Functional Concurrent Regression Mixture Models Using Spiked Ewens-Pitman Attraction Priors.

Area of Science:

• Functional Data Analysis
• Bayesian Statistics
• Machine Learning

Background:

• Functional concurrent regression models analyze data where both predictors and outcomes are functions observed over time.
• Existing methods often address functional variable selection and clustering of subject trajectories separately.
• A simultaneous approach is needed to integrate these tasks for a more comprehensive analysis.

Purpose of the Study:

• To develop a novel fully Bayesian functional concurrent regression mixture model.
• To simultaneously perform functional variable selection and clustering of subject-specific trajectories.
• To investigate dynamic relationships between smoking behaviors and risk factors in a smoking cessation study.

Main Methods:

• Proposed a fully Bayesian functional concurrent regression mixture model.
• Introduced a novel spiked Ewens-Pitman attraction prior for joint clustering and variable selection.
• Utilized auxiliary covariate patterns to inform clustering allocation.
• Evaluated performance using simulated data and compared with alternative spiked processes.

Main Results:

• The proposed model effectively performs simultaneous functional variable selection and clustering.
• Demonstrated robust performance in clustering, variable selection, and parameter estimation via simulations.
• Identified dynamic relationships between smoking behaviors and risk factors in a real-world smoking cessation intervention.

Conclusions:

• The novel Bayesian approach offers a unified framework for functional variable selection and clustering.
• This method provides a powerful tool for analyzing complex functional data in various scientific domains.
• The application highlights the model's utility in understanding individual-level dynamics in health interventions.