Bayesian modeling of nearly mutually orthogonal processes

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 interpretability, but is computationally challenging. In this work, we introduce nearly mutually orthogonal processes, which can be used to effectively enforce mutual orthogonality of the 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.