Table 11: The mean and mse of estimated response probabilities for each latent classes of LCDM model based on 100 simulation runs. structure is 96.5%. We calculate the mean and mean square error of the estimators of the LCDM model. The results are listed in Table 12. We apply the proposed method to a subset of the National Epidemiological Survey on Alcohol and Related Conditions (NESARC) (Grant et al., 2003 [10]) concerning social phobia. There are in total 13 questions that are presented in Table 13. We fit the latent Dirichlet allocation model and estimate the partial information structure via the procedure in Section 4. The results are summarized as follows. To obtain meaningful and stable estimates, we consider large latent classes whose probabilities are over 2%. According to the fitted model, there are five such latent classes, each of which is over 2% of the population. The estimated posterior probability of each class is π$_{1}$ = 0 . 11, π$_{2}$ = 0 . 37, π$_{3}$ = 0 . 10, π$_{4}$ = 0 . 20, and π$_{5}$ = 0 . 15. They add up to 93% of the population. The estimated probabilities are presented in Table 14. 25 6 Real data analysis I Estimated prob MSE of prob C1 C2 C3 C4 C5 C6 C7 C8 C1 C2 C3 C4 C5 C6 C7 C8 1 0.88 0.12 0.12 0.88 0.88 0.12 0.88 0.12 6e-4 7e-4 5e-4 6e-4 5e-4 4e-4 1e-2 7e-4 2 0.88 0.12 0.12 0.88 0.88 0.12 0.87 0.13 6e-4 7e-4 6e-4 6e-4 6e-4 7e-4 3e-3 9e-4 3 0.88 0.12 0.12 0.88 0.88 0.12 0.88 0.12 6e-4 5e-4 6e-4 5e-4 5e-4 6e-4 7e-4 7e-4 4 0.12 0.88 0.12 0.88 0.12 0.88 0.88 0.12 7e-4 6e-4 6e-4 6e-4 8e-4 6e-4 3e-3 9e-4 5 0.12 0.88 0.12 0.88 0.12 0.88 0.88 0.12 6e-4 7e-4 5e-4 6e-4 8e-4 7e-4 1e-3 9e-4 6 0.12 0.88 0.12 0.88 0.12 0.88 0.87 0.13 5e-4 6e-4 6e-4 5e-4 6e-4 6e-4 2e-3 6e-4 7 0.12 0.12 0.88 0.12 0.88 0.88 0.88 0.12 6e-4 5e-4 7e-4 7e-4 7e-4 6e-4 3e-3 3e-3 8 0.12 0.12 0.88 0.12 0.88 0.88 0.88 0.13 8e-4 4e-4 6e-4 6e-4 5e-4 6e-4 8e-4 4e-3 9 0.12 0.12 0.88 0.12 0.88 0.88 0.87 0.12 7e-4 5e-4 6e-4 8e-4 7e-4 6e-4 1e-2 1e-2 10 0.50 0.51 0.12 0.88 0.50 0.49 0.88 0.12 8e-4 1e-3 6e-4 5e-4 1e-3 1e-3 8e-4 1e-3 11 0.50 0.50 0.12 0.88 0.50 0.50 0.87 0.12 1e-3 1e-3 6e-4 7e-4 1e-3 1e-3 5e-3 4e-3 12 0.50 0.12 0.50 0.49 0.88 0.50 0.88 0.12 1e-3 6e-4 1e-3 1e-3 6e-4 1e-3 2e-3 8e-3 13 0.50 0.12 0.50 0.50 0.88 0.49 0.88 0.12 1e-3 4e-4 9e-4 1e-3 5e-4 1e-3 2e-3 4e-3 14 0.12 0.50 0.50 0.49 0.50 0.88 0.88 0.12 6e-4 1e-3 2e-3 1e-3 1e-3 6e-4 3e-3 3e-3 15 0.12 0.50 0.50 0.50 0.50 0.88 0.88 0.12 6e-4 1e-3 1e-3 1e-3 1e-3 6e-4 9e-4 1e-3 16 0.27 0.27 0.27 0.50 0.50 0.50 0.87 0.12 1e-3 1e-3 9e-4 1e-3 1e-3 1e-3 1e-2 9e-4