Abstract

This paper proposes new non-model based partial/conditional association measures for ordinal contingency table where the main interest is the association between two ordinal variables of interest, adjusting for the effect of the covariate(s). We first develop a new type of scores for the ordinal variables, subcopula scores, taking into account the ordering of the categories of the variables and derive the subcopula regressions describing the relationships between the ordinal variables and the covariate(s). The proposed subcopula scores and subcopula regressions are obtained from the subcopula which uniquely links the joint distribution for the ordinal variables with their marginal distributions. We then define the new partial/conditional association measures between two ordinal variables to be the correlations between two sets of subcopula scores for them adjusted by the subcopula regressions of two response variables on the covariate(s). We theoretically investigate the properties of the proposed partial/conditional measures and their corresponding estimators. Finally, the performance of the proposed measures are evaluated by simulation studies and real-data examples.

摘要

本文提出了新的基于非模型的序数列联表的部分/条件关联度量，其中主要兴趣是两个感兴趣的序数变量之间的关联，调整协变量的影响。我们首先为序数变量开发一种新型分数，即subcopula 分数，考虑到变量类别的顺序并推导subcopula 回归描述序数变量和协变量之间的关系。所提出的子联结得分和子联结回归是从子联结中获得的，该子联结将序数变量的联合分布与其边缘分布唯一地联系起来。然后，我们将两个序数变量之间新的部分/条件关联测度定义为它们的两组子系分数之间的相关性，并通过协变量上两个响应变量的子系回归进行调整。我们从理论上研究了所提出的部分/条件测量及其相应估计量的属性。最后，通过模拟研究和真实数据示例评估所提出措施的性能。