Vector Vine Copula Models for Multivariate Longitudinal Data

2026-09-16

AI Summary

研究引入了向量可绘制藤蔓（VD-vine）copula模型，以处理多变量纵向数据中的非高斯边缘、非线性动态和变化的响应向量组成问题。

Abstract

Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1,093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence.

Problem

• multivariate longitudinal data
• non-Gaussian margins
• nonlinear dynamics

Innovation

• Vector Drawable Vine (VD-vine) Copula
• Multivariate Marginals
• Linking Vector Copulas
• Recursive Conditional Transports