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J Am Stat Assoc. 2018;113(523):1003-1015. doi: 10.1080/01621459.2017.1379403. Epub 2017 Sep 29.

Modeling motor learning using heteroskedastic functional principal components analysis.

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Department of Biostatistics, Mailman School of Public Health, Columbia University.
Department of Neurology, Columbia University Medical Center.
Departments of Neurology and Neuroscience, Johns Hopkins University.


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.


Functional Data; Kinematic Data; Motor Control; Probabilistic PCA; Variance Modeling; Variational Bayes

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