Evaluating SEM Model Fit with Small Degrees of Freedom
Open accessAbstract
Research has revealed that the performance of root mean square error of approximation (RMSEA) in assessing structural equation models with small degrees of freedom ( df ) is suboptimal, often resulting in the rejection of correctly specified or closely fitted models. This study investigates the performance of standardized root mean square residual (SRMR) and comparative fit index (CFI) in small df models with various levels of factor loadings, sample sizes, and model misspecifications. We find that, in comparison with RMSEA, population SRMR and CFI are less susceptible to the effects of df . In small df models, the sample SRMR and CFI could provide more useful information to differentiate models with various levels of misfit. The confidence intervals and p -values of a close fit were generally accurate for all three fit indices. We recommend researchers use caution when interpreting RMSEA for models with small df and to rely more on SRMR and CFI.
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Confirmatory factor analysis showed acceptable fit for the one-factor self-efficacy model, with CFI 0.99, TLI 0.98, SRMR 0.06, and an elevated RMSEA of 0.11 likely inflated by low degrees of freedom.
“The model demonstrated excellent incremental fit (CFI = 0.99, TLI = 0.98) and acceptable absolute fit (SRMR = 0.06).Although the RMSEA value was elevated (RMSEA = 0.11), this likely reflects the known tendency of RMSEA to over-reject correctly specified models with small degrees of freedom.”
From A comparative study on Earthquake Preparedness of Japanese and International Students in a Nankai Trough Earthquake-threatened Area in Shikoku, Japan (2026) · cites this paper as [39]
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- Authors
- Shi, D., DiStefano, C., Maydeu-Olivares, A., & Lee, T.
- Affiliations
- University of South Carolina (US)
- Department of Psychology, University of South Carolina
- Chung-Ang University (KR)
- Corresponding author
- Shi, Dexin
- Lee, Taehun
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2021-02-12
- Volume
- 57
- Issue
- 2-3
- Pages
- 179-207
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W3129005096
- Cited by
- 256
- References
- 11
- Citations by year
- 2026: 104 · 2025: 56 · 2024: 39 · 2023: 29 · 2022: 22 · 2021: 6
- FWCI
- 13.81
- Type
- journal article
- Language
- en
- Open access
- green
- figshare.com
- Licence
- cc-by
- Locations
- Multivariate Behavioral Research (publishedVersion)
- PubMed (publishedVersion)
- Figshare (submittedVersion, cc-by)
- Figshare (cc-by)
- Funders
- National Science Foundation (SES-, 936)
- National Research Foundation of Korea (424, 581)
- 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
- RMSEA, comparative fit index, model fit indices, model misspecification, confidence intervals, p-values, sample size
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