Functional data analysis and mixed effect models

Panel studies in econometrics as well as longitudinal studies in biomedical applications provide data from a sample of individual units where each unit is observed repeatedly over time (age, etc.). In this context, mixed effect models are often applied to analyze the behavior of a response variable in dependence of a number of covariates. In some important applications it is necessary to assume that individual effects vary over time (age, etc.). In the paper it is shown that in many situations a sensible analysis may be based on a semiparametric approach relying on tools from functional data analysis. The basic idea is that time-varying individual effects may be represented as a a sample of smooth functions which can be characterized by its Karhunen-Loeve decomposition. An important application is the estimation of time-varying technical inefficiencies of individual firms in stochastic frontier analysis.