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Regularized Latent Class Analysis with Application in Cognitive Diagnosis

Published online by Cambridge University Press:  01 January 2025

Yunxiao Chen ,
Xiaoou Li ,
Jingchen Liu  and
Zhiliang Ying
Yunxiao Chen
Affiliation:
Emory University
Xiaoou Li
Affiliation:
University of Minnesota
Jingchen Liu*
Affiliation:
Columbia University
Zhiliang Ying
Affiliation:
Columbia University
*
Correspondence should be made to Jingchen Liu , Department of Statistics, Columbia University, New York, NY, USA. Email: [email protected]
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Abstract

Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation–maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.

Keywords

diagnostic classification modelslatent class analysisregularizationconsistencyEM algorithm
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 660 - 692
Copyright
Copyright © 2016 The Psychometric Society

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