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Positive Loadings and Factor Correlations from Positive Covariance Matrices

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 P. Krijnen, Department of Psychological Methods, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands. E-mail: Wim.Krijnen@hetnet.nl
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Abstract

In many instances it is reasonable to assume that the population covariance matrix has positive elements. This assumption implies for the single factor analysis model that the loadings and regression weights for best linear factor prediction are positive. For the multiple factor analysis model where each variable loads on a single factor and a hierarchical factor model, it implies that the loadings and the factor correlations are positive. For the latter model it also implies that the regression weights for first- and second-order factor prediction are positive.

Keywords

Classical test theorycongeneric testsstructural equation modelshierarchical factor analysisregression weightsbest linear factor prediction

Information

Type
Note and Comments
Information
Psychometrika , Volume 69 , Issue 4 , December 2004 , pp. 655 - 660
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

I would like to thank Conor Dolan for fruitful discussions on factor analysis, and the associate editor as well as three reviewers for making useful remarks on earlier versions of the manuscript.

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