Bayesian Functional Principal Component Analysis using Relaxed Mutually Orthogonal Processes

Abstract

Functional Principal Component Analysis (FPCA) is a prominent tool to characterize variability and reduce dimension of longitudinal and functional datasets. Bayesian implementations of FPCA are advantageous because of their ability to propagate uncertainty in subsequent modeling. To ease computation, many modeling approaches rely on the restrictive assumption that functional principal components can be represented through a pre-specified basis. Under this assumption, inference is sensitive to the basis, and misspecification can lead to erroneous results. Alternatively, we develop a flexible Bayesian FPCA model using Relaxed Mutually Orthogonal (ReMO) processes. We define ReMO processes to enforce mutual orthogonality between principal components to ensure identifiability of model parameters. The joint distribution of ReMO processes is governed by a penalty parameter that determines the degree to which the processes are mutually orthogonal and is related to ease of posterior computation. In comparison to other methods, FPCA using ReMO processes provides a more flexible, computationally convenient approach that facilitates accurate propagation of uncertainty. We demonstrate our proposed model using extensive simulation experiments and in an application to study the effects of breastfeeding status, illness, and demographic factors on weight dynamics in early childhood. Code is available on GitHub: https://github.com/jamesmatuk/ReMO-FPCA.