Penalized Functional Regression

By J. Goldsmith, J. Bobb, Ciprian M. Crainiceanu, Brian C. Caffo, Daniel Reich. Journal of Computational And Graphical Statistics, 2011

323 citations recorded by the source corpus.

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.

Subfields: Orthopedics and Sports Medicine, Radiology, Nuclear Medicine and Imaging, Surgery

View Paper: https://www.semanticscholar.org/paper/1b6f57c6b37e4dbdd18d6e25335464f2fa5490ec

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Citations in the corpus

Functional Regression (2014, unknown): “Ivanescu et al. (2012) extended PFR of Goldsmith et al. (2011a) to the function-on-function setting, using PC expansions of the functional predictors while keeping many PCs, and regularizing the functional coefficient using P-splines.”
A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis (2016, methodology): “In the brain, water diffuses isotropically in both grey matter and cerebrospinal fluid and anisotropically in the white matter regions, which makes DTI an ideal approach to study the white matter tracts (Goldsmith et al., 2012). There are several well-identified white matter tracts in the brain: the”
The functional linear array model (2015, methodology): “This approach was proposed by Goldsmith et al. (2011) for scalar responses and by Ivanescu et al. (2014) and Scheipl et al. (2014) for functional responses.”