Estimation of Association for Multivariate Binary Data

描述（由申请人提供）：多元二元结果之间的相关性和关联的估计在各种环境中都很有趣，包括家庭研究，社区研究，社会网络分析和医疗实践数据分析。本项目涉及这类模型的三个方面；参数空间，估计和回归诊断。首先，我们提出了参数空间的理论研究，以发展对边缘模型的存在性和唯一性问题的理解。这对于此类模型的任何估计、计算和模拟都至关重要。其次，我们最近开发了一种基于正交化残差的新方法，用于构建比值比、矩相关和kappas等关联参数的估计方程。在这个项目中，我们建议通过效率计算在大样本中改进和评估这种方法，并通过模拟研究在小样本中进行评估。我们还建议将这种方法与基于估计方程、交替逻辑回归和伪似然的现有方法进行比较。特别强调适度和可变的簇大小，在这种情况下，现有方法的性能需要进一步研究。第三个主要目标是发展回归诊断的方法和计算工具，包括在关联参数回归模型背景下的杠杆作用和影响。这将在基于正交化残差的估计方程提供的框架中进行。总体而言，该项目将为多元二元结果的关联建模提供新的理解、知识、方法和工具，并最终更好地分析来自医学、公共卫生和社会研究的此类数据。

DESCRIPTION (provided by applicant): Estimation of correlation and association between multivariate binary outcomes is of interest in various settings including family studies, community studies, analysis of social networks and analysis of medical practice data. This project deals with three aspects of such models; the parameter space, estimation and regression diagnostics. First, we propose a theoretical study of the parameter space to develop an understanding of issues of existence and uniqueness of marginal models. This is pivotal to any estimation, computation and simulation of such models. Second, we have recently developed a new method based on orthogonalized residuals for constructing estimating equations for estimation of association parameters such as odds ratios, moment correlations and kappas. In this project we propose to refine and evaluate this approach in large samples via efficiency calculations and in small samples via simulation studies. We also propose to compare this approach to existing methods based on estimating equations, alternating logistic regressions and pseudo-likelihoods. Special emphasis is given to moderate and variable cluster sizes, a case where the performance of existing methods needs further investigation. The third major aim is the development of methodology and computational tools for regression diagnostics including leverage and influence in the context of regression models for association parameters. This will be carried out in the framework provided by the estimating equations based on orthogonalized residuals. Overall, this project will develop new understanding, knowledge, methods and tools for modeling association in multivariate binary outcomes, and eventually lead to better analysis of such data from medical, public health and social studies.