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On the Construction of all Factors of the Model for Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Wim P. Krijnen
Wim P. Krijnen*
Affiliation:
University of Amsterdam
*
Requests for reprints should be sent to Wim Krijnen, Developmental Psychology, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, THE NETHERLANDS. E-Mail: wim.krijnen@hetnet.nl
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Abstract

A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are “correctly” selected by the best linear factor predictor.

Keywords

indeterminacyfactor scoresconfirmatory factor analysisexploratory factor analysisdistance between factors
Type
Articles
Information
Psychometrika , Volume 67 , Issue 1 , March 2002 , pp. 161 - 172
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

I would like to thank Willem Schaafsma for useful discussions pertaining to the model for factor analysis. I am indebted to Peter Molenaar and Conor Dolan for their comments on the manuscript. Additionally, I thank the reviewers for the constructive remarks on an earlier draft of the paper.

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