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Title: Multivariate functional additive mixed models Authors:  Alexander Volkmann - LMU Munich (Germany)
Almond Stoecker - Humboldt University of Berlin (Germany)
Fabian Scheipl - Ludwig-Maximilians-Universitaet Muenchen (Germany)
Sonja Greven - LMU Munich (Germany) [presenting]
Abstract: Functional data are often multivariate, i.e. they simultaneously measure different functional aspects of a process. So far, few regression methods have been developed to efficiently handle the full amount of information provided by multivariate functional data. We develop a multivariate functional additive mixed model (MFAMM). The dependency structure between the different dimensions is incorporated using multivariate functional principal component analysis. The model accounts for correlation within the functions, between the multivariate functional dimensions as well as potentially further between-function correlation - which is often induced by the study design - via multivariate functional random intercepts. Multivariate functional data generated in a speech production study with a crossed study design are analyzed. The analysis is more parsimonious compared to fitting independent univariate models to the data and generates insight into the dependency structure between acoustic and articulatory processes. Application results also suggest that estimated confidence regions might be more efficient for the MFAMM than for the univariate approach.