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.

翻译：多元混合类型结果的联合建模存在困难，当边际效应与相依结构均随协变量（如年龄或时间）变化时，问题复杂度进一步增加。现有方法常施加较强的相依性假设，或缺乏在统一框架内容纳异质响应类型的充分灵活性。针对该问题，本文提出一种用于变系数多元条件Copula回归的贝叶斯非参数框架。所提模型将自适应样条边际回归与高斯Copula的无限混合模型相结合，其中混合权重通过probit stick-breaking过程随协变量变化。该构造在避免对函数相关矩阵施加显式全局约束的前提下，实现了灵活的协变量相依相依性建模。进一步地，我们建立了所提Copula表示的逼近性结果，并开发了用于后验推断的马尔可夫链蒙特卡洛算法。模拟研究表明，该模型在Copula正确设定时能准确恢复参数，在Copula误设时仍保持稳健性能。对BRFSS 2023数据的分析显示，所提模型揭示了多个健康结局间的年龄变化边际效应与相依模式，为超越独立边际分析的多病共患联合视角提供了连贯性。