Varying-Smoother Models for Brain Development

• Activity Number: 441
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Imaging
• Author(s): Philip T. Reiss*+ and Lei Huang and Huaihou Chen and Stan Colcombe
• Companies: New York University School of Medicine and Johns Hopkins University and New York University and Nathan Kline Institute
• Keywords: curve estimation ; functional principal component analysis ; linear mixed effects model ; longitudinal neuroimaging ; magnetic resonance imaging ; neurodevelopmental trajectory

Abstract

Motivated by studies of human brain development, we consider estimation of a bivariate smooth function when the data are spatially smooth functional responses, but scientific interest centers on smoothness in the temporal direction. Analogously to varying-coefficient models, which are linear with respect to time, the "varying-smoother'' models that we consider exhibit nonlinear dependence on time that varies smoothly over space. We focus on two spline-based approaches to estimating varying-smoother models: (i) methods that apply a tensor product penalty, and (ii) two-step methods consisting of an initial smooth in the temporal direction, followed by a postprocessing step. We propose a novel approach to pointwise model selection, and discuss extensions to longitudinal neuroimaging studies.