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Comparative fit indexes in structural models.

Bentler, P. M.·1990·Psychological Bulletin

DOI 10.1037/0033-2909.107.2.238

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Abstract

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

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Authors: Bentler, P. M.
Affiliations: University of California, Los Angeles (US)
Corresponding author: Bentler, P. M.
ORCID: Bentler, P. M.
Venue: Psychological Bulletin
Publisher: American Psychological Association (APA)
Published: 1990
Volume: 107
Issue: 2
Pages: 238-246
ISSN: 0033-2909 (ISSN-L)
1939-1455
DOI: 10.1037/0033-2909.107.2.238
OpenAlex: W2018201949
Cited by: 25,266
References: 26
Citations by year: 2026: 819 · 2025: 1270 · 2024: 1256 · 2023: 1284 · 2022: 1450 · 2021: 1427 · 2020: 1212 · 2019: 1213 · 2018: 1190 · 2017: 1105 · 2016: 1164 · 2015: 1143 · 2014: 1130 · 2013: 1110 · 2012: 998
FWCI: 84.24
Type: journal article
Language: en
Open access: closed
Locations: Psychological Bulletin (publishedVersion)
PubMed (publishedVersion)
Funders: National Institute on Drug Abuse (DA01070, DA-00017, P01DA001070)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords: comparative fit index, structural equation modeling, model fit assessment, noncentrality parameter, nested models, Wald statistic, small sample bias, model misspecification
MeSH terms: Humans, Personality Tests, Psychometrics, Reference Values, Models, Statistical

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Comparative fit indexes in structural models.

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