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Unidimensional factor models imply weaker partial correlations than zero-order correlations

Published online by Cambridge University Press:  01 January 2025

Riet van Bork Open the ORCID record for Riet van Bork [Opens in a new window] ,
Raoul P. P. P. Grasman  and
Lourens J. Waldorp
Riet van Bork*
Affiliation:
Department of Psychological Methods, University of Amsterdam
Raoul P. P. P. Grasman
Affiliation:
Department of Psychological Methods, University of Amsterdam
Lourens J. Waldorp
Affiliation:
Department of Psychological Methods, University of Amsterdam
*
Correspondence should be made to Riet van Bork, Department of Psychological Methods, University of Amsterdam, Nieuwe Achtergracht 129-B, 1018 WS Amsterdam, The Netherlands. Email: r.vanbork@uva.nl
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Abstract

In this paper we present a new implication of the unidimensional factor model. We prove that the partial correlation between two observed variables that load on one factor given any subset of other observed variables that load on this factor lies between zero and the zero-order correlation between these two observed variables. We implement this result in an empirical bootstrap test that rejects the unidimensional factor model when partial correlations are identified that are either stronger than the zero-order correlation or have a different sign than the zero-order correlation. We demonstrate the use of the test in an empirical data example with data consisting of fourteen items that measure extraversion.

Keywords

factor modelspartial correlationszero-order correlations
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 2 , June 2018 , pp. 443 - 452
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

We would like to thank Mijke Rhemtulla and Denny Borsboom for their help in constructing the theory that later resulted in the proof presented in this paper. We would like to thank Sacha Epskamp for his helpful comments.

Electronic supplementary material The online version of this article (doi:https://doi.org/10.1007/s11336-018-9607-z) contains supplementary material, which is available to authorized users.

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