  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, smoothness of
the observed data is not required; the method can be applied to the sparsely
observed data that is often encountered in longitudinal studies.
