Penalized functional regression

Jeff Goldsmith, Jennifer Bobb, Ciprian M. Crainiceanu, Brian Caffo, Daniel Reich

Research output: Contribution to journalArticlepeer-review

128 Scopus citations


We develop fast fitting methods for generalized functional linear models. The functional predictor is projected onto a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression; confidence intervals based on the mixed model framework are obtained. Our method can be applied to many functional data designs including functions measured with and without error, sparsely or densely sampled. The methods also extend to the case of multiple functional predictors or functional predictors with a natural multilevel structure. The approach can be implemented using standard mixed effects software and is computationally fast. The methodology is motivated by a study of white-matter demyelination via diffusion tensor imaging (DTI). The aim of this study is to analyze differences between various cerebral white-matter tract property measurements of multiple sclerosis (MS) patients and controls. While the statistical developments proposed here were motivated by the DTI study, the methodology is designed and presented in generality and is applicable to many other areas of scientific research. An online appendix provides R implementations of all simulations.

Original languageEnglish (US)
Pages (from-to)830-851
Number of pages22
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Dec 2011


  • Functional regression
  • Mixed models
  • Principal components
  • Smoothing splines

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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