The Analysis of Covariance Structures: Goodness-of-Fit Indices
Abstract
A major problem encountered in covariance structure analyses involves decisions concerning whether or not a given theoretical model adequately represents the data used for its assessment. Given that X 2 goodness-of-fit tests are joint functions of the difference between theoretical and empirical covariance structures and sample size, gauging the impact of sample size on such tests is essential. In this paper, we propose a simple index (critical N) and tentative acceptance criterion, which, by focusing on sample size, provide an improved method for assessing goodness-of-fit. Both small- and large-sample examples are presented, illustrating the utility of the proposed method for assessing theoretical models.
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Hoelter (1983) introduced the Critical N (CN) statistic for the evaluation of SEM sample size, where CN ≥ 200 was considered adequate.
“Hoelter (1983) introduced the Critical N (CN) statistic for the evaluation of SEM sample size, where CN ≥ 200 was considered adequate.”
From Applied Psychometrics: Sample Size and Sample Power Considerations in Factor Analysis (EFA, CFA) and SEM in General (2018) · cites this paper as Hoelter, 1983
The Hoelter(0.05) estimate (n=264) suggests that the lack of absolute fit can be explained by sample size.
“However, the Hoelter(0.05)(Hoelter, 1983) estimate (n=264) suggests that the lack of absolute fit can be explained by sample size.”
From How the interplay between consumer motivations and values influences organic food identity and behavior (2018) · cites this paper as Hoelter, 1983
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- Authors
- HOELTER, J. W.
- Affiliations
- University of Cincinnati (US)
- Corresponding author
- HOELTER, JON W.
- Venue
- Sociological Methods & Research
- Publisher
- SAGE Publications
- Published
- 1983-02
- Volume
- 11
- Issue
- 3
- Pages
- 325-344
- ISSN
- 0049-1241 (ISSN-L)
- 1552-8294
- OpenAlex
- W2023172395
- Cited by
- 1,624
- References
- 20
- Citations by year
- 2026: 48 · 2025: 82 · 2024: 74 · 2023: 82 · 2022: 83 · 2021: 73 · 2020: 62 · 2019: 72 · 2018: 58 · 2017: 51 · 2016: 75 · 2015: 72 · 2014: 65 · 2013: 65 · 2012: 61
- FWCI
- 19.05
- 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 Methods and Applications
- Keywords
- structural equation modeling, goodness-of-fit tests, sample size, model fit assessment, chi-square test, small sample inference, acceptance criteria
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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