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On the Identifiability of Diagnostic Classification Models

Published online by Cambridge University Press:  01 January 2025

Guanhua Fang Open the ORCID record for Guanhua Fang [Opens in a new window] ,
Jingchen Liu  and
Zhiliang Ying
Guanhua Fang
Affiliation:
Columbia University
Jingchen Liu*
Affiliation:
Columbia University
Zhiliang Ying
Affiliation:
Columbia University
*
Correspondence should be made to Jingchen Liu, Columbia University, New York, USA. Email: [email protected]; URL: http://stat.columbia.edu/jcliu/
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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

identifiabilitydiagnostic classification modelsDirichlet allocation
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 19 - 40
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-09658-x) contains supplementary material, which is available to authorized users.

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