On the Identifiability of Diagnostic Classification Models

TL;DR

This paper provides fundamental identifiability results for diagnostic classification models, ensuring reliable parameter estimation, and introduces consistent estimators validated through simulations and real data examples.

Contribution

It establishes general identifiability conditions for DCM parameters and develops consistent estimators applicable across various model specifications.

Findings

Identifiability of item response probabilities and attribute distributions.

Consistent estimators perform well in simulations.

Real data example demonstrates practical applicability.

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.