Assigning Variability in Functional Data Analysis

• Activity Number: 230
• Type: Invited
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Theo Gasser*+
• Companies: Universitaet Zuerich
• Keywords: functional data ; principal component analysis ; registration ; smoothing

Abstract

A peculiar feature of functional data is the coexistence of amplitude and time variability (events displaced from curve to curve). Classical approaches as PCA (and repeated measures ANOVA) deal only with amplitude variability, which can lead to misallocation of variance. Thus a registration step has to precede PCA. There are various methods to achieve alignment of functions (landmark registration, time warping, penalized monotone fitting), but none has become a standard. We will discuss the pros and the cons of these methods. Usually, the registration or warping functions are considered a nuisance, but in many fields they are also of interest: in growth, for example, they quantify the maturational tempo of a child. We propose that in such cases two FDAs should be performed: one for the registered amplitude functions and one for the registration functions. It will be outlined how this double decomposition can be achieved. If time permits, we will discuss problems and solution with interpretation of functional components: the components obtained are oftennot easy to interpret and this may be still true after VARIMAX rotation. Illustrations are based on classical and simulated data.