A0502
Title: Geodesic mixed effects models for repeatedly observed/longitudinal random objects
Authors: Satarupa Bhattacharjee - University of Florida (United States) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Mixed effect modelling for longitudinal data is challenging when the observed data are random objects, which are complex data-taking values in a general metric space without either global linear or local linear (Riemannian) structure. In such settings, the classical additive error model and distributional assumptions are unattainable. Due to the rapid advancement of technology, longitudinal data containing complex random objects, such as covariance matrices, data on Riemannian manifolds, and probability distributions, are becoming more common. Addressing this challenge, a mixed-effects regression is developed for data in geodesic spaces, where the underlying mean response trajectories are geodesics in the metric space, and the deviations of the observations from the model are quantified by perturbation maps or transports. A key finding is that the geodesic trajectories assumption for the case of random objects is a natural extension of the linearity assumption in the standard Euclidean scenario to the case of general geodesic metric spaces. Geodesics can be recovered from noisy observations by exploiting a connection between the geodesic path and the path obtained by global Frachet regression for random objects. The effect of baseline Euclidean covariates on the geodesic paths are modelled by another Frachet regression step. The asymptotic convergence of the proposed estimates is studied, and illustrations are provided through simulations and real-data applications.
