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In Search of Golden Rules: Comment on Hypothesis-Testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing Hu and Bentler's (1999) Findings

Marsh, Herbert W., Hau, Kit-Tai, Wen, Zhonglin·2004·Structural Equation Modeling: A Multidisciplinary Journal

DOI 10.1207/s15328007sem1103_2

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Abstract

Goodness-of-fit (GOF) indexes provide "rules of thumb"—recommended cutoff values for assessing fit in structural equation modeling. Hu and Bentler (1999) proposed a more rigorous approach to evaluating decision rules based on GOF indexes and, on this basis, proposed new and more stringent cutoff values for many indexes. This article discusses potential problems underlying the hypothesis-testing rationale of their research, which is more appropriate to testing statistical significance than evaluating GOF. Many of their misspecified models resulted in a fit that should have been deemed acceptable according to even their new, more demanding criteria. Hence, rejection of these acceptable-misspecified models should have constituted a Type 1 error (incorrect rejection of an "acceptable" model), leading to the seemingly paradoxical results whereby the probability of correctly rejecting misspecified models decreased substantially with increasing N. In contrast to the application of cutoff values to evaluate each solution in isolation, all the GOF indexes were more effective at identifying differences in misspecification based on nested models. Whereas Hu and Bentler (1999) offered cautions about the use of GOF indexes, current practice seems to have incorporated their new guidelines without sufficient attention to the limitations noted by Hu and Bentler (1999).

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10.1037//0033-2909.88.3.588 · DOI
10.1037//1040-3590.12.4.371 · DOI
10.1037//1082-989X.3.1.3 · DOI
10.1037//0021-843X.109.4.624 · DOI
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10.1037//0033-2909.103.3.391 · DOI
10.1037//0033-2909.107.2.247 · DOI

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Authors: Marsh, H. W., Hau, K.-T., & Wen, Z.
Affiliations: Western Sydney University (AU)
Chinese University of Hong Kong (HK)
South China Normal University (CN)
ORCID: Marsh, Herbert W.
Hau, Kit-Tai
Wen, Zhonglin
Venue: Structural Equation Modeling: A Multidisciplinary Journal
Publisher: Informa UK Limited
Published: 2004-07
Volume: 11
Issue: 3
Pages: 320-341
ISSN: 1070-5511 (ISSN-L)
1532-8007
DOI: 10.1207/s15328007sem1103_2
OpenAlex: W2025781576
Cited by: 6,691
References: 20
Citations by year: 2026: 630 · 2025: 545 · 2024: 421 · 2023: 452 · 2022: 485 · 2021: 490 · 2020: 480 · 2019: 413 · 2018: 345 · 2017: 310 · 2016: 292 · 2015: 315 · 2014: 278 · 2013: 253 · 2012: 221
FWCI: 88.92
Type: journal article
Language: en
Open access: closed
Locations: Structural Equation Modeling A Multidisciplinary Journal (publishedVersion)
Research Bank (Australian Catholic University) (submittedVersion)
Funders: Australian Research Council
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: goodness of fit index, cut-off values, model misspecification, type I error, nested models, hypothesis testing, structural equation modeling, model fit assessment

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In Search of Golden Rules: Comment on Hypothesis-Testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing Hu and Bentler's (1999) Findings

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