Longitudinal scalar-on-functions regression with application to tractography data

Jan Gertheiss, Jeff Goldsmith, Ciprian Crainiceanu, Sonja Greven

Research output: Contribution to journalArticlepeer-review


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'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.

Original languageEnglish (US)
Pages (from-to)447-461
Number of pages15
Issue number3
StatePublished - Jul 2013


  • Diffusion tensor imaging
  • Functional principal components
  • Functional regression
  • Longitudinal functional principal components regression
  • Multiple sclerosis
  • Repeated measurements

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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