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Title: A functional additive mixed model for multivariate functional data Authors:  Alexander Volkmann - Humboldt University of Berlin (Germany) [presenting]
Almond Stoecker - Humboldt University of Berlin (Germany)
Fabian Scheipl - Ludwig-Maximilians-Universitaet Muenchen (Germany)
Sonja Greven - Humboldt University of Berlin (Germany)
Abstract: Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like acoustics and articulation in speech production. We propose a multivariate functional additive mixed model (MFAMM) and show its application to these data situations. The approach models the dependency structure between the dimensions directly using multivariate functional principal component analysis. Multivariate functional random intercepts capture the correlation within the functions and between the multivariate functional dimensions. They also allow us to extend the model to include further between-function correlation as induced by e.g. repeated observations. The applications show that a multivariate modeling approach is more parsimonious compared to fitting independent univariate models to the data. Modeling the dependency structure between the dimensions can also generate additional insight into the properties of the multivariate functional process. A direct comparison of the multivariate and univariate approach also suggests that the estimated confidence regions might be more efficient for the MFAMM.