Regularized Latent Class Analysis with Application in Cognitive Diagnosis

Yunxiao Chen, Xiaoou Li, Jingchen Liu, Zhiliang Ying

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)660-692
Number of pages33
Issue number3
StatePublished - Sep 1 2017

Bibliographical note

Funding Information:
This work was supported by NSF (grant nos. SES-1323977, IIS-1633360), Army Research Office (grant no. W911NF-15-1-0159), and NIH (grant no. R01GM047845).

Publisher Copyright:
© 2016, The Psychometric Society.


  • EM algorithm
  • consistency
  • diagnostic classification models
  • latent class analysis
  • regularization

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