live on a low-dimensional manifold that is indeed a measure zero set. Therefore, the results in [1] cannot be applied in this context. The results of this paper stand on the fundamental results of Kruskal [15] concerning the rank of three-dimensional arrays. We investigate the special structures of diagnostic classification models, adapt Kruskal’s analysis to this particular context, and develop identifiability results. In the analysis of diagnostic classification models, Bayesian models and inference are popular. Technically speaking, model identifiability is a lesser issue for Bayesian inference that is valid as long as the posterior distribution is well defined. On the other hand, this seemingly plausible solution in fact could be misleading in that, in case of nonidentifiability, the likelihood function does not provide information to differentiate among certain parameters and thus it all relies on the prior information that is mostly subjective. Computational issues may also exist under this situation. Thus, identifiability results are of importance to Bayesian models as well. Besides developing identifiability results for the item parameters, we also provide discussion of the Q -matrix that is a key quantity in the specification of diagnostic classification models. The Q -matrix provides a qualitative description of the item-attribute relationship. However, this precise relationship depends on the specific model parameterization and the interaction among attributes. This paper develops general results applicable to essentially all DCMs instead of specific parametric models. We consider a slightly different estimand implied by the Q -matrix, the partial information structure for each item that will be defined in the subsequent discussion. We develop identifiability results for the partial information structure for each item. Under specific model parameterizations, the Q -matrix can also be reconstructed based on the estimated partial information for each item. This will be illustrated via a real data analysis. To illustrate the identifiability results, we consider estimation of the item response parameters, the attribute distribution, and the partial information structure under a latent class model with Dirichlet allocation. This model is proposed for exploratory analysis. It contains infinitely many mixtures and thus is a saturated and over-parameterized model. To regularize the overfitting (the 3