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Variable Selection for Fixed and Random Effects in Multilevel Functional Mixed Effects Models
Rahul Ghosal1, Marcos Matabuena2, Enakshi Saha1
1Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, USA.
Statistics in Medicine
|August 9, 2026
Summary
We introduce a new method for selecting effects in multilevel functional regression, analyzing physical activity patterns. This approach accurately identifies age and race-specific variations in covariate effects across the lifespan.
Area of Science:
- Statistics
- Biostatistics
- Functional Data Analysis
Background:
- Multilevel functional regression models are crucial for analyzing complex data with hierarchical structures and time-varying effects.
- Existing variable selection methods in functional regression often focus on fixed effects and single-level data, limiting their application to multilevel scenarios.
- Understanding heterogeneity in covariate effects on diurnal physical activity patterns is vital for public health insights.
Purpose of the Study:
- To develop a novel method for simultaneous fixed and random effects selection in multilevel functional regression.
- To identify age and race-specific heterogeneity in covariate effects on diurnal physical activity patterns using real-world data.
- To address limitations of existing methods in handling high-dimensional multilevel functional data.
Main Methods:
- Proposed a multilevel functional mixed effects selection (MuFuMES) method.
- Employed splines for modeling fixed and random functional effects.
- Utilized spike-and-slab group lasso (SSGL) priors and an Expectation Conditional Maximization (ECM) algorithm for efficient estimation.
Main Results:
- Simulation studies demonstrated high selection accuracy with negligible false-positive and false-negative rates.
- The MuFuMES method effectively identified age and race-specific heterogeneity in covariate effects on physical activity.
- Biologically meaningful insights were recovered from the National Health and Nutrition Examination Survey (NHANES) accelerometer data.
Conclusions:
- The developed MuFuMES method provides a robust approach for variable selection in high-dimensional multilevel functional regression.
- The method successfully uncovers complex patterns of heterogeneity in covariate effects, crucial for understanding health-related behaviors.
- Application to NHANES data highlights the utility of MuFuMES in revealing nuanced, population-specific insights from functional data.
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