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Simultaneous Factor Analysis in Several Populations

Published online by Cambridge University Press:  01 January 2025

K. G. Jöreskog
K. G. Jöreskog*
Affiliation:
Educational Testing Service†
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Abstract

This paper is concerned with the study of similarities and differences in factor structures between different groups. A common situation occurs when a battery of tests has been administered to samples of examinees from several populations.

A very general model is presented, in which any parameter in the factor analysis models (factor loadings, factor variances, factor covariances, and unique variances) for the different groups may be assigned an arbitrary value or constrained to be equal to some other parameter. Given such a specification, the model is estimated by the maximum likelihood method yielding a large sample x2 of goodness of fit. By computing several solutions under different specifications one can test various hypotheses.

The method is capable of dealing with any degree of invariance, from the one extreme, where nothing is invariant, to the other extreme, where everything is invariant. Neither the number of tests nor the number of common factors need to be the same for all groups, but to be at all interesting, it is assumed that there is a common core of tests in each battery that is the same or at least content-wise comparable.

Keywords

CovarianceGeneral ModelPublic PolicyFactor StructureFactor Loading
Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 4 , December 1971 , pp. 409 - 426
Copyright
Copyright © 1971 The Psychometric Society

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Footnotes

*

This research was supported by grant NSF-GB-12959 from National Science Foundation. My thanks are due to Michael Browne for his comments on an earlier draft of this paper and to Marielle van Thillo who checked the mathematical derivations and wrote and debugged the computer program SIFASP.

†

Now at Statistics Department, University of Uppsala, Sweden.

References

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