Bayesian Nonparametric Modeling for Multivariate Conditional Copula Regression with Varying Coefficients

TL;DR

This paper introduces a Bayesian nonparametric framework for multivariate conditional copula regression with varying coefficients, enabling flexible modeling of complex dependence structures that change with covariates.

Contribution

It combines adaptive spline-based marginal regressions with an infinite mixture of Gaussian copulas, allowing covariate-dependent dependence modeling without restrictive assumptions.

Findings

Accurately recovers dependence structures in simulations.

Performs robustly under copula misspecification.

Reveals age-varying dependence patterns in health data.

Abstract

Multivariate mixed-type outcomes are difficult to model jointly, and additional complexity arises when both marginal effects and dependence structures vary with a covariate such as age or time. Existing approaches often impose restrictive dependence assumptions or lack sufficient flexibility to accommodate heterogeneous response types in a unified framework. To address this issue, we propose a Bayesian nonparametric framework for multivariate conditional copula regression with varying coefficients. The proposed model combines adaptive spline-based marginal regressions with an infinite mixture of Gaussian copulas whose weights vary with the covariate through a probit stick-breaking process. This construction provides flexible covariate-dependent dependence modeling while avoiding explicit global constraints on functional correlation matrices. We further establish approximation results for the proposed copula representation and develop a Markov chain Monte Carlo algorithm for posterior inference. Simulation studies show accurate recovery under correct specification and robust performance under copula misspecification. In an analysis of the BRFSS 2023 data, the proposed model reveals age-varying marginal effects and dependence patterns among multiple health outcomes, providing a coherent joint view of multimorbidity beyond separate marginal analyses.