Functional data analysis in longitudinal settings using smoothing splines

Abstract

Data in many experiments arise as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is termed functional data analysis (FDA). In longitudinal studies, recent developments in FDA have extended classical linear models and linear mixed effects models to functional linear models (also termed varying-coefficient models) and functional mixed effects models. In this paper we focus our review on the functional mixed effects models using smoothing splines, because functional linear models are special cases of this more general framework. Due to the connection between smoothing splines and linear mixed effects models, functional mixed effects models can be fitted using existing software such as SAS Proc Mixed. A case study is presented as an illustration.