  In this work, we present a new approach for constructing models for
correlation matrices with a user-defined graphical structure. The graphical
structure makes correlation matrices interpretable and avoids the quadratic
increase of parameters as a function of the dimension. We suggest an automatic
approach to define a prior using a natural sequence of simpler models within
the Penalized Complexity framework for the unknown parameters in these models.
  We illustrate this approach with three applications: a multivariate linear
regression of four biomarkers, a multivariate disease mapping, and a
multivariate longitudinal joint modelling. Each application underscores our
method's intuitive appeal, signifying a substantial advancement toward a more
cohesive and enlightening model that facilitates a meaningful interpretation of
correlation matrices.
