Functional Modeling of Longitudinal Data

SUMMARY Functional data analysis provides an inherently nonparametric approach for the analysis of data which consist of samples of time courses or random trajectories. It is a relatively young field aiming at modeling and data exploration under very flexible model assumptions with no or few parametric components. Basic tools of functional data analysis are smoothing, functional principal components, functional linear models and time-warping. Warping or curve registration aims at adjusting for random time distortions. While in the usual functional data analysis paradigm the sample functions were considered as continuously observed, in longitudinal data analysis one mostly deals with sparsely and irregularly observed data that also are corrupted with noise. Adjustments of functional data analysis techniques which take these particular features into account are needed to use them to advantage for longitudinal data. We review some techniques that have been recently proposed to connect functional data analysis methodology with longitudinal data. The extension of functional data analysis towards longitudinal data is a fairly recent undertaking that presents a promising avenue for future research. This article provides a review of some of the recent developments.