Penalized Functional Regression

2011/01/01 by Jeff Goldsmith, Jennifer Bobb, Jennifer F. Bobb +4 · 13 citations
Medicine · #Advanced Neuroimaging Techniques and Applications #Bone and Joint Diseases #Scoliosis diagnosis and treatment

paper · doi:10.1198/jcgs.2010.10007

openalex publication_date 2011/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

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