Cited by 16,280Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceEducational Assessment and Pedagogy

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Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

Cheung, Gordon W., Rensvold, Roger B.·2002·Structural Equation Modeling: A Multidisciplinary Journal

DOI 10.1207/s15328007sem0902_5

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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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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
DOI: 10.1207/s15328007sem0902_5
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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Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

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