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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 [44] to achieve accurate parameter estimates and reliable goodness-of-fit tests under Bayesian estimation.”
In the citing paper
“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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Metadata
- 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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