A graphical framework for interpretable correlation matrix models for multivariate regression

Anna Freni-Sterrantino (), Denis Rustand (), Janet van Niekerk (), Elias Teixeira Krainski () and Håvard Rue ()
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Anna Freni-Sterrantino: The Alan Turing Institute
Denis Rustand: King Abdullah University of Science and Technology
Janet van Niekerk: King Abdullah University of Science and Technology
Elias Teixeira Krainski: King Abdullah University of Science and Technology
Håvard Rue: King Abdullah University of Science and Technology

Statistical Methods & Applications, 2025, vol. 34, issue 3, No 2, 409-447

Abstract: Abstract 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.

Keywords: Complexity penalized priors; Correlation matrix modelling; Graphical structure; Multivariate joint modelling (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10260-025-00788-y

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