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Biometrika 2008 95(3):601-619; doi:10.1093/biomet/asn035
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© 2008 Biometrika Trust

Articles

Joint modelling of paired sparse functional data using principal components

Lan Zhou, Jianhua Z. Huang and Raymond J. Carroll

Department of Statistics, Texas A & M University, College Station, Texas 77843, U.S.A. lzhou{at}stat.tamu.edu jianhua{at}stat.tamu.edu carroll{at}stat.tamu.edu

Received for publication 1 December 2006. Revision received 1 March 2008.
  Abstract

We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed-effects model framework for model fitting, prediction and inference. The proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals. Use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates.

Key Words: Functional data • Longitudinal data • Mixed-effects model • Penalized spline • Principal component • Reduced-rank model


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