Structured Penalties for Generalized Functional Linear Models (GFLM)

• Activity Number: 499
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jaroslaw Harezlak*+ and Tim Randolph and Ziding Feng
• Companies: Indiana University School of Medicine and Fred Hutchinson Cancer Research Center and Fred Hutchinson Cancer Research Center
• Keywords: Functional data analysis ; GLM ; joint spectral decomposition ; regularization ; penalized regression

Abstract

GFLMs are often used to estimate the relationship between a predictor function and a response. Approaches used either reduce the functions by estimating their principal components or project the functions onto the span of fixed bases. A major challenge in GFLM is to incorporate the structural properties of the functions into the analysis. This presentation provides an extension of a recently proposed method - PEER (partially empirical eigenvectors for regression) for FLM to GLFM. The PEER approach to FLMs incorporates the structure of the functions via a joint spectral decomposition of the predictor functions and a penalty operator into the estimation process via a generalized singular value decomposition. We extend this approach to GFLMs and compare the estimation performance with the classical methods. Finally, we apply our methodology to a mass spectrometry data with binary outcomes.