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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
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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“The criterion of the model fit was RMSEA <0.08, CFI >0.90, TLI >0.90 and SRMR <0.08 (Marsh et al., 2004).”
From Design and validation of the AI literacy questionnaire: The affective, behavioural, cognitive and ethical approach (2024) · cites this paper as Marsh et al., 2004
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Metadata
- 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)
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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