Comparative fit indexes in structural models.

1990/01/01 by Peter M. Bentler, P. M. Bentler · 24,005 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Computer science #Econometrics #Estimator #Index (typography) #Mathematics #Multi-Criteria Decision Making #Statistical Methods and Bayesian Inference #Statistics

paper · doi:10.1037/0033-2909.107.2.238

published in Psychological Bulletin 107(2), 238-246 (American Psychological Association)

openalex publication_date 1990/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

Citations

• Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions
• A Reliability Coefficient for Maximum Likelihood Factor Analysis
• The Effect of Sampling Error on Convergence, Improper Solutions, and Goodness-of-Fit Indices for Maximum Likelihood Confirmatory Factor Analysis
• On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics

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