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Comparative Fit Indexes in Structural Models

Comparative Fit Indexes in Structural Models Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statisticsfor evaluating the fit of a structural model. A drawback of existing indexes is that theyestimate no known population parameters. A new coefficient is proposed to summarize therelative reduction in the noncentrality parameters of two nested models. Two estimators of thecoefficient yield new normed (CFI) and nonnormed (FI) fit indexes. CFI avoids theunderestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI). FI is a linearfunction of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extremeunderestimation and overestimation often found in NNFI. Asymptotically, CFI, FI, NFI, and a newindex developed by Bollen are equivalent measures of comparative fit, whereas NNFI measuresrelative fit by comparing noncentrality per degree of freedom. All of the indexes aregeneralized to permit use of Wald and Lagrange multiplier statistics. An example illustratesthe behavior of these indexes under conditions of correct specification and misspecification.The new fit indexes perform very well at all sample sizes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychological Bulletin American Psychological Association

Comparative Fit Indexes in Structural Models

Bentler, P. M.
Psychological Bulletin , Volume 107 (2): 9 – Mar 1, 1990
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Publisher
American Psychological Association
Copyright
Copyright © 1990 American Psychological Association
ISSN
0033-2909
eISSN
1939-1455
DOI
10.1037/0033-2909.107.2.238
Publisher site
See Article on Publisher Site

Abstract

Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statisticsfor evaluating the fit of a structural model. A drawback of existing indexes is that theyestimate no known population parameters. A new coefficient is proposed to summarize therelative reduction in the noncentrality parameters of two nested models. Two estimators of thecoefficient yield new normed (CFI) and nonnormed (FI) fit indexes. CFI avoids theunderestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI). FI is a linearfunction of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extremeunderestimation and overestimation often found in NNFI. Asymptotically, CFI, FI, NFI, and a newindex developed by Bollen are equivalent measures of comparative fit, whereas NNFI measuresrelative fit by comparing noncentrality per degree of freedom. All of the indexes aregeneralized to permit use of Wald and Lagrange multiplier statistics. An example illustratesthe behavior of these indexes under conditions of correct specification and misspecification.The new fit indexes perform very well at all sample sizes.

Journal

Psychological Bulletin – American Psychological Association

Published: Mar 1, 1990

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