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Finite Mixtures in Confirmatory Factor-Analysis Models

Published online by Cambridge University Press:  01 January 2025

Yiu-Fai Yung
Yiu-Fai Yung*
Affiliation:
L. L. Thurstone Psychometric Laboratory, University of North Carolina, Chapel Hill
*
Requests for reprints should be sent to Yiu-Fai Yung, CB#3270 Davie Hall, L. L. Thurstone Psychometric Laboratory, UNC-CH, Chapel Hill NC 27599.
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Abstract

In this paper, various types of finite mixtures of confirmatory factor-analysis models are proposed for handling data heterogeneity. Under the proposed mixture approach, observations are assumed to be drawn from mixtures of distinct confirmatory factor-analysis models. But each observation does not need to be identified to a particular model prior to model fitting. Several classes of mixture models are proposed. These models differ by their unique representations of data heterogeneity. Three different sampling schemes for these mixture models are distinguished. A mixed type of the these three sampling schemes is considered throughout this article. The proposed mixture approach reduces to regular multiple-group confirmatory factor-analysis under a restrictive sampling scheme, in which the structural equation model for each observation is assumed to be known. By assuming a mixture of multivariate normals for the data, maximum likelihood estimation using the EM (Expectation-Maximization) algorithm and the AS (Approximate-Scoring) method are developed, respectively. Some mixture models were fitted to a real data set for illustrating the application of the theory. Although the EM algorithm and the AS method gave similar sets of parameter estimates, the AS method was found computationally more efficient than the EM algorithm. Some comments on applying the mixture approach to structural equation modeling are made.

Keywords

covariance structuresmean structuresmixture modelsfactor analysis

Information

Type
Article
Information
Psychometrika , Volume 62 , Issue 3 , September 1997 , pp. 297 - 330
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

Note: This paper is one of the Psychometric Society's 1995 Dissertation Award papers.—Editor

This article is based on the dissertation of the author. The author would like to thank Peter Bentler, who was the dissertation chair, for guidance and encouragement of this work. Eric Holman, Robert Jennrich, Bengt Muthén, and Thomas Wickens, who served as the committee members for the dissertation, had been very supportive and helpful. Michael Browne is appreciated for discussing some important points about the use of the approximate information in the dissertation. Thanks also go to an anonymous associate editor, whose comments were very useful for the revision of an earlier version of this article.

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