Wavelet-Based Principal Component Analysis for Functional Mixed Effects Models

• Activity Number: 194
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Xiaochen Cai*+ and R. Todd Ogden
• Companies: Columbia University and Columbia University
• Keywords: Functional data analysis ; Mixed effects model ; Wavelets ; Principal component analysis

Abstract

We consider a wavelet-based functional mixed effects model for the analysis of multilevel functional data. Transforming the data into the wavelet domain allows for a sparse representation of the underlying processes. Analogous to the classical mixed effects model, the total variation is decomposed into the subject specific variation, the subject-session specific variation and measurement error. After removing coefficients with low variance, standard principal component analysis (PCA) is performed on the estimated variance-covariance matrix of each level of functional random effects. The methodology is illustrated by application to data from a study of human vision.