The Measurement of Association in a Contingency Table: Three Extensions of the Cross-Ratios and Metrics Methods
列联表关联度量：交叉比与度量方法的三项扩展AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究一般列联表关联度量，没有明确的离散选择行为模型、因果效应或其他所列领域证据。
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列联表关联度量：交叉比与度量方法的三项扩展
- 研究问题
- 如何度量三维列联表的不同关联结构，并将交叉比方法扩展到含删除单元的二维表及两个列联表之间的关联比较？
- 方法与思路
- 作者通过交叉比、等价类与类上的度量区分三维表的四种关联，并讨论特定度量的渐近后验分布和删格情形。
- 材料陈述的贡献
- 摘要称，论文扩展了关联度量框架，说明不同三维关联类型的关系，并处理删格列联表及跨表关联比较问题。
- 阅读关注点
- 应核对四种关联的定义、等价类和度量的构造，特别查看删除单元的含义及渐近后验结论所需条件。
- 阅读边界
- 仅依据所给 Crossref 摘要，无法确定完整度量公式、先验设定或删格限制；关联度量不自动具有因果解释。
原文摘要
Summary The methods of cross-ratios, equivalence classes and metrics that were introduced in a previous paper (Altham 1970) are extended to three further problems. First the interdependence of the rows, columns and layers of a three-way contingency table is discussed. There are essentially four different types of association to be considered: the complete dependence of rows, columns and layers, the dependence of rows and columns conditional on a given layer, the dependence of the two classifications “rows-and-columns” and layers, and the second-order interaction of rows, columns and layers. The relations between these four types of association are discussed in terms of the appropriate equivalence classes. In order to obtain measures of dependence of rows, columns and layers, metrics are defined on the equivalence classes. Some examples of metrics are given. The consideration of three-way tables is concluded by a discussion of the asymptotic posterior distributions of certain special metrics, which are suggested by the work of Lindley (1964), and Plackett (1962). Cross-ratios methods are also extended to the problem of measuring association in a two-way table with some cells deleted. The paper is concluded by consideration of the problem of comparing associations in two distinct contingency tables, some of whose cells may be deleted.