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 at https://github.com/jamesmatuk/ReMO-FPCA
翻译:功能性主要组成部分分析(FPCA)是确定差异和减少纵向和功能性数据集范围的突出工具。Bayesian FPCA的实施具有优势,因为其能够传播随后建模的不确定性。为了便于计算,许多示范方法都基于以下限制性假设:功能性主要组成部分可以通过预先指定的基础得到代表。根据这一假设,推论对基础很敏感,分辨错误可能导致错误结果。或者,我们开发了一个灵活的Bayesian FPCA模型,使用放松的相互交替(REMO)程序。我们定义了在主要组成部分之间执行相互或交替的ReMO程序,以确保模型参数的可识别性。ReMO程序的联合分布受惩罚参数的制约,该参数决定程序相互或交替地代表主要组成部分的程度,并且与离子计算有关。与其他方法相比,FPCA程序提供了更灵活、计算更方便的方法,便于准确传播不确定性。我们用广泛的模拟实验和应用程序展示了我们提议的模型,用于研究母乳喂养状况、REBAFA/人口动态在儿童期、RECA/Rimal Compal上的影响。