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Asymptotic Biases in Exploratory Factor Analysis and Structural Equation Modeling

Published online by Cambridge University Press:  01 January 2025

Haruhiko Ogasawara
Haruhiko Ogasawara*
Affiliation:
Otaru University of Commerce
*
Requests for reprints should be sent to Haruhiko Ogasawaxa, Department of Information and Management Science, Otaru University of Commerce, 3-5-21, Midori, Otaru 047-8501 JAPAN. E-mail: hogasa@res.otaru-uc.ac.jp
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Abstract

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas for the models of standardized variables are also provided. Numerical examples with Monte Carlo simulations in factor analysis show the accuracy of the formulas and suggest the asymptotic robustness of the asymptotic biases with normality assumption against nonnormal data. Some relationships between the asymptotic biases and other asymptotic values are discussed.

Keywords

Asymptotic biasesstructural equation modelingasymptotic variancesnonnormal dataasymptotic robustnessfactor analysis
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 2 , June 2004 , pp. 235 - 256
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

The author is indebted to the editor and anonymous reviewers for their comments, corrections, and suggestions on this paper, and to Yutaka Kano for discussion on biases.

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