  We propose a flexible regression framework to model the conditional
distribution of multilevel generalized multivariate functional data of
potentially mixed type, e.g. binary and continuous data. We make pointwise
parametric distributional assumptions for each dimension of the multivariate
functional data and model each distributional parameter as an additive function
of covariates. The dependency between the different outcomes and, for
multilevel functional data, also between different functions within a level is
modelled by shared latent multivariate Gaussian processes. For a parsimonious
representation of the latent processes, (generalized) multivariate functional
principal components are estimated from the data and used as an empirical basis
for these latent processes in the regression framework. Our modular two-step
approach is very general and can easily incorporate new developments in the
estimation of functional principal components for all types of (generalized)
functional data. Flexible additive covariate effects for scalar or even
functional covariates are available and are estimated in a Bayesian framework.
We provide an easy-to-use implementation in the accompanying R package 'gmfamm'
on CRAN and conduct a simulation study to confirm the validity of our
regression framework and estimation strategy. The proposed multivariate
functional model is applied to four dimensional traffic data in Berlin, which
consists of the hourly numbers and mean speed of cars and trucks at different
locations.
