Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

Cheung, Gordon W.; Rensvold, Roger B.

doi:10.1207/s15328007sem0902_5

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

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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McDonald's omega and composite reliability values ≥ 0.70 were interpreted as acceptable indicators of reliability.
“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]
An increase in RMSEA exceeding 0.01 suggests non-invariance and leads to rejection of the model.
“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
The configural, metric, scalar, and strict invariance models were reliable cross-gender.
“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
Chi-square difference tests are known to be sensitive to sample size and minor model misspecifications, so recent studies suggest complementing this information with changes in CFIs and RMSEAs in tests of measurement invariance.
“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
The parsimonious constrained model would be selected if four criteria suggested by Cheung and Rensvold (2002) and Chen (2007) were met.
“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)

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THE UTILITY OF ALTERNATIVE FIT INDICES IN TESTS OF 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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