Semiparametric Functional Mixed Models for Longitudinal Functional Data, with Application to Glaucoma Data

• Activity Number: 20
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Wonyul Lee* and Jeffrey Morris and Veera Baladandayuthapani
• Companies: and MD Anderson Cancer Center and MD Anderson Cancer Center
• Keywords: Funtional mixed model ; Semi-parametric ; longitudinal functional data

Abstract

Functional response regression involves the regression of functional responses on a set of scalar predictors. Many existing methods for functional response regression focus on functional linear effects of the predictors, which may not be flexible enough to capture complex structure in data. In this work, we develop semi-parametric functional mixed models with design matrices consisting of Demmler-Reinsch spline bases allowing the model to incorporate nonparametric functional additive terms. The model can also capture between-function correlation of longitudinally observed functions through random functional effects. The model is fitted through a basis transform approach with fully Bayesian MCMC. We also present strategies to perform model selection, choosing among fixed and random terms, deciding whether they should be parametric, or nonparametric. Our method works for a wide range of basis functions, and we describe some strategies that can be utilized in the model selection process for selecting which basis functions appear to best capture the structure in the functional data. We will introduce these methods in the context of a glaucoma study investigating scleral strain tensors.