On the Identifiability of Diagnostic Classification Models Guanhua Fang, Jingchen Liu, and Zhiliang Ying June 6, 2017 This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In particular, we establish identifiability results of various modeling parameters, notably item response probabilities, attribute distribution, and Q -matrix- induced partial information structure. Consistent estimators are constructed. Simulation results show that these estimators perform well under various modeling settings. We also use a real example to illustrate the new method. The results are stated under the setting of general latent class models. For DCM with a specific parameterization, the conditions may be adapted accordingly. Cognitive diagnosis is an important area which has become increasingly popular in educational assessment, psychiatric evaluation, and many other disciplines. An incomplete list of recent devel- opments of cognitive diagnosis models include the rule space method [27, 28], the reparameterized unified/fusion model (RUM) [8, 11, 29], the conjunctive (noncompensatory) DINA and NIDA models [14, 26, 7, 30], the compensatory DINO and NIDO models [31, 30], the attribute hierarchy method [17], clustering methods [5], and the G-DINA model [6]; see also [13, 33, 22] for more approaches to cognitive diagnosis. A comprehensive review of diagnostic classification models can be found in [21]. Statistical inference methods have also been developed for these models, such as item parameter estimation/calibration [20, 24], Q -matrix estimation [3, 4, 18, 19]. 1 arXiv:1706.01240v1 [math.ST] 5 Jun 2017 Abstract 1 Introduction