🤖 AI Summary
This study addresses the challenge of modeling edge effects and dependence structures that evolve with covariates—such as age—in multivariate responses of mixed types. Existing approaches are often hindered by strong assumptions or insufficient flexibility. To overcome these limitations, this work proposes a Bayesian nonparametric framework that integrates adaptive spline-based marginal regression with a covariate-dependent Gaussian copula infinite mixture model. A probit stick-breaking process is introduced to flexibly capture the covariate-driven evolution of dependence patterns, avoiding restrictive global correlation matrix constraints. The method unifies heterogeneous response types and dynamic dependencies through varying-coefficient copula regression and employs Markov chain Monte Carlo algorithms for posterior inference. Simulation studies demonstrate its accuracy and robustness, while empirical analysis of the 2023 Behavioral Risk Factor Surveillance System (BRFSS) data reveals complex age-varying marginal and dependence structures in health outcomes.
📝 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.