  Multivariate functional data can be intrinsically multivariate like movement
trajectories in 2D or complementary like precipitation, temperature, and wind
speeds over time at a given weather station. We propose a multivariate
functional additive mixed model (multiFAMM) and show its application to both
data situations using examples from sports science (movement trajectories of
snooker players) and phonetic science (acoustic signals and articulation of
consonants). The approach includes linear and nonlinear covariate effects and
models the dependency structure between the dimensions of the responses using
multivariate functional principal component analysis. Multivariate functional
random intercepts capture both the auto-correlation within a given function and
cross-correlations between the multivariate functional dimensions. They also
allow us to model between-function correlations as induced by e.g.\ repeated
measurements or crossed study designs. Modeling the dependency structure
between the dimensions can generate additional insight into the properties of
the multivariate functional process, improves the estimation of random effects,
and yields corrected confidence bands for covariate effects. Extensive
simulation studies indicate that a multivariate modeling approach is more
parsimonious than fitting independent univariate models to the data while
maintaining or improving model fit.
