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Building an Identifiable Latent Class Model with Covariate Effects on Underlying and Measured Variables

Published online by Cambridge University Press:  01 January 2025

Guan-Hua Huang  and
Karen Bandeen-Roche
Guan-Hua Huang*
Affiliation:
University of Wisconsin, Madison, Wisconsin
Karen Bandeen-Roche
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
*
Requests for reprints should be sent to Guan-Hua Huang, Institute of Statistics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30050, TAIWAN
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Abstract

In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators' substantive associations with predictors are built directly and indirectly in unique model parameters. In this paper, we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership, but that also allow direct effects of secondary covariates on the indicators themselves. Theory for model identification is developed. We detail an Expectation-Maximization algorithm for parameter estimation, standard error calculation, and convergent properties. Comparison of the proposed model with models underlying existing latent class modeling software is provided. A detailed analysis of how visual impairments affect older persons' functioning requiring distance vision is used for illustration.

Keywords

EM algorithmfinite mixture modelidentifiabilitymultiple discrete indicatorsvisual functioning
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 1 , March 2004 , pp. 5 - 32
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

This work was supported by National Institute on Aging (NIA) Program Project P01-AG-10184-03 and National Institutes of Mental Health grant R01-MH-56639-01A1. Dr. Bandeen-Roche is a Brookdale National Fellow. The authors wish to thank Drs. Gary Rubin and Sheila West for kindly making the Salisbury Eye Evaluation data available. We also thank the Editor, the Associate Editor, and three referees for their valuable comments.

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