@article {814,
	title = {Longitudinal scalar-on-functions regression with application to tractography data.},
	journal = {Biostatistics},
	volume = {14},
	year = {2013},
	month = {2013 Jul},
	pages = {447-61},
	abstract = {<p>We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study{\textquoteright}s primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.</p>},
	keywords = {Anisotropy, Biostatistics, Brain, Diffusion Tensor Imaging, Humans, Linear Models, Models, Statistical, Multiple Sclerosis, Principal Component Analysis, Regression Analysis},
	issn = {1468-4357},
	doi = {10.1093/biostatistics/kxs051},
	author = {Gertheiss, Jan and Goldsmith, Jeff and Crainiceanu, Ciprian and Greven, Sonja}
}
