多元二元分布的方向可塌缩参数化
Directionally collapsible parameterizations of multivariate binary distributions
摘要：
比值比和对数线性参数是不可折叠的，这意味着将一个变量纳入分析或从中省略一个变量，可能会改变其余变量之间的关联强度。甚至连联想的方向也可能颠倒过来，这一事实经常被称为辛普森悖论。如果这种反转不能发生，则关联参数是方向可折叠的。本文研究了方向可塌的组合参数的存在性。它表明，受两个简单的假设，没有参数的关联，它只依赖于条件分布，像比值比，可以是定向崩溃。主要结果是，每个方向可折叠的关联参数给出了相同的关联方向的细胞概率的线性对比。处理辛普森悖论的含义是，在任何表中，只有一种方法将方向与关联联系起来，因此悖论永远不会发生
英文摘要：
Odds ratios and log-linear parameters are not collapsible, meaning that including a variable into the analysis or omitting one from it, may change the strength of association among the remaining variables. Even the direction of association may be reversed, a fact that is often discussed under the name of Simpson's paradox. A parameter of association is directionally collapsible, if this reversal cannot occur. The paper investigates the existence of parameters of association which are directionally collapsible. It is shown, that subject to two simple assumptions, no parameter of association, which depends only on the conditional distributions, like the odds ratio does, can be directionally collapsible. The main result is that every directionally collapsible parameter of association gives the same direction of association as a linear contrast of the cell probabilities does. The implication for dealing with Simpson's paradox is that there is exactly one way to associate direction with the association in any table, so that the paradox never occurs
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
