Effect of the number of variables on measures of fit in structural equation modeling
Abstract
There has been relatively little systematic investigation of the effect of the number of variables on measures of model fit in structural equation modeling. There is conflicting evidence as to whether measures of fit tend to improve or decline as more variables are added to the model. We consider 3 different types of specification error: minor factors, 2-factor models, and method errors. Using a formal method based on the noncentrality parameter (NCP), we find that root mean squared error of approximation (RMSEA) tends to improve regardless of the type of specification error and that the comparative fit index (CFI) and Tucker-Lewis Index (TLI), generally, though not always, tend to worsen as the number of variables in the model increases. The formal method that we develop can be used to investigate other measures of fit and other types of misspecification.
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The eight-factor model of the PSAT showed good to excellent fit to the observed data (CFI = 0.902, RMSEA = 0.054, SRMR = 0.054).
“CFA results show an excellent fit of the data to the hypothesized measurement structure. Specifically, the fit indices for the eight factor model include the comparative fit index (CFI = 0.902), root mean square error of approximation (RMSEA = 0.054) and standardized root mean square residual (SRMR = 0.054). All indicate good to excellent fit (27–29).”
From Assessing the sustainability capacity of evidence-based programs in community and health settings (2022) · cites this paper as [27]
With an increasing number of indicators, the CFI increasingly underestimates model fit.
“With an increasing number of indicators, the CFI increasingly underestimates model fit (Kenny & McCoach, 2003).”
From Cultural norm fulfillment, interpersonal belonging, or getting ahead? A large-scale cross-cultural test of three perspectives on the function of self-esteem. (2015) · cites this paper as Kenny & McCoach, 2003
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- Authors
- Kenny, D. A., & McCoach, D. B.
- Affiliations
- University of Connecticut (US)
- Venue
- Structural Equation Modeling: A Multidisciplinary Journal
- Publisher
- Informa UK Limited
- Published
- 2003-07-01
- Volume
- 10
- Issue
- 3
- Pages
- 333-351
- ISSN
- 1070-5511 (ISSN-L)
- 1532-8007
- OpenAlex
- W2034820849
- Cited by
- 1,231
- References
- 21
- Citations by year
- 2026: 82 · 2025: 82 · 2024: 84 · 2023: 59 · 2022: 87 · 2021: 106 · 2020: 83 · 2019: 80 · 2018: 70 · 2017: 77 · 2016: 66 · 2015: 86 · 2014: 72 · 2013: 48 · 2012: 30
- FWCI
- 12.08
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Structural Equation Modeling A Multidisciplinary Journal (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
- model fit measures, number of variables, model misspecification, two-factor model, method error, noncentrality parameter, comparative fit index
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