The Performance of RMSEA in Models With Small Degrees of Freedom
Abstract
Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ( df). Unfortunately, most previous work on the RMSEA and its confidence interval has focused on models with a large df. Building on the work of Chen et al. to examine the impact of small df on the RMSEA, we conducted a theoretical analysis and a Monte Carlo simulation using correctly specified models with varying df and sample size. The results of our investigation indicate that when the cutoff values are used to assess the fit of the properly specified models with small df and small sample size, the RMSEA too often falsely indicates a poor fitting model. We recommend not computing the RMSEA for small df models, especially those with small sample sizes, but rather estimating parameters that were not originally specified in the model.
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These measurement models were considered appropriate despite higher RMSEA values, as in simple models with few degrees of freedom, the RMSEA can underestimate the model fit.
“These measurement models were considered appropriate despite higher RMSEA values, as in simple models with few degrees of freedom, as was the case here, the RMSEA can underestimate the model fit (Kenny et al., 2015).”
From Why They Speak Up (or Don’t): Reasons For and Against Cybergrooming Disclosure Among Adolescent Victims (2025) · cites this paper as Kenny et al., 2015
The chi-squared test and root mean square error of approximation were not appropriate for this study because the model has a small degree of freedom.
“The chi- squared test and root mean square error of approximation were not appropriate for the current study, as the current model has a small degree of freedom (Kenny et al., 2015).”
From The role of critical thinking on undergraduates' reliance behaviours on generative <scp>AI</scp> in problem‐solving (2025) · cites this paper as Kenny et al., 2015
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 [38]
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- Authors
- Kenny, D. A., Kaniskan, B., & McCoach, D. B.
- Affiliations
- University of Connecticut (US)
- National Conference of Bar Examiners (NCBE) Madison, WI, USA
- Corresponding author
- Kenny, David A.
- Venue
- Sociological Methods & Research
- Publisher
- SAGE Publications
- Published
- 2014-07-24
- Volume
- 44
- Issue
- 3
- Pages
- 486-507
- ISSN
- 0049-1241 (ISSN-L)
- 1552-8294
- OpenAlex
- W2170467533
- Cited by
- 2,841
- References
- 27
- Citations by year
- 2026: 574 · 2025: 386 · 2024: 281 · 2023: 275 · 2022: 264 · 2021: 232 · 2020: 180 · 2019: 156 · 2018: 161 · 2017: 140 · 2016: 96 · 2015: 46 · 2014: 27 · 2013: 16 · 2012: 3
- FWCI
- 130.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Sociological Methods & Research (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- 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, goodness-of-fit indices, structural equation modeling, model fit, small sample size, cut-off values, model misspecification
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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