Geodesic Mixed Effects Models for Repeatedly Observed/Longitudinal Random Objects

• 成果类型: Article; Early Access
• 署名作者: Bhattacharjee, Satarupa; Mueller, Hans-Georg
• 署名单位: State University System of Florida; University of Florida; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2474267
• 发表日期: 2025
• 关键词: frechet regression; Nonparametric Regression; SPACE; geometry; matrices

摘要

Mixed effect modeling 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, we develop a mixed-effects regression 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 Fr & eacute;chet regression for random objects. The effect of baseline Euclidean covariates on the geodesic paths is modeled by another Fr & eacute;chet regression step. We study the asymptotic convergence of the proposed estimates and provide illustrations through simulations and real-data applications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.