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Identifiability of Latent Class Models with Covariates

Author

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  • Jing Ouyang

    (University of Michigan)

  • Gongjun Xu

    (University of Michigan)

Abstract

Latent class models with covariates are widely used for psychological, social, and educational research. Yet the fundamental identifiability issue of these models has not been fully addressed. Among the previous research on the identifiability of latent class models with covariates, Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) studied the local identifiability conditions. However, motivated by recent advances in the identifiability of the restricted latent class models, particularly cognitive diagnosis models (CDMs), we show in this work that the conditions in Huang and Bandeen-Roche (Psychometrika 69:5–32, 2004) are only necessary but not sufficient to determine the local identifiability of the model parameters. To address the open identifiability issue for latent class models with covariates, this work establishes conditions to ensure the global identifiability of the model parameters in both strict and generic sense. Moreover, our results extend to the polytomous-response CDMs with covariates, which generalizes the existing identifiability results for CDMs.

Suggested Citation

  • Jing Ouyang & Gongjun Xu, 2022. "Identifiability of Latent Class Models with Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1343-1360, December.
    • Handle: RePEc:spr:psycho:v:87:y:2022:i:4:d:10.1007_s11336-022-09852-y
    DOI: 10.1007/s11336-022-09852-y
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    References listed on IDEAS

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    1. Beth A. Reboussin & Edward H. Ip & Mark Wolfson, 2008. "Locally dependent latent class models with covariates: an application to under‐age drinking in the USA," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 877-897, October.
    2. Guan-Hua Huang & Karen Bandeen-Roche, 2004. "Building an identifiable latent class model with covariate effects on underlying and measured variables," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 5-32, March.
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    4. Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    5. Yunxiao Chen & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2015. "Statistical Analysis of Q -Matrix Based Diagnostic Classification Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 850-866, June.
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    14. Yuqi Gu & Gongjun Xu, 2019. "The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 468-483, June.
    15. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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    Cited by:

    1. Di Mari, Roberto & Bakk, Zsuzsa & Oser, Jennifer & Kuha, Jouni, 2023. "A two-step estimator for multilevel latent class analysis with covariates," LSE Research Online Documents on Economics 119994, London School of Economics and Political Science, LSE Library.
    2. Zhenghao Zeng & Yuqi Gu & Gongjun Xu, 2023. "A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 580-612, June.

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