N=dim(Design_array)[1]J=nrow(Q_matrix)K=ncol(Q_matrix)L=dim(Design_array)[3]

tau<-numeric(K)for(kin1:K){  tau[k]<-runif(1,.2,.6)}R=matrix(0,K,K)# Initial alphasp_mastery<-c(.5,.5,.4,.4)Alphas_0<-matrix(0,N,K)for(iin1:N){for(kin1: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  10Smats<-matrix(runif(J*K,.1,.3),c(J,K))Gmats<-matrix(runif(J*K,.1,.3),c(J,K))# Simulate rRUM parametersr_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)#> 0output_rRUM_indept#>#> Model: rRUM_indept#>#> Sample Size: 350#> Number of Items:#> Number of Time Points:#>#> Chain Length: 100, burn-in: 50summary(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:  0.6145a<-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] 0.9309798AAR_vec<-numeric(L)for(tin1:L){  AAR_vec[t]<-mean(Alphas[,,t]==a$Alphas_est[,,t])}AAR_vec#> [1] 0.8457143 0.9042857 0.9285714 0.9521429 0.9664286PAR_vec<-numeric(L)for(tin1:L){  PAR_vec[t]<-mean(rowSums((Alphas[,,t]-a$Alphas_est[,,t])^2)==0)}PAR_vec#> [1] 0.5200000 0.6857143 0.7600000 0.8400000 0.8828571

a$DIC#>              Transition Response_Time Response    Joint    Total#> D_bar          2103.685            NA 17736.25 1876.355 21716.29#> D(theta_bar)   2032.666            NA 17178.03 1855.554 21066.25#> DIC            2174.703            NA 18294.48 1897.156 22366.34head(a$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 0.78head(a$PPP_item_means)#> [1] 0.38 0.56 0.56 0.54 0.60 0.66head(a$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