The relationship between root mean square error of approximation and model misspecification in confirmatory factor analysis models
Abstract
The fit index root mean square error of approximation (RMSEA) is extremely popular in structural equation modeling. However, its behavior under different scenarios remains poorly understood. The present study generates continuous curves where possible to capture the full relationship between RMSEA and various “incidental parameters,” such as factor loadings and model size, for different types of misspecification. Population RMSEA is studied, removing the influence of sampling fluctuations and making the findings directly applicable to tests of close fit and not-close fit, which require the specification of a population cutoff value. Confirmatory factor analysis models are studied. The results introduce many new findings, including that RMSEA is often insensitive to multiple omitted cross-loadings and to clusters of correlated residuals, that it sometimes behaves counterintuitively as a function of model size, and that it is insensitive to the underlying number of latent factors when a model with one factor is fit.
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The RMSEA can result in artificially lower estimates when there are weak factor loadings, as was the case in this model.
“However, the RMSEA will result in artificially lower estimates when there are weak factor loadings (Heene et al., 2011; Savalei, 2012), as is the case in this model, which can lead to an acceptance of a larger saturated model (Rigdon, 1996).”
From A psychometric analysis of the reading the mind in the eyes test: toward a brief form for research and applied settings (2015) · cites this paper as Savalei, 2012
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Examination of the Weighted Root Mean Square Residual: Evidence for Trustworthiness?
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- Authors
- Savalei, V.
- Affiliations
- University of British Columbia (CA)
- Corresponding author
- Savalei, Victoria
- ORCID
- Savalei, Victoria
- Venue
- Educational and Psychological Measurement
- Publisher
- SAGE Publications
- Published
- 2012-09-10
- Volume
- 72
- Issue
- 6
- Pages
- 910-932
- ISSN
- 0013-1644 (ISSN-L)
- 1552-3888
- OpenAlex
- W2130969147
- Cited by
- 117
- References
- 5
- Citations by year
- 2026: 6 · 2025: 20 · 2024: 7 · 2023: 20 · 2022: 12 · 2021: 5 · 2020: 4 · 2019: 9 · 2018: 11 · 2017: 7 · 2016: 4 · 2015: 3 · 2014: 6 · 2013: 2 · 2012: 1
- FWCI
- 5.09
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Educational and Psychological Measurement (publishedVersion)
- 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 Methods and Applications
- Keywords
- RMSEA, model misspecification, confirmatory factor analysis, model fit indices, correlated residuals, model size, structural equation modeling
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