Title: Identifiability and multicollinearity in scalar-on-functions regression
Authors: Clara Happ - LMU Munich (Germany) [presenting]
Sonja Greven - LMU Munich (Germany)
Abstract: Data with functional features arises in more and more disciplines, bringing new possibilities and challenges to practitioners and statisticians. One key method in functional data analysis is modeling the relationship of one or more functional predictor variables and a scalar response, which is referred to as scalar-on-functions regression. As for all regression models, there is need for identifiable coefficient functions as a necessary condition for obtaining interpretable results. The issue of non-identifiability of scalar-on-function terms and its natural extension, functional multicollinearity, is discussed for the functional linear model. Starting from a theoretical point of view, practical diagnostic criteria are developed and countermeasures are proposed for the two main estimation approaches, penalized scalar-on-function regression and functional principal component regression. The theoretical results are verified in an extensive simulation study and their relevance is illustrated in an application to biomedical data.