Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4.
Stat Med. 2011 Jan 30;30(2):175-85. doi: 10.1002/sim.4087. Epub 2010 Oct 20.
This paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas. Our approach entails specifying marginal regression models for the outcomes, and combining them via a copula to form a joint model. Specifically, we propose marginal regression models (e.g. generalized linear models) to link the outcomes' marginal means to covariates. To account for associations between outcomes, we adopt the Gaussian copula to indirectly specify their joint distributions. Our approach has two advantages over current methods: one, regression parameters in models for both outcomes are marginally meaningful, and two, the association is 'margin-free', in the sense that it is characterized by the copula alone. By assuming a latent variable framework to describe discrete outcomes, the copula used still uniquely determines the joint distribution. In addition, association measures between outcomes can be interpreted in the usual way. We report results of simulations concerning the bias and efficiency of two likelihood-based estimation methods for the model. Finally, we illustrate the model using data on burn injuries.
本文关注的是使用 Copulas 构建的相关混合离散和连续结果的回归模型。我们的方法需要为结果指定边缘回归模型，并通过 Copula 将它们组合起来形成联合模型。具体来说，我们提出了边缘回归模型（例如广义线性模型），将结果的边缘均值与协变量联系起来。为了说明结果之间的相关性，我们采用高斯 Copula 来间接指定它们的联合分布。与当前方法相比，我们的方法有两个优势：一是两个结果的模型中的回归参数在边缘上是有意义的，二是相关性是“无边缘的”，也就是说，它仅由 Copula 来描述。通过假设描述离散结果的潜在变量框架，使用的 Copula 仍然可以唯一地确定联合分布。此外，还可以以通常的方式解释结果之间的关联度量。我们报告了关于模型两种基于似然的估计方法的偏差和效率的模拟结果。最后，我们使用烧伤数据来说明该模型。
