Variable Selection for Fixed and Random Effects in Multilevel Functional Mixed Effects Models

TL;DR

This paper introduces MuFuMES, a novel multilevel functional mixed effects variable selection method using splines and spike-and-slab group lasso priors, effectively identifying heterogeneity in high-dimensional functional data.

Contribution

The paper develops MuFuMES, a new method for simultaneous fixed and random effects selection in multilevel functional regression models, with efficient MAP estimation and demonstrated accuracy.

Findings

Accurately selects relevant effects with low false-positive/negative rates.

Effectively identifies age and race-specific heterogeneity in physical activity.

Provides biologically meaningful insights from NHANES accelerometer data.

Abstract

We develop a new method for simultaneously selecting fixed and random effects in a multilevel functional regression model. The proposed method is motivated by accelerometer-derived physical activity data from the 2011-12 cohort of the National Health and Nutrition Examination Survey (NHANES), where we are interested in identifying age and race-specific heterogeneity in covariate effects on the diurnal patterns of physical activity across the lifespan. Existing methods for variable selection in function-on-scalar regression have primarily been designed for fixed effect selection and for single-level functional data. In high-dimensional multilevel functional regression, the presence of cluster-specific heterogeneity in covariate effects could be detected through sparsity in fixed and random effects, and for this purpose, we propose a multilevel functional mixed effects selection (MuFuMES) method. The fixed and random functional effects are modelled using splines, with spike-and-slab group lasso (SSGL) priors on the unknown parameters of interest and a computationally efficient MAP estimation approach is employed for mixed effect selection through an Expectation Conditional Maximization (ECM) algorithm. Numerical analysis using simulation study illustrates the satisfactory selection accuracy of the variable selection method in having a negligible false-positive and false-negative rate. The proposed method is applied to the accelerometer data from the NHANES 2011-12 cohort, where it effectively identifies age and race-specific heterogeneity in covariate effects on the diurnal patterns of physical activity, recovering biologically meaningful insights.