Table 1: Q-matrix and parameters setting for NIDA model simulation We fit the model in Section 4 and the parameter estimates (averaging over 100 independent replications) are given in Tables 3 and 4. We can see our estimated response probabilities are very close to the true. The mean squared errors of the estimators are computed based on 100 independent replicates. The mixture probabilities of other classes except these eight are less than 5e-3. Our proposed method can recover the number of classes very well. The frequentist properties of estimation of response probabilities are listed in Table 3. We apply the K-means method to the estimated response probabilities of each item. We use the average Silhouette method to choose the number of clusters. We obtain the estimated partial information structure and reconstruct the Q -matrix accordingly. The proportion of the correctly estimated item’s partial information structure is 88.4%. Table 2: The mean and mse of the estimated class probabilities based on 100 simulation runs. Item Q-matrix G and S parameters s1 g1 s2 g2 s3 g3 1 1 0 0 0.1 0.1 - - - - 2 1 0 0 0.1 0.1 - - - - 3 1 0 0 0.1 0.1 - - - - 4 0 1 0 - - 0.1 0.2 - - 5 0 1 0 - - 0.1 0.2 - - 6 0 1 0 - - 0.1 0.2 - - 7 0 0 1 - - - - 0.1 0.3 8 0 0 1 - - - - 0.1 0.3 9 0 0 1 - - - - 0.1 0.3 10 1 1 0 0.1 0.5 0.1 0.5 - - 11 1 0 1 0.1 0.5 - - 0.1 0.5 12 0 1 1 - - 0.1 0.5 0.1 0.5 13 1 1 1 0.1 0.5 0.1 0.5 0.1 0.5 C1 C2 C3 C4 C5 C6 C7 C8 Averaged estimates 0.141 0.144 0.145 0.091 0.095 0.100 0.150 0.097 MSE 3e-4 3e-4 4e-4 2e-4 3e-4 2e-4 2e-4 4e-4 19