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Factor Analysis for Non-Normal Variables

Published online by Cambridge University Press:  01 January 2025

Ab Mooijaart
Ab Mooijaart*
Affiliation:
Leiden University
*
Requests for reprints should be sent to Ab Mooijaart, Department of Psychology, Leiden University, Hooigracht 15, 2312 KM LEIDEN, THE NETHERLANDS.
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Abstract

Factor analysis for nonnormally distributed variables is discussed in this paper. The main difference between our approach and more traditional approaches is that not only second order cross-products (like covariances) are utilized, but also higher order cross-products. It turns out that under some conditions the parameters (factor loadings) can be uniquely determined. Two estimation procedures will be discussed. One method gives Best Generalized Least Squares (BGLS) estimates, but is computationally very heavy, in particular for large data sets. The other method is a least squares method which is computationally less heavy. In one example the two methods will be compared by using the bootstrap method. In another example real life data are analyzed.

Keywords

factor analysisnonnormalitythird order cross-productsunique factor loadingsBGLS estimatesbootstrap
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 3 , September 1985 , pp. 323 - 342
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

This paper has partly been written while the author was a visiting scholar at the Department of Psychology, University of California, Los Angeles. He wants to thank Peter Bentler who made this stay at UCLA possible and for his valuable contributions to this paper. This research was supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O) under number R56-150 and by USPHS Grant DA01070.

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