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Unpublished Paper
PENALIZED FUNCTIONAL REGRESSION
Johns Hopkins University, Dept. of Biostatistics Working Papers
  • Jeff Goldsmith, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
  • Jennifer Feder, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
  • Ciprian M. Crainiceanu, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
  • Brian Caffo, Johns Hopkins Bloomberg School of Public Health, Department of Biostatistics
  • Daniel Reich, Translational Neuroradiolgy Unit, Neuroimmunology Branch, National Institute of Neurological Disorders and Stroke, Johns Hopkins University, Department of Neurology
Date of this Version
1-21-2010
Abstract
We develop fast fitting methods for generalized functional linear models. An undersmooth of the functional predictor is obtained by projecting on a large number of smooth eigenvectors and the coefficient function is estimated using penalized spline regression. 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. Our approach can be implemented using standard mixed effects software and is computationally fast. Our methodology is motivated by a diffusion tensor imaging (DTI) study. 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.
Citation Information
Jeff Goldsmith, Jennifer Feder, Ciprian M. Crainiceanu, Brian Caffo, et al.. "PENALIZED FUNCTIONAL REGRESSION" (2010)
Available at: http://works.bepress.com/ciprian_crainiceanu/6/