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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Fang, S., Huang, M., & Wang, Y. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.1051661 · Cited by 12
“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).”
Result
Factor structure and measurement invariance of the Multidimensional Psychological Flexibility Inventory (MPFI) in Chinese samples
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Hein, S., Weeland, J., Square, A., Haeffel, G. J., Chapman, J., Macomber, D., Lee, M., Foley Geib, C., & Grigorenko, E. L. (2020) · International Journal of Law and Psychiatry · doi:10.1016/j.ijlp.2020.101626 · Cited by 12
Assessing Short-Video Dependence for e-Mental Health: Development and Validation Study of the Short-Video Dependence Scale
Jiang, A., Li, S., Wang, H., Ni, H., Chen, H., Dai, J., Xu, X., Li, M., & Dong, G.-H. (2025) · Journal of Medical Internet Research · doi:10.2196/66341 · Cited by 13
Mediation Effects of Social Cognition on the Relationship between Neurocognition and Social Functioning in Major Depressive Disorder and Schizophrenia Spectrum Disorders
Uchino, T., Okubo, R., Takubo, Y., Aoki, A., Wada, I., Hashimoto, N., Ikezawa, S., & Nemoto, T. (2023) · Journal of Personalized Medicine · doi:10.3390/jpm13040683 · Cited by 12
Measurement Invariance of the WISC-V across a Clinical Sample of Children and Adolescents with ADHD and a Matched Control Group
Becker, A. B. C., Maurer, J., Daseking, M., & Pauls, F. (2024) · Journal of Intelligence · doi:10.3390/jintelligence12010006 · Cited by 11
Impact of a short-term professional development teacher training on students' perceptions and use of errors in mathematics learning
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Further Validation of a Dutch Translation of the Sussex Oxford Compassion for the Self Scale in Samples of Crisis Line Volunteers, Military Personnel and Nursing Students
de Krijger, E., Willems, R., ten Klooster, P., Bakker, E., Miedema, H., Drossaert, C., & Bohlmeijer, E. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.895850 · Cited by 11
The assessment of executive functions using the BASC-2.
Karr, J. E., & Garcia-Barrera, M. A. (2017) · Psychological Assessment · doi:10.1037/pas0000418 · Cited by 10
Hypothesized drivers of the bias blind spot—cognitive sophistication, introspection bias, and conversational processes
Mandel, D. R., Collins, R. N., Walker, A. C., Fugelsang, J. A., & Risko, E. F. (2022) · Judgment and Decision Making · doi:10.1017/s1930297500009475 · Cited by 10
Psychometric properties of the short form of the Freiburg Mindfulness Inventory in the Arabic language
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Age and Gender Invariance in the Taiwan Wechsler Intelligence Scale for Children, Fifth Edition: Higher Order Five-Factor Model
Chen, H., Zhu, J., Liao, Y.-K., & Keith, T. Z. (2020) · Journal of Psychoeducational Assessment · doi:10.1177/0734282920930542 · Cited by 8
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“…χ2 difference test is highly sensitive to sample size, statistical differences between models were assessed through the difference between comparative fit indices (ΔCFI), where a value equal or lower than .01 indicates strong invariance, i.e., equivalence between groups (Cheung & Rensvold, 2002).”
Background
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“Models were compared based on change in CFI, with an increase in CFI at or above .01 indicating significant improvement in model fit (Cheung & Rensvold, 2002).”
Method
Cosmetics and detergents with recycled CO2: a cross-country study with a modified by risk perception values–beliefs–norms model
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“…restrictions), weak (i.e., equal loadings), strong (i.e., equal loadings and intercepts) and strict (i.e., equal loadings, intercepts and residuals) invariant models, were tested for statistical significance using the difference of the χ2-values (Chen et al., 2001; Cheung & Rensvold, 2002).”
Method
Psychometric validation and measurement invariance of the Health-Promoting Lifestyle Profile II in Honduran university students
Castillo-Díaz, M. A., & Periañez, C. A. H. (2025) · BMC Public Health · doi:10.1186/s12889-025-25899-9 · Cited by 4
“Research based on simulation studies indicates that, in large samples (n > 1,000), even a CFI difference of 0.005 can represent a meaningful improvement in model fit [61].”
Influential
Advancing Undergraduate Student Mental Healthcare of Social Anxiety Disorder: Evaluating the Acceptance of AR-Assisted Cognitive Behavioral Therapy Through TAM-Based Constructs.
Zhou, Z., Zhou, Y., Ouyang, B., Man, S. S., & Chan, A. H. S. (2026) · Healthcare · doi:10.3390/healthcare14131978
Predictors of developmental change in attention-deficit/hyperactivity disorder: a 25-year prospective study
Mathewson, K. J., Brook, C. A., Van Lieshout, R. J., & Schmidt, L. A. (2026) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-026-03170-9

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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