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Might “Unique” Factors be “Common”? On the Possibility of Indeterminate Common–Unique Covariances

Published online by Cambridge University Press:  01 January 2025

Dave Grayson
Dave Grayson*
Affiliation:
School of Psychology, University of Sydney
*
Requests for reprints should be sent to Dave Grayson, 14 Poplar Grove, Lawson, NSW 2783, Australia. E-mail: dgrayson1@pnc.com.au
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Abstract

The present paper shows that the usual factor analytic structured data dispersion matrix Λ Ψ Λ’ + Δ can readily arise from a set of scores y = Λ η + ε, where the “common” (η) and “unique” (ε) factors have nonzero covariance: Γ = Cov(ε,η) ≠ 0. Implications of this finding are discussed for the indeterminacy of factor scores, and for the issue of invariance of factor analytic covariance models. The size of the problem is explored with numerical examples.

Keywords

factor analysisfactor score indeterminacyfactorial invariancecommon factor
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 521 - 528
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

I would like to acknowledge the large amount of effort and stimulating input supplied on the previous drafts of this paper from the reviewers, Associate Editor, and Editors of Psychometrika. Particular thanks go to William Meredith for his assistance with the final draft.

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