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Sample Size and Bentler and Bonett's Nonnormed Fit Index

Published online by Cambridge University Press:  01 January 2025

Kenneth A. Bollen
Kenneth A. Bollen*
Affiliation:
Department of Sociology, University of North Carolina at Chapel Hill
*
Requests for reprints should be sent to Kenneth A. Bollen, Department of Sociology, Hamilton Hall 070A, University of North Carolina, Chapel Hill, NC 27514.
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Abstract

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.

Keywords

nonnormed fit indexgoodness of fitLISRELanalysis of covariance structures
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986 , pp. 375 - 377
Copyright
Copyright © 1986 The Psychometric Society

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References

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