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Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures
Open accessAbstract
For structural equation models, a huge variety of fit indices has been developed. These indices, however, can point to conflicting conclusions about the extent to which a model actually matches the observed data. The present article provides some guidelines that should help applied researchers to evaluate the adequacy of a given structural equation model. First, as goodness-of-fit measures depend on the method used for parameter estimation, maximum likelihood (ML) and weighted least squares (WLS) methods are introduced in the context of structural equation modeling. Then, the most common goodness-of-fit indices are discussed and some recommendations for practitioners given. Finally, we generated an artificial data set according to a "true" model and analyzed two misspecified and two correctly specified models as examples of poor model fit, adequate fit, and good fit.
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“Furthermore, additional fit indices such as GFI = 0.92, AGFI = 0.89 and RMS = 0.06 also indicated an acceptable fit of the data to the model (Schermelleh-Engel et al., 2003).”
From Psychometric Evaluation of the Polish Version of the Mindfulness Inventory for Sport (MIS-PL) (2024) · cites this paper as Schermelleh-Engel et al., 2003
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Metadata
- Authors
- Schermelleh-Engel, K., Moosbrugger, H., & Müller, H.
- Affiliations
- Goethe University Frankfurt (DE)
- University of Erfurt (DE)
- Venue
- Department of Psychology - University of Koblenz-Landau
- Publisher
- Department of Psychology - University of Koblenz-Landau
- Published
- 2003
- Volume
- 8
- Pages
- 23-74
- OpenAlex
- W1627191216
- Cited by
- 8,975
- References
- 73
- Citations by year
- 2026: 128 · 2025: 749 · 2024: 891 · 2023: 928 · 2022: 910 · 2021: 879 · 2020: 837 · 2019: 538 · 2018: 489 · 2017: 420 · 2016: 392 · 2015: 395 · 2014: 348 · 2013: 284 · 2012: 212
- FWCI
- 19.63
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- Locations
- Psychology Archives
- 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
- structural equation modeling, model fit assessment, goodness-of-fit indices, significance tests, maximum likelihood estimation, weighted least squares estimation, 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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