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Heterogeneous Factor Analysis Models: A Bayesian Approach

Published online by Cambridge University Press:  01 January 2025

Asim Ansari ,
Kamel Jedidi  and
Laurette Dube
Asim Ansari*
Affiliation:
Columbia University
Kamel Jedidi
Affiliation:
Columbia University
Laurette Dube
Affiliation:
McGill University
*
Requests for reprints should be sent to Asim Ansaxi, 517 Uris Hall, Columbia University, 3022 Broadway, New York, NY, 10027. E-Mail: maa48@columbia.edu
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Abstract

Multilevel factor analysis models are widely used in the social sciences to account for heterogeneity in mean structures. In this paper we extend previous work on multilevel models to account for general forms of heterogeneity in confirmatory factor analysis models. We specify various models of mean and covariance heterogeneity in confirmatory factor analysis and develop Markov Chain Monte Carlo (MCMC) procedures to perform Bayesian inference, model checking, and model comparison.

We test our methodology using synthetic data and data from a consumption emotion study. The results from synthetic data show that our Bayesian model perform well in recovering the true parameters and selecting the appropriate model. More importantly, the results clearly illustrate the consequences of ignoring heterogeneity. Specifically, we find that ignoring heterogeneity can lead to sign reversals of the factor covariances, inflation of factor variances and underappreciation of uncertainty in parameter estimates. The results from the emotion study show that subjects vary both in means and covariances. Thus traditional psychometric methods cannot fully capture the heterogeneity in our data.

Keywords

confirmatory factor analysismultilevel modelsrandom coefficient modelsMCMC methodsGibbs samplingMetropolis-Hastings
Type
Articles
Information
Psychometrika , Volume 67 , Issue 1 , March 2002 , pp. 49 - 77
Copyright
Copyright © 2002 The Psychometric Society

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