Bayesian modeling of nearly mutually orthogonal processes

TL;DR

This paper introduces nearly mutually orthogonal processes for functional factor analysis, enabling efficient and interpretable modeling of complex longitudinal data with orthogonality constraints.

Contribution

It proposes a novel approach to enforce near-orthogonality in functional loadings, balancing model simplicity and computational efficiency.

Findings

Effective enforcement of mutual orthogonality in functional loadings.

Application to childhood weight dynamics demonstrates interpretability.

Code available at GitHub for reproducibility.

Abstract

Functional factor analysis is an important dimension reduction method for functional and longitudinal data. Factor loadings give insight into patterns of variability of the observations, while latent factors provide a low-dimensional representation of the data that is useful for inferential tasks. Constraining the functional factor loadings to be mutually orthogonal is desirable for model parsimony but is computationally challenging. In this work, we introduce nearly mutually orthogonal processes, which can be used to effectively enforce mutual orthogonality of factor loadings while maintaining computational simplicity and efficiency. The joint distribution 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. We demonstrate that our approach can be used for flexible and interpretable inference in an application to studying the effects of breastfeeding status, illness, and demographic factors on weight dynamics in early childhood. Code is available on GitHub: https://github.com/jamesmatuk/NeMO-FFA