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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

Information

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.

References

Bollen, K.A., Ting, K., (1993). Confirmatory tetrad analysis, Sociological Methodology, 23, 147–175.CrossRefGoogle Scholar
Browne, M.W., Cudeck, R., (1992). Alternative ways of assessing model fit, Sociological Methods & Research, 21, 230–258.CrossRefGoogle Scholar
Chen, B., & Pearl, J., (2014). Graphical tools for linear structural equation modeling. Technical Report R-432, Department of Computer Science, University of California, Los Angeles, CA. Psychometrika (forthcoming). http://ftp.cs.ucla.edu/pub/stat%20ser/r432.pdf.CrossRefGoogle Scholar
Claeskens, G., Hjort, N.L.Model selection and model averaging 2008 Cambridge:Cambridge University Press.Google Scholar
Clark, L.A., Watson, D., (1995). Constructing validity: Basic issues in objective scale development, Psychological Assessment, 7, 309–319.CrossRefGoogle Scholar
Cramer, A.O.J., van der Sluis, S., Noordhof, A., Wichers, M., Geschwind, N., Aggen, S.H., Borsboom, D., (2012). Dimensions of normal personality as networks in search of equilibrium: You can’t like parties if you don’t like people, European Journal of Personality, 26, 414–431.CrossRefGoogle Scholar
de Fátima Salgueiro, M., Smith, P.W., McDonald, J.W., (2008). The manifest association structure of the single-factor model: Insights from partial correlations, Psychometrika, 73, 665–670.CrossRefGoogle Scholar
Ellis, J.L., (2014). An inequality for correlations in unidimensional monotone latent variable models for binary variables, Psychometrika, 79, 303–316.CrossRefGoogle ScholarPubMed
Elshout, J. J., & Akkerman, A. E., (1975). Vijf persoonlijkheidsfactoren test 5PFT: Handleiding (The Five Personality Factor Test (5PFT): Manual). Nijmegen: Berkhout B.V..Google Scholar
Eysenck, H. J., (1983). Psychophysiology and personality: Extraversion, neuroticism and psychoticism. In: Individual differences and psychopathology (pp. 13–30). Elsevier.CrossRefGoogle Scholar
Guttman, L., (1940). Multiple rectilinear prediction and the resolution into components, Psychometrika, 5, 75–99.CrossRefGoogle Scholar
Guttman, L., (1953). Image theory for the structure of quantitative variates, Psychometrika, 18, 277–296.CrossRefGoogle Scholar
Holland, P.W., Rosenbaum, P.R., (1986). Conditional association and unidimensionality in monotone latent variable models, The Annals of Statistics, 14, 1523–1543.CrossRefGoogle Scholar
Langford, E., Schwertman, N., Owens, M., (2001). Is the property of being positively correlated transitive?, The American Statistician, 55, 322–325.CrossRefGoogle Scholar
Lord, F.M., (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ:Erlbaum.Google Scholar
Rosenbaum, P.R., (1984). Testing the conditional independence and monotonicity assumptions of item response theory, Psychometrika, 49, 425–435.CrossRefGoogle Scholar
Saris, W.E., Satorra, A., Van der Veld, W.M., (2009). Testing structural equation models or detection of misspecifications?, Structural Equation Modeling, 16, 561–582.CrossRefGoogle Scholar
Sherman, J., Morrison, W.J., (1950). Adjustment of an inverse matrix corresponding to a change in one element of a given matrix, The Annals of Mathematical Statistics, 21, 124–127.CrossRefGoogle Scholar
Smits, I.A.M., Dolan, C.V., Vorst, H.C., Wicherts, J.M., Timmerman, M.E., (2013). Data from "cohort differences in big five personality factors over a periof of 25 years", Journal of Open Psychology Data, 1, 1–3.Google Scholar
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