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Fixed or Random Effects: Analysis of Clustered Data
Kevin He1,2, Xiangeng Fang1,2, Yubo Shao1,2
1Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA.
Statistics in Medicine
|August 6, 2026
Summary
Random effects (RE) and fixed effects (FE) models are used for clustered data. This study quantifies bias in RE models when cluster effects correlate with covariates, clarifying practical implications.
Area of Science:
- Econometrics
- Statistical Modeling
- Biostatistics
Background:
- Clustered data analysis commonly employs random effects (RE) and fixed effects (FE) models.
- RE models assume cluster effects are uncorrelated with covariates, while FE models treat them as fixed.
- Violation of the RE assumption can lead to biased estimates, but the practical significance is debated.
Purpose of the Study:
- To theoretically evaluate and practically quantify the bias in random effects models.
- To compare the bias of RE models against fixed effects models under covariate correlation.
- To reconcile differing conclusions in existing literature regarding RE model bias.
Main Methods:
- Theoretical derivation of an approximate formula for asymptotic bias in RE models.
- Simulation studies to verify the accuracy of the derived bias formula.
- Application of the methods to real-world clustered data.
Main Results:
- An approximate formula for quantifying RE model bias was derived and validated.
- The derived formula helps explain discrepancies in previous studies on RE bias.
- The relationship between RE bias and FE/correlated random-effects models was clarified.
Conclusions:
- The study provides analytical clarification and practical quantification of RE model bias.
- Understanding RE bias is crucial for accurate analysis of correlated clustered data.
- The findings aid in choosing appropriate models for clustered data analysis.
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