We propose a novel method for estimating population-level and subject-specific effects of covariates on the variability of functional data. We extend the functional principal components analysis framework by modeling the variance of principal component scores as a function of covariates and subject-specific random effects. In a setting where principal components are largely invariant across subjects and covariate values, modeling the variance of these scores provides a flexible and interpretable way to explore factors that affect the variability of functional data. Our work is motivated by a novel dataset from an experiment assessing upper extremity motor control, and quantifies the reduction in motion variance associated with skill learning.
Keywords: Functional Data; Kinematic Data; Motor Control; Probabilistic PCA; Variance Modeling; Variational Bayes.