Reiss PT, Goldsmith J, Shang HL, Ogden RT. Methods for scalar-on-function regression.
Int Stat Rev 2017;
85:228-249. [PMID:
28919663 PMCID:
PMC5598560 DOI:
10.1111/insr.12163]
[Citation(s) in RCA: 72] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Accepted: 12/28/2015] [Indexed: 01/16/2023]
Abstract
Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. 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, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.
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