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Standard Errors of Fit Indices using Residuals in 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 Ogasawara, 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

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.

Keywords

standardized residualscorrelation residualsasymptotic standard errorsRMRcovariance structuresmean structuresstructural means
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 421 - 436
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

The author is indebted to the reviewers for their comments and suggestions which have led to an improvement of this work.

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