Functional Regression and Principal Components Analysis for Sparse Longitudinal Data

• Activity Number: 230
• Type: Invited
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Fang Yao*+ and Hans-Georg Muller and Jane-Ling Wang
• Companies: University of California, Davis and University of California, Davis and University of California, Davis
• Keywords: functional data ; nonparametric functional regression ; longitudinal data ; samples of curves ; smoothing

Abstract

We propose a nonparametric method to perform functional regression and principal components analysis for sparse longitudinal data that consist of noisy measurements with underlying smooth random trajectories for each subject in a sample. The number of repeated measurements available per subject is typically small, and their spacing is irregular. Our proposal includes determination of the most appropriate function basis from the data. The proposed conditional method is simple and straightforward to implement and includes estimation of the covariance stucture and of the variance of the measurements. It is also suitable for functional regression where both the predictor and response are functions of a covariate such as time. The resulting technique is flexible and allows for different timing of measurements for predictor and response functions. Asymptotic properties are investigated under mild conditions, using tools from functional analysis. We illustrate the methods with a simulation study, longitudinal CD4 data in AIDS patients and a functional regression analysis of the dynamic relationship of immunoproteins.