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

Functional concurrent, or varying-coefficient, regression models are a form of functional data analysis methods in which functional covariates and outcomes are collected concurrently. Two active areas of research for this class of models are identifying influential functional covariates and clustering their relations across observations. In various applications, researchers have applied and developed methods to address these objectives separately. However, no approach currently performs both tasks simultaneously. In this paper, we propose a fully Bayesian functional concurrent regression mixture model that simultaneously performs functional variable selection and clustering for subject-specific trajectories. Our approach introduces a novel spiked Ewens-Pitman attraction prior that identifies and clusters subjects' trajectories marginally for each functional covariate while using similarities in subjects' auxiliary covariate patterns to inform clustering allocation. Using simulated data, we evaluate the clustering, variable selection, and parameter estimation performance of our approach and compare its performance with alternative spiked processes. We then apply our method to functional data collected in a novel, smartphone-based smoking cessation intervention study to investigate individual-level dynamic relations between smoking behaviors and potential risk factors.