English

A graphical framework for interpretable correlation matrix models

Methodology 2025-04-02 v3

Abstract

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.

Keywords

Cite

@article{arxiv.2312.06289,
  title  = {A graphical framework for interpretable correlation matrix models},
  author = {Anna Freni Sterrantino and Denis Rustand and Janet van Niekerk and Elias Teixeira Krainski and Håvard Rue},
  journal= {arXiv preprint arXiv:2312.06289},
  year   = {2025}
}