  We consider analysis of dependent functional data that are correlated because
of a longitudinal-based design: each subject is observed at repeated time
visits and for each visit we record a functional variable. We propose a novel
parsimonious modeling framework for the repeatedly observed functional
variables that allows to extract low dimensional features. The proposed
methodology accounts for the longitudinal design, is designed for the study of
the dynamic behavior of the underlying process, and is computationally fast.
Theoretical properties of this framework are studied and numerical
investigation confirms excellent behavior in finite samples. The proposed
method is motivated by and applied to a diffusion tensor imaging study of
multiple sclerosis. Using Shiny (Chang et al., 2015) we implement interactive
plots to help visualize longitudinal functional data as well as the various
components and prediction obtained using the proposed method.
