Evaluation of the Bayesian and Maximum Likelihood Approaches in Analyzing Structural Equation Models with Small Sample Sizes
Abstract
The main objective of this article is to investigate the empirical performances of the Bayesian approach in analyzing structural equation models with small sample sizes. The traditional maximum likelihood (ML) is also included for comparison. In the context of a confirmatory factor analysis model and a structural equation model, simulation studies are conducted with the different magnitudes of parameters and sample sizes n = da, where d = 2, 3, 4 and 5, and a is the number of unknown parameters. The performances are evaluated in terms of the goodness-of-fit statistics, and various measures on the accuracy of the estimates. The conclusion is: for data that are normally distributed, the Bayesian approach can be used with small sample sizes, whilst ML cannot.
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Sample sizes equal to four times the number of parameters are needed to achieve accurate parameter estimates and reliable goodness-of-fit tests under Bayesian estimation.
“sample sizes equal to four times the number of parameters are needed [44] to achieve accurate parameter estimates and reliable goodness-of-fit tests under Bayesian estimation.”
The Bayesian approach was found to outperform the maximum likelihood approach in terms of accuracy of parameter estimates in factor analysis with small sample sizes (N < 200).
“The Bayesian approach was found to outperform the maximum likelihood approach in terms of accuracy of parameter estimates in factor analysis with small sample sizes (N < 200) [44].”
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Salesperson CLV orientation's effect on performance
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- Authors
- Lee, S.-Y., & Song, X.-Y.
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2004-10
- Volume
- 39
- Issue
- 4
- Pages
- 653-686
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W1999291824
- Cited by
- 488
- References
- 46
- Citations by year
- 2026: 20 · 2025: 33 · 2024: 29 · 2023: 23 · 2022: 35 · 2021: 37 · 2020: 44 · 2019: 38 · 2018: 32 · 2017: 41 · 2016: 24 · 2015: 43 · 2014: 22 · 2013: 21 · 2012: 14
- FWCI
- 2.71
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Multivariate Behavioral Research (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- Bayesian structural equation modeling, maximum likelihood estimation, small sample size, confirmatory factor analysis, goodness-of-fit statistics, estimation accuracy, simulation study, normal data
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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.
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