  We develop a model-based boosting approach for multivariate distributional
regression within the framework of generalized additive models for location,
scale, and shape. Our approach enables the simultaneous modeling of all
distribution parameters of an arbitrary parametric distribution of a
multivariate response conditional on explanatory variables, while being
applicable to potentially high-dimensional data. Moreover, the boosting
algorithm incorporates data-driven variable selection, taking various different
types of effects into account. As a special merit of our approach, it allows
for modelling the association between multiple continuous or discrete outcomes
through the relevant covariates. After a detailed simulation study
investigating estimation and prediction performance, we demonstrate the full
flexibility of our approach in three diverse biomedical applications. The first
is based on high-dimensional genomic cohort data from the UK Biobank,
considering a bivariate binary response (chronic ischemic heart disease and
high cholesterol). Here, we are able to identify genetic variants that are
informative for the association between cholesterol and heart disease. The
second application considers the demand for health care in Australia with the
number of consultations and the number of prescribed medications as a bivariate
count response. The third application analyses two dimensions of childhood
undernutrition in Nigeria as a bivariate response and we find that the
correlation between the two undernutrition scores is considerably different
depending on the child's age and the region the child lives in.
