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Implications of Indeterminate Factor-Error Covariances for Factor Construction, Prediction, and Determinacy

Published online by Cambridge University Press:  01 January 2025

Wim P. Krijnen
Wim P. Krijnen*
Affiliation:
Department of Psychology, Psychological Methods, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands
*
Requests for reprints should be sent to Wim P. Krijnen, Lisdodde 1, 9679 MC Scheemda, The Netherlands. E-mail:wim.krijnen@hetnet.nl
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Abstract

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.

Keywords

factor indeterminacyfactor-error indeterminacyfactor score predictionConfirmatory Factor AnalysisCommon Factor Analysisdeterminate factor
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 503 - 519
Copyright
Copyright © 2006 The Psychometric Society

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