Song Peter X-K, Li Mingyao, Yuan Ying
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Biometrics. 2009 Mar;65(1):60-8. doi: 10.1111/j.1541-0420.2008.01058.x. Epub 2008 May 28.
This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.
本文涉及一种用于相关数据分析的新的联合建模方法。利用高斯 copula，我们提出了一种统一且灵活的机制，将单独的一维广义线性模型（GLM）整合到连续、离散和混合相关结果的联合回归分析中。这本质上导致了单变量 GLM 理论的多变量类似物，从而在回归系数估计中提高了效率。联合概率模型的可用性使我们能够进行完整的最大似然推断。数值示例集中在离散相关数据的回归模型上，包括多维逻辑回归模型以及混合正态和二元结果的联合模型。在模拟研究中，将所提出的基于 copula 的联合模型与流行的广义估计方程进行了比较，广义估计方程是一种用于连接单变量 GLM 的基于矩的估计方程方法。文中使用了两个实际数据示例进行说明。
