  The article develops marginal models for multivariate longitudinal responses.
Overall, the model consists of five regression submodels, one for the mean and
four for the covariance matrix, with the latter resulting by considering
various matrix decompositions. The decompositions that we employ are intuitive,
easy to understand, and they do not rely on any assumptions such as the
presence of an ordering among the multivariate responses. The regression
submodels are semiparametric, with unknown functions represented by basis
function expansions. We use spike-slap priors for the regression coefficients
to achieve variable selection and function regularization, and to obtain
parameter estimates that account for model uncertainty. An efficient Markov
chain Monte Carlo algorithm for posterior sampling is developed. The simulation
studies presented investigate the effects of priors on posteriors, the gains
that one may have when considering multivariate longitudinal analyses instead
of univariate ones, and whether these gains can counteract the negative effects
of missing data. We apply the methods on a highly unbalanced longitudinal
dataset with four responses observed over of period of 20 years
