Functional Regression Models with Highly Irregular Designs

Abstract

In this work we present a new approach to fitting functional data models with sparsely and irregularly sampled data. The limitations of current methods have created major challenges in fitting more complex nonlinear models. Indeed, currently many models cannot be consistently estimated unless one assumes that the number of observed points per curve grows sufficiently quickly with the sample size. In contrast, we demonstrate an approach that has the potential to produce consistent estimates without such an assumption. Just as importantly, our approach propagates the uncertainty of not having completely observed curves, allowing for a more accurate assessment of the uncertainty of parameter estimates, something that most methods currently cannot accomplish. This work is motivated by a longitudinal study on macrocephaly among children, in which electronic medical records allow for the collection of a great deal of data. However, the sampling is highly variable from child to child. Using our new approach we explore the effect of head circumference growth on the development of pathologies related to macrocephaly.