Joint Modeling of Paired Sparse Functional Data Using Principal Components

• Activity Number: 619
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lan Zhou*+ and Jianhua Huang and Raymond Carroll
• Companies: Texas A&M University and Texas A&M University and Texas A&M University
• Keywords: Functional data ; Longitudinal data ; Mixed-effects model ; Penalized spline ; Principal component ; Reduced-rank model

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. 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.