Functional generalized linear models with images as predictors

Philip T. Reiss, R. Todd Ogden

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)61-69
Number of pages9
JournalBiometrics
Volume66
Issue number1
DOIs
StatePublished - Mar 2010
Externally publishedYes

Keywords

  • B-splines
  • Functional principal component regression
  • Positron emission tomography
  • Simultaneous confidence bands
  • Smoothing parameter

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability

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