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<p>In this work, we present a new approach for constructing models for covariance matrices by considering the decomposition into marginal variances and a correlation matrix. The correlation structure is deduced from 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 propose 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 simulation studies of multivariate longitudinal joint modelling, where we demonstrate some properties of the method and two real data applications: a multivariate linear regression of four biomarkers and a multivariate disease mapping. 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.</p>

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A graphical framework for interpretable correlation matrix models for multivariate regression

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月10日

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  • Anna Freni-Sterrantino,
  • Denis Rustand,
  • Janet van Niekerk,
  • Elias Teixeira Krainski,
  • Håvard Rue

摘要

In this work, we present a new approach for constructing models for covariance matrices by considering the decomposition into marginal variances and a correlation matrix. The correlation structure is deduced from 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 propose 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 simulation studies of multivariate longitudinal joint modelling, where we demonstrate some properties of the method and two real data applications: a multivariate linear regression of four biomarkers and a multivariate disease mapping. 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.