JSM 2005 - Toronto

Abstract #302942

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 94
Type: Topic Contributed
Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #302942
Title: Generalized Linear Models with Images as Predictors
Author(s): Philip Reiss*+ and Todd Ogden
Companies: Columbia University and Columbia University
Address: , New York, NY, , United States
Keywords: brain imaging ; functional data analysis ; partial least squares ; positron emission tomography ; principal component regression
Abstract:

Psychiatrists studying depression are interested in using PET images of the brain to predict treatment outcome. We place this problem in the framework of regression of scalar outcomes on functional predictors, a topic that has received much attention in the functional data analysis (FDA) literature. The fitted coefficients in a regression of this type form a function that can be viewed as an image. The number of predictors far exceeds the number of observations, a difficulty tackled in previous related work by either the FDA approach of projecting the coefficient image onto a basis of smooth functions or principal component regression (PCR) and partial least squares (PLS), a pair of methods popular in chemometrics. We propose to combine the advantages of both approaches with a smooth PCR/PLS model. The method is first demonstrated for linear regression on one-dimensional signals from a chemometric dataset. From there, we proceed to generalized linear regression on images, exemplified by our target application: logistic regression with PET images of the brain as predictors.

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Revised March 2005