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The DOI matches its Crossref record; 20 of the 21 references it cites were found in a registry or an index.

Effect of the Number of Variables on Measures of Fit in Structural Equation Modeling

Kenny, David A., McCoach, D. Betsy·2003·Structural Equation Modeling: A Multidisciplinary Journal
DOI 10.1207/s15328007sem1003_1
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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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  1. 10.1037//0021-9010.76.5.732 · DOI · Paper page
  2. 10.1037//0033-2909.88.3.588 · DOI
  3. Breivik, E. & Olsson, U. H. (2001). Adding variables to improve model fit: The effect of model size on fit assessment in LISREL. In R. Cudeck, S. Du Toit, & D. Sorbom (Eds.), Structural equation modeling: Present and future (pp. 169-194). Lincolnwood, IL: Scientific Software International.
  4. Chau, H. & Hocevar, D. (1995, April). The effects of number of measured variables on goodness- of-fit in confirmatory factor analysis. Paper presented at the annual conference of the American Educational Research Association, San Francisco.
  5. 10.1037//1082-989X.1.1.16 · DOI · Paper page
  6. Fouladi, R. T. & Steiger, J. H. (1999). Tests of an identity correlation structure. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 167-194). Thousand Oaks, CA: Sage.
  7. 10.1037//1082-989X.3.1.3 · DOI
  8. 10.1037//0033-2909.103.3.391 · DOI
  9. 10.1037//0021-9010.71.4.606 · DOI
  10. Wolfram, S. (1996). The Mathematica book (3rd ed.). New York: Cambridge University Press.

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Metadata

Authors
Kenny, D. A., & McCoach, D. B.
Affiliations
University of Connecticut (US)
ORCID
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
DOI
10.1207/s15328007sem1003_1
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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