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Functional Generalized Linear Models with Images as Predictors
Author(s) -
Reiss Philip T.,
Ogden R. Todd
Publication year - 2010
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2009.01233.x
Subject(s) - generalized linear model , linear model , functional data analysis , generalized additive model , mathematics , computer science , statistics
Summary 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.