Functional generalized linear models with images as predictors.
Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors.
Department of Child and Adolescent Psychiatry, New York University, New York, New York 10016, USA. phil.reiss@nyumc.org
Philip T
PT
Reiss
R Todd
RT
Ogden
D000465:Algorithms; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D016014:Linear Models; D009716:Numerical Analysis, Computer-Assisted; D011379:Prognosis; D012044:Regression Analysis