  Vine copulas are a highly flexible class of dependence models, which are
based on the decomposition of the density into bivariate building blocks. For
applications one usually makes the simplifying assumption that copulas of
conditional distributions are independent of the variables on which they are
conditioned. However this assumption has been criticised for being too
restrictive. We examine both simplified and non-simplified vine copulas in
three dimensions and investigate conceptual differences. We show and compare
contour surfaces of three-dimensional vine copula models, which prove to be
much more informative than the contour lines of the bivariate marginals. Our
investigation shows that non-simplified vine copulas can exhibit arbitrarily
irregular shapes, whereas simplified vine copulas appear to be smooth
extrapolations of their bivariate margins to three dimensions. In addition to a
variety of constructed examples, we also investigate a three-dimensional subset
of the well-known uranium data set and visually detect that a non-simplified
vine copula is necessary to capture its complex dependence structure.
