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Identifiability of Latent Class Models with Covariates

Published online by Cambridge University Press:  01 January 2025

Jing Ouyang  and
Gongjun Xu Open the ORCID record for Gongjun Xu [Opens in a new window]
Jing Ouyang
Affiliation:
University Of Michigan
Gongjun Xu*
Affiliation:
University Of Michigan
*
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI48109, USA. Email: [email protected]
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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.

Keywords

identifiabilitylatent class modelscognitive diagnosis models
Type
Theory & Methods (T&M)
Information
Psychometrika , Volume 87 , Issue 4 , December 2022 , pp. 1343 - 1360
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/S0033312300005494a.

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