On the Identifiability of Diagnostic Classification Models

Abstract

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.

References in corpus (2)

• Identifiability of parameters in latent structure models with many observed variables
• The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model

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• Latent Theme Dictionary Model for Finding Co-occurrent Patterns in Process Data
• A Joint MLE Approach to Large-Scale Structured Latent Attribute Analysis
• Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses