  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 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. Code is available on
GitHub: https://github.com/jamesmatuk/NeMO-FFA
