  We propose a model for unbalanced longitudinal data, where the univariate
margins can be selected arbitrarily and the dependence structure is described
with the help of a D-vine copula. We show that our approach is an extremely
flexible extension of the widely used linear mixed model if the correlation is
homogeneous over the considered individuals. As an alternative to joint
maximum-likelihood a sequential estimation approach for the D-vine copula is
provided and validated in a simulation study. The model can handle missing
values without being forced to discard data. Since conditional distributions
are known analytically, we easily make predictions for future events. For model
selection we adjust the Bayesian information criterion to our situation. In an
application to heart surgery data our model performs clearly better than
competing linear mixed models.
