Variable selection in the functional linear concurrent model.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Modeling associations between functional responses and predictors is crucial in many scientific fields.
• Complex, time-varying data (e.g., daily blood pressure, physical activity) require advanced statistical methods.
• Existing methods may not adequately handle the variable selection for concurrent functional data.

Purpose of the Study:

• To develop and evaluate methods for variable selection in concurrent functional linear models.
• To address the challenge of identifying influential functional predictors for a functional response.
• To provide a robust framework for analyzing complex, time-dependent health data.

Main Methods:

• Estimation of functional linear model coefficients using variational Bayes.
• Joint modeling of residual correlations via functional principal components analysis.
• Incorporation of variable selection through latent binary indicators partitioning coefficient functions.

Main Results:

• Proposed methods demonstrated effectiveness in simulations and real-data analyses.
• Successful identification of relevant functional predictors influencing blood pressure.
• The approach provides a statistically sound framework for complex functional data analysis.

Conclusions:

• The developed methods offer a powerful tool for variable selection in concurrent functional data analysis.
• The approach enhances the interpretability of models involving time-varying exposures and outcomes.
• Implementation in an R package facilitates practical application and visualization in research.