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. In particular, we are interested in testing for the necessity of functional effects against standard linear models. 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 which support recent findings regarding the relationship between cognitive impairment and white matter demyelination. R-code and data are provided to reproduce the application.
Biostatistics | Neurosciences
Swihart, Bruce J.; Goldsmith, Jeff; and Crainiceanu, Ciprian M., "RESTRICTED LIKELIHOOD RATIO TESTS FOR FUNCTIONAL EFFECTS IN THE FUNCTIONAL LINEAR MODEL" (June 2013). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 247.