A Compound Logistic Regression Model for Binary Responses

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.