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Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance
Abstract
Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the overall fit measures. We propose critical values of these ΔGFIs that indicate measurement invariance.
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“Values of both coefficients ≥ 0.70 were interpreted as acceptable indicators of reliability [60, 61].”
From Psychometric validation and measurement invariance of the Health-Promoting Lifestyle Profile II in Honduran university students (2025) · cites this paper as [61]
In the citing paper
“An increase in the root mean square error of approximation (RMSEA) exceeding 0.01 suggests non-invariance and leads us to reject the model (Cheung and Rensvold, 2002; Chen, 2007).”
From Common Predictive Factors of Social Media Addiction and Eating Disorder Symptoms in Female College Students: State Anxiety and the Mediating Role of Cognitive Flexibility/Sustained Attention (2022) · cites this paper as Cheung and Rensvold, 2002
In the citing paper
“The results indicated that the Configural invariance model, the metric invariance model, the scalar invariance model, and the strict invariance model were reliable cross-gender (Cheung and Rensvold, 2002; Chen, 2007).”
From Measuring self-as-context in Chinese college students: Validity and reliability of the Chinese version of self-as-context scale (C-SACS) (2022) · cites this paper as Cheung and Rensvold, 2002
In the citing paper
“Like the chisquare, chi-square difference tests present a known sensitivity to sample size and minor model misspecifications so that recent studies suggest complementing this information with changes in CFIs and RMSEAs (Chen, 2007;Cheung & Rensvold, 2002) in the context of tests of measurement invariance.”
From A test of work motivation profile similarity across four distinct samples of employees (2020) · cites this paper as Cheung & Rensvold, 2002
In the citing paper
“The parsimonious model (constrained model) would be selected if the following four criteria suggested by Cheung and Rensvold (2002) and Chen (2007) were met: (a) the constrained model did not generate a significantly worse fit than the unconstrained model (the multiple-group baseline model) according to the chi-square test; (b) the difference in RMSEA ( RMSEA) was lower than .01;(c) the difference”
From Psychometric properties of the Cognitive Fusion Questionnaire in Colombia (2017) · cites this paper as Cheung and Rensvold (2002)
In the citing paper
“The difference in CFI values did not exceed 0.01 [45], indicating that invariance is supported and lending further support for the constrained model.”
From ADHD and the externalizing spectrum: direct comparison of categorical, continuous, and hybrid models of liability in a nationally representative sample (2014) · cites this paper as [45]
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Metadata
- Authors
- Cheung, G. W., & Rensvold, R. B.
- Affiliations
- Chinese University of Hong Kong (HK)
- City University of Hong Kong (HK)
- ORCID
- Cheung, Gordon W.
- Venue
- Structural Equation Modeling: A Multidisciplinary Journal
- Publisher
- Informa UK Limited
- Published
- 2002-04
- Volume
- 9
- Issue
- 2
- Pages
- 233-255
- ISSN
- 1070-5511 (ISSN-L)
- 1532-8007
- OpenAlex
- W2089871805
- Cited by
- 16,280
- References
- 59
- Citations by year
- 2026: 1791 · 2025: 1391 · 2024: 1235 · 2023: 1334 · 2022: 1220 · 2021: 1260 · 2020: 1112 · 2019: 1016 · 2018: 935 · 2017: 829 · 2016: 756 · 2015: 695 · 2014: 595 · 2013: 522 · 2012: 396
- FWCI
- 42.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Structural Equation Modeling A Multidisciplinary Journal (publishedVersion)
- Funders
- University Grants Committee
- 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
- Social Sciences › Education › Educational Assessment and Pedagogy
- Keywords
- measurement invariance, goodness of fit index, multi-group confirmatory factor analysis, comparative fit index, critical values, simulation study
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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.
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