论文标题
图片的价值一千个单词：以经验可能性的逻辑回归模型中可视化n维重叠
A Picture's Worth a Thousand Words: Visualizing n-dimensional Overlap in Logistic Regression Models with Empirical Likelihood
论文作者
论文摘要
在本说明中，从灵敏度测试的角度引入了二进制响应模型的最大似然估计的存在和唯一性的条件。众所周知的Silvapulle条件被翻译为经验可能性最大化，现有R代码可以使评估重叠状态的过程机械化。翻译转移了重叠的含义，这是由两个presstrestor群体的几何特性定义的，从其凸锥的交叉点是非空的，对于更易于理解的要求，其差异的凸面包含零。该代码用于通过检查最小重叠结构并将其分类的尺寸少于四个，以揭示重叠的特征。提供了重叠的最小较高维度结构的规则。补充材料可在线提供。
In this note, conditions for the existence and uniqueness of the maximum likelihood estimate for multidimensional predictor, binary response models are introduced from a sensitivity testing point of view. The well known condition of Silvapulle is translated to be an empirical likelihood maximization which, with existing R code, mechanizes the process of assessing overlap status. The translation shifts the meaning of overlap, defined by geometrical properties of the two-predictor groups, from the intersection of their convex cones is non-empty to the more understandable requirement that the convex hull of their differences contains zero. The code is applied to reveal the character of overlap by examining minimal overlapping structures and cataloging them in dimensions fewer than four. Rules to generate minimal higher dimensional structures which account for overlap are provided. Supplementary materials are available online.
