On the Identifiability of Diagnostic Classification Models

Guanhua Fang (), Jingchen Liu () and Zhiliang Ying ()
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Guanhua Fang: Columbia University
Jingchen Liu: Columbia University
Zhiliang Ying: Columbia University

Psychometrika, 2019, vol. 84, issue 1, No 2, 19-40

Abstract: Abstract This paper establishes fundamental results for statistical analysis based on diagnostic classification models (DCMs). The results are developed at a high level of generality and are applicable to essentially all diagnostic classification models. In particular, we establish identifiability results for various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. These results are stated under a general setting of latent class models. Through a nonparametric Bayes approach, we construct an estimator that can be shown to be consistent when the identifiability conditions are satisfied. Simulation results show that these estimators perform well under various model settings. We also apply the proposed method to a dataset from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).

Keywords: identifiability; diagnostic classification models; Dirichlet allocation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s11336-018-09658-x

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