关于二元连接函数的预测性质
On the Predictive Properties of Binary Link Functions
摘要：
本文提供了一个理论和计算的理由，长期以来一直声称，在二进制分类中经常使用的概率和logit链接函数的相似性。尽管这两个链接功能之间的强烈相似性得到了广泛的认可，但很少有研究人员（如果有的话）专门花时间进行正式的研究，旨在建立和确定所有方面的相似性和差异。本文提出了一种基于链接函数的二元回归模型的结构等价和预测等价的定义，并探讨了它们相似或不相似的各种方式。从预测分析的角度来看，事实证明，不仅probit和logit完全预测一致，而且其他链接函数，如cauchit和互补log log，具有非常高的预测等效性。在本文中，模拟和现实生活中的例子证明了所有的等价结果，我们从理论上证明。
英文摘要：
This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have dedicated time to carry out a formal study aimed at establishing and characterizing firmly all the aspects of the similarities and differences. This paper proposes a definition of both structural and predictive equivalence of link functions-based binary regression models, and explores the various ways in which they are either similar or dissimilar. From a predictive analytics perspective, it turns out that not only are probit and logit perfectly predictively concordant, but the other link functions like cauchit and complementary log log enjoy very high percentage of predictive equivalence. Throughout this paper, simulated and real life examples demonstrate all the equivalence results that we prove theoretically.
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。
