Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1, and there are many applications for which this constraint is inappropriate. More flexible models have been proposed for this application, most proceeding by supplementing the logistic response function with additional parameters. In this article we extend these models to allow correlated responses and the inclusion of covariates. This is achieved through the \emph{compound logistic regression model}, for which the mean response is a function of several logistic regression functions. This permits a greater variety of models, while retaining the advantages of logistic regression.

翻译：逻辑回归是构建二值响应预测模型最常用的方法。然而，该方法的一个显著缺陷在于逻辑响应函数的渐近线被固定为0和1，而在许多应用场景中这种约束并不适用。针对这一问题，已有研究提出了更灵活的模型，其主流方法是通过为逻辑响应函数引入额外参数来实现。本文进一步扩展了此类模型，使其能够处理相关响应并纳入协变量。这一扩展通过构建\emph{复合逻辑回归模型}实现，该模型的平均响应表现为多个逻辑回归函数的复合函数。该方法在保持逻辑回归优势的同时，显著提升了模型的适用范围与灵活性。