Additive Mixed Models for Generalized Functional Data

• Activity Number: 162
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Fabian Scheipl*+
• Keywords: Functional Data ; Principal componets ; Splines ; Penalized regression ; Mixed models ; Smoothing

Abstract

We propose and evaluate an extensive framework for additive regression models for correlated functional responses from exponential families whose natural parameter varies smoothly over the functions' arguments. Our proposal allows for multiple partially nested or crossed functional random effects with flexible correlation structures as well as linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the argument of the functional response. It accommodates densely or sparsely or irregularly observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard generalized additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms.