Restricted likelihood ratio tests for functional effects in the functional linear model

Bruce J. Swihart, Jeff Goldsmith, Ciprian M. Crainiceanu

Research output: Contribution to journalArticlepeer-review


The goal of our article is to provide a transparent, robust, and computationally feasible statistical approach for testing in the context of scalar-on-function linear regression models. Assuming linearity between response and predictors, we are interested in testing for the necessity of functional effects. Our methods are motivated by and applied to a large longitudinal study involving diffusion tensor imaging of intracranial white matter tracts in a susceptible cohort. In the context of this study, we conduct hypothesis tests that are motivated by anatomical knowledge and support recent findings regarding the relationship between cognitive impairment and white matter demyelination. R code and data are in the examples of refund::rlrt.pfr(). Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)483-493
Number of pages11
Issue number4
StatePublished - Oct 2 2014


  • Functional data analysis
  • Nonparametric smoothing
  • Nonregular problem
  • Penalized splines
  • Variance components

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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