Filtrated Grouping in Multiple Functional Regression
Shuhao Jiao, Hernando Ombao, Ian W. McKeague
[stat.ME,stat.CO]
To understand and communicate the risk of chronic joint disease associated with aging, it is essential to investigate how age is associated with gait patterns, particularly through gait angular kinematics. Motivated by this need, and by the critical role of joint coordination in gait, we propose a novel covariate grouping framework within the context of multiple functional regression, where a scalar response is linked to multiple functional covariates. We apply this approach to investigate the relationship between chronological age and gait angular kinematics, aiming to uncover biomechanical patterns that signal age-related gait pattern evolution. Specifically, we develop a forest-structured covariate grouping framework in which different functional covariates are aggregated hierarchically based on the level of coefficient homogeneity. This approach allows for the analysis of both common and idiosyncratic effects of covariates in a nuanced, multi-resolution manner. The identification of the forest structure is entirely data-driven and requires no prior knowledge, providing valuable insights into the interdependence among covariates. Compared to existing methods, the proposed regression framework demonstrates superior predictive power and offers more insightful interpretability on joint coordination. In addition, the proposed framework is broadly applicable and can be readily extended to analyze multivariate functional data in other scientific domains.