title: Longitudinal scalar-on-functions regression with application to tractography data.
abstract: We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study's primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.
authors.affiliation: Department of Animal Sciences, Georg-August-Universität Göttingen, 37075 Göttingen, Germany. jgerthe@uni-goettingen.de
authors.forename: Jan
authors.initials: J
authors.lastname: Gertheiss
authors.forename: Jeff
authors.initials: J
authors.lastname: Goldsmith
authors.forename: Ciprian
authors.initials: C
authors.lastname: Crainiceanu
authors.forename: Sonja
authors.initials: S
authors.lastname: Greven
mesh_terms: D016880:Anisotropy; D056808:Biostatistics; D001921:Brain / Q000473:pathology*; D056324:Diffusion Tensor Imaging / Q000706:statistics & numerical data*; D006801:Humans; D016014:Linear Models; D015233:Models, Statistical; D009103:Multiple Sclerosis / Q000473:pathology; D025341:Principal Component Analysis; D012044:Regression Analysis
keywords: Diffusion tensor imaging; Functional principal components; Functional regression; Longitudinal functional principal components regression; Multiple sclerosis; Repeated measurements