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The fixed versus random effects debate and how it relates to centering in multilevel modeling
Ellen L Hamaker1, Bengt Muthén2
1Methodology and Statistics.
Psychological Methods
|October 16, 2019
Summary
Researchers often use longitudinal panel data to study causal relationships. This study reveals that random effects versus fixed effects and grand mean versus group mean centering address the same core issue in statistical modeling.
Area of Science:
- Multidisciplinary research
- Quantitative psychology
- Econometrics
- Sociology
- Educational sciences
Background:
- Longitudinal panel data are crucial for investigating causal relationships between variables across various disciplines.
- Disciplinary conventions and concerns regarding the analysis of such data differ significantly.
- Key concerns include random effects versus fixed effects (econometrics/sociology) and grand mean versus group mean centering (psychology/educational sciences).
Purpose of the Study:
- To demonstrate that the distinct concerns of random/fixed effects and mean centering address the same fundamental statistical issue.
- To compare different modeling approaches for longitudinal panel data, including multilevel modeling and structural equation modeling.
- To provide practical guidelines for selecting appropriate statistical models for analyzing intensive longitudinal data.
Main Methods:
- Comparison of multilevel regression modeling (long format data) and structural equation modeling (wide format data).
- Simulation studies to evaluate the performance of different modeling approaches.
- Extension of the multilevel model to include random slopes.
- Application to an empirical dataset with time-varying and time-invariant covariates.
Main Results:
- The study demonstrates that random effects/fixed effects and grand mean/group mean centering are fundamentally related concepts.
- Multilevel modeling and structural equation modeling approaches yield comparable results when applied appropriately.
- The inclusion of random slopes can have significant consequences for model interpretation and results.
Conclusions:
- The choice between different statistical modeling techniques for longitudinal panel data depends on specific research questions and data characteristics.
- Understanding the equivalence between different modeling conventions facilitates more robust causal inference.
- Guidelines are provided to aid researchers in selecting the most suitable modeling strategy for their intensive longitudinal data analysis.
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