Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification

Hu, Li-tze; Bentler, Peter M.

doi:10.1037/1082-989x.3.4.424

Cited by 12,298Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Distribution Estimation and Applications

Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification

Hu, Li-tze, Bentler, Peter M.·1998·Psychological Methods

DOI 10.1037/1082-989x.3.4.424

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Abstract

This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution. The effect of violating assumptions of asymptotic robustness theory also was ex-amined. Standardized root-mean-square residual (SRMR) was the most sensitive index to models with misspecified factor covariance(s), and Tucker-Lewis Index (1973; TLI), Bollen's fit index (1989; BL89), relative noncentrality index (RNI), comparative fit index (CFI), and the ML- and GLS-based gamma hat, McDonald's centrality index (1989; Me), and root-mean-square error of approximation (RMSEA) were the most sensitive indices to models with misspecified factor loadings. With ML and GLS methods, we recommend the use of SRMR, supple-mented by TLI, BL89, RNI, CFI, gamma hat, Me, or RMSEA (TLI, Me, and RMSEA are less preferable at small sample sizes). With the ADF method, we recommend the use of SRMR, supplemented by TLI, BL89, RNI, or CFI. Finally, most of the ML-based fit indices outperformed those obtained from GLS and ADF

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Based on Hu and Bentler (1998) guidelines, there was good fit for the WISC/four-factor and CHC/five-factor models.
“Based on guidelines for goodness-of-fit values (RMSEA, CFI, and TLI) proposed by Hu and Bentler (1998), there was good fit for the WISC/four-factor and CHC/five factor models.”
From Structure of the Wechsler Intelligence Scale for Children – Fourth Edition in a Group of Children with ADHD (2016) · cites this paper as Hu and Bentler (1998)
CFI and IFI values were above .95, indicating adequate fit.
“The CFI and IFI showed adequate fit, with values above .95(Hu & Bentler, 1998).”
From The Argentinian version of the cognitive fusion questionnaire: Psychometric properties and the role of cognitive fusion as a predictor of pathological worry (2022) · cites this paper as Hu & Bentler, 1998
RMSEA and SRMR values of 0.05 or lower as well as TLI and CFI values of 0.97 or higher indicate good model fit.
“RMSEA and SRMR values of 0.05 or lower as well as TLI and CFI values of 0.97 or higher indicate good model fit.”
From Procrastination, depression and anxiety symptoms in university students: a three-wave longitudinal study on the mediating role of perceived stress (2024) · cites this paper as [47]
CFI > 0.90, RMSEA and SRMR < 0.08, and χ2/df < 3 indicate good model fit.
“CFI > 0.90, RMSEA and SRMR <0.08, and χ2/df < 3 indicate good model fit (Hu and Bentler, 1998).”
From Efficacy and mechanisms of mobile application-delivered Acceptance and Commitment Therapy for posttraumatic stress disorder in China: Study protocol for a randomized controlled trial (2022) · cites this paper as Hu and Bentler, 1998
Cut off values of less than .06 for RMSEA, less than .08 for SRMR and greater than .95 for the CFI and IFI are indicative of good model fit.
“Hu and Bentler (1998) suggest that cut off values of less than .06 for RMSEA, less than .08 for SRMR and greater than .95 for the CFI and IFI are indicative of good model fit.”
From The development and initial validation of the cognitive fusion questionnaire (2014) · cites this paper as Hu and Bentler, 1998

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Self-citation
Effects of sample size, model misspecification and the number of indicators on fit indices for covariance structure modeling: A Monte Carlo study
Patelis, T. (1994) · Fordham Research Commons (Fordham University)

Authors: Hu, L.-T., & Bentler, P. M.
Affiliations: University of California, Santa Cruz (US)
ORCID: Bentler, Peter M.
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 1998-12
Volume: 3
Issue: 4
Pages: 424-453
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/1082-989x.3.4.424
OpenAlex: W2005092827
Semantic Scholar: a92c9726361d9c1d165dbf2ea781b6c48363a816
Cited by: 12,298
References: 66
Citations by year: 2026: 639 · 2025: 1003 · 2024: 1076 · 2023: 1094 · 2022: 934 · 2021: 884 · 2020: 738 · 2019: 665 · 2018: 600 · 2017: 512 · 2016: 465 · 2015: 450 · 2014: 474 · 2013: 433 · 2012: 386
FWCI: 43.57
Type: journal article
Language: en
Open access: closed
Locations: Psychological Methods (publishedVersion)
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: model fit indices, model misspecification, structural equation modeling, comparative fit index, RMSEA, asymptotic robustness, factor loadings, sample size, distributional assumptions

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Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification

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