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Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation
Mariola Moeyaert1, David Rindskopf2, Patrick Onghena3
1Department of Educational Psychology and Counseling, University at Albany.
Psychological Methods
|March 31, 2017
Summary
Bayesian estimation and maximum likelihood (ML) methods yield similar treatment effect estimates in single-case data. Variance estimates improve with more participants, and informative priors enhance precision, especially with small sample sizes.
Area of Science:
- Psychology
- Statistics
- Behavioral Science
Background:
- Single-case experimental designs (SCEDs) are crucial in behavioral research.
- Multilevel modeling (MLM) is increasingly used for analyzing SCED data.
- Bayesian estimation offers an alternative to traditional maximum likelihood (ML) methods.
Purpose of the Study:
- To describe Bayesian estimation techniques for SCED data, including prior distribution construction.
- To compare parameter recovery between Bayesian and ML frameworks in multilevel SCED analyses.
- To evaluate the impact of prior informativeness on estimation accuracy.
Main Methods:
- Utilized multilevel modeling for single-case experimental data.
- Implemented Bayesian estimation with varying prior distributions (weakly informative and informative).
- Compared Bayesian results against maximum likelihood estimation.
Main Results:
- Bayesian and ML methods produced comparable treatment effect estimates.
- Both methods showed biased and imprecise variance estimates with small participant numbers (n=3).
- Increasing participants to 5 or 7 improved variance estimate precision for most methods.
- Informative priors in Bayesian analysis led to more precise fixed and random effect estimates, even with n=3.
Conclusions:
- Bayesian estimation is a viable alternative to ML for SCED data, particularly with informative priors.
- Sample size significantly impacts the precision of variance component estimates in multilevel SCED models.
- Careful prior specification in Bayesian analysis can mitigate issues related to small sample sizes.
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