r$_{jk}$ , 0 < r$_{jk}$ < 1, is the penalty parameter for not possessing the k -th attribute. The corresponding item parameters are θ = { φ$_{j}$, r$_{jk}$ : j = 1 , · · · , J, k = 1 , · · · , K } . Based on Table 15, we could parameterize each class, C 1 = (1 , 1 , 0), C 2 = (1 , 0 , 0), C 3 = (1 , 0 , 1), C 4 = (0 , 0 , 0), and C 5 = (1 , 1 , 1). Also, an estimated Q -matrix under this parameterization is provided in Table 16. The estimated parameters for the reduced NC-RUM model under estimated Q -matrix are given in Table 17. In this parameterization, we obtain an approximate interpretation that attribute 1 corresponds to “public performance”, attribute 2 to “scrutiny”, and attribute 3 to “interaction”. Table 14 presents posterior mean of the response probability for each item under each class. Based on the loadings in this table, we may interpret these latent classes as follows. Class 1 is strongly associated with items 1-4 which are related to public performance and items 5-8 which are related to close scrutiny. Thus, this group is characterized by strong fear of public performance and close scrutiny. Class 2 has high response probabilities of items 1-4. This shows that it possesses attribute 1 only, i.e. those people in this class are afraid of public performance, but not close scrutiny and interaction. Class 3 has relatively high response probabilities of items 1-4 and 9-13 and relatively low response probability of items 5-8, which means that this class is more likely related with attributes 1 and 3. In other words, people from group 3 may have “fears” of public performance and interaction with other people. Class 4 is loosely associated with all items. The all item response probabilities are low which indicates that this class may not be connected with any attributes. Class 5 has the highest response probabilities among all items. This shows that class 5 is associated with all items. Hence, people from class 5 are likely to possess 3 attributes. In other words, class 5 corresponds to, using a technical term, the generalized social anxiety disorder subtype (“fears most social situations”; American Psychiatric Association, 1994 [2]). This paper deals with certain fundamental issues in latent class models under a general framework. In particular, it does not require the usual Q -matrix structure which is commonly assumed in most 7 Discussion 27