Fast Function-on-Scalar Regression with Penalized Basis Expansions

Reiss Philip T., Huang Lei and Mennes Maarten
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Reiss Philip T.: New York University and Nathan S. Kline Institute for Psychiatric Research
Huang Lei: New York University
Mennes Maarten: New York University

The International Journal of Biostatistics, 2010, vol. 6, issue 1, 30

Abstract: Regression models for functional responses and scalar predictors are often fitted by means of basis functions, with quadratic roughness penalties applied to avoid overfitting. The fitting approach described by Ramsay and Silverman in the 1990s amounts to a penalized ordinary least squares (P-OLS) estimator of the coefficient functions. We recast this estimator as a generalized ridge regression estimator, and present a penalized generalized least squares (P-GLS) alternative. We describe algorithms by which both estimators can be implemented, with automatic selection of optimal smoothing parameters, in a more computationally efficient manner than has heretofore been available. We discuss pointwise confidence intervals for the coefficient functions, simultaneous inference by permutation tests, and model selection, including a novel notion of pointwise model selection. P-OLS and P-GLS are compared in a simulation study. Our methods are illustrated with an analysis of age effects in a functional magnetic resonance imaging data set, as well as a reanalysis of a now-classic Canadian weather data set. An R package implementing the methods is publicly available.

Keywords: cross-validation; functional data analysis; functional connectivity; functional linear model; smoothing parameters; varying-coefficient model (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (27)

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DOI: 10.2202/1557-4679.1246

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