 0.5257143 0.6714286 0.7828571 0.8685714 0.8971429a$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,] 0.96These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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