"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Functional Generalized Additive Models

David Ruppert, Cornell University, School of Operations Research and Information Engineering

Monday, December 5, 2011

4:00 p.m., room 223, Weber Bldg

ABSTRACT

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t),t}; where F(.;.) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number of principal components as in Muller and Yao (2008), our model incorporates the functional predictor directly and we regard our model as the natural functional extension of generalized additive models. We estimate F(.;.) using tensor-product B-splines with roughness penalties. A pointwise quantile transformation of the functional predictor is also considered to ensure each tensor-product B-spline has observed data on its support. We evaluate the model using simulated data and compare its predictive performance with some other popular scalar-on-function regression models. We illustrate the usefulness of our approach through an application to brain tractography, where X(t) is taken to be a signal from diffusion tensor imaging at position, t, along a tract in the brain. In one example, the response is disease-status (case or control) and in a second example, it is score on a cognitive test.