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Selecting the Number of Classes Under Latent Class Regression: A Factor Analytic Analogue

Published online by Cambridge University Press:  01 January 2025

Guan-Hua Huang
Guan-Hua Huang*
Affiliation:
National Chiao Tung University
*
Request for reprints should be sent to Guan-Hua Huang, Institute of Statistics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan. E-mail: ghuang@stat.nctu.edu.tw. Webpage: http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/
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Abstract

Recently, the regression extension of latent class analysis (RLCA) model has received much attention in the field of medical research. The basic RLCA model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves. To reduce complexity and enhance interpretability, one usually fixes the number of classes in a given RLCA. Often, goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes. In this paper, we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting. Two ideas with application to many settings other than ours are synthesized in deriving the method: a connection between latent class models and factor analysis, and techniques of covariate marginalization and elimination. A Monte Carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches. Data from a study of how measured visual impairments affect older persons’ functioning are used for illustration.

Keywords

categorical datafactor analysisfinite mixture modelgoodness of fit testlatent profile modelmarginalizationresiduals in generalized linear modelsMonte Carlo simulation.
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 2 , June 2005 , pp. 325 - 345
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

This work was supported by National Institute on Aging (NIA) Program Project P01-AG-10184-03. The author wishes to thank Dr. Karen Bandeen-Roche for her stimulating comments and helpful discussions, and Drs. Gary Rubin and Sheila West for kindly making the Salisbury Eye Evaluation data available.

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