Warped functional analysis of variance.
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour beetles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smootheness of the observed data is not required; the method can be applied to irregular time grids, which are common in longitudinal studies.
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee, Wisconsin 53201, U.S.A.
Daniel
D
Gervini
School of Biological Sciences, Washington State University, PO Box 644236, Pullman, Washington 99164, U.S.A.
Patrick A
PA
Carter
D000465:Algorithms; D000704:Analysis of Variance; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D008137:Longitudinal Studies; D015233:Models, Statistical
Karhunen–Loève decomposition; Longitudinal data; Phase variability; Quantitative genetics; Random‐effect models