Methods for scalar-on-function regression

Philip T. Reiss, Jeff Goldsmith, Han Lin Shang, R. Todd Ogden

Research output: Contribution to journalArticlepeer-review

Abstract

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so on are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non-linear and non-parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.

Original languageEnglish
Pages (from-to)228-249
Number of pages22
JournalInternational Statistical Review
Volume85
Issue number2
DOIs
StatePublished - 2017

Bibliographical note

Funding Information:
We thank the Co-Editor-in-Chief, Prof. Marc Hallin, and the Associate Editor and referees, whose feedback enabled us to improve the manuscript significantly. We also thank Prof. Martin Lindquist for providing the pain data, whose collection was supported by the U.S. National Institutes of Health through grants R01MH076136-06 and R01DA035484-01, and Pei-Shien Wu for assistance with the bibliography. Philip Reiss’ work was supported in part by grant 1R01MH095836-01A1 from the National Institute of Mental Health. Jeff Goldsmith’s work was supported in part by grants R01HL123407 from the National Heart, Lung, and Blood Institute and R21EB018917 from the National Institute of Biomedical Imaging and Bioengineering. Han Lin Shang’s work was supported in part by a Research School Grant from the ANU College of Business and Economics. Todd Ogden’s work was supported in part by grant 5R01MH099003 from the National Institute of Mental Health.

Funding Information:
We thank the Co-Editor-in-Chief, Prof. Marc Hallin, and the Associate Editor and referees, whose feedback enabled us to improve the manuscript significantly. We also thank Prof. Martin Lindquist for providing the pain data, whose collection was supported by the U.S. National Institutes of Health through grants R01MH076136-06 and R01DA035484-01, and Pei-Shien Wu for assistance with the bibliography. Philip Reiss? work was supported in part by grant 1R01MH095836-01A1 from the National Institute of Mental Health. Jeff Goldsmith?s work was supported in part by grants R01HL123407 from the National Heart, Lung, and Blood Institute and R21EB018917 from the National Institute of Biomedical Imaging and Bioengineering. Han Lin Shang?s work was supported in part by a Research School Grant from the ANU College of Business and Economics. Todd Ogden?s work was supported in part by grant 5R01MH099003 from the National Institute of Mental Health.

Publisher Copyright:
© 2016 The Authors and International Statistical Institute.

Keywords

  • Functional additive model
  • Functional generalised linear model
  • Functional linear model
  • Functional polynomial regression
  • Functional single-index model
  • Non-parametric functional regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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