Modeling Motor Learning Using Heteroscedastic Functional Principal Components Analysis

• Published in: Journal of the American Statistical Association Vol. 113; no. 523; pp. 1003 - 1015
• Main Authors: Backenroth, Daniel, Goldsmith, Jeff, Harran, Michelle D., Cortes, Juan C., Krakauer, John W., Kitago, Tomoko
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.07.2018; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Applications and Case Studies; data collection; equations; Functional data; heteroskedasticity; Injuries; Kinematic data; Learning; Materials recovery; Modelling; Motor control; Population statistics; principal component analysis; Principal components analysis; Probabilistic PCA; Random effects; Regression analysis; Statistical methods; Statistics; Upper limbs; Variability; Variance; Variance modeling; Variational Bayes
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2017.1379403

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 movement variability associated with skill learning. The proposed methods can be applied broadly to understand movement variability, in settings that include motor learning, impairment due to injury or disease, and recovery. Supplementary materials for this article are available online.