🤖 AI Summary
Traditional logistic regression models are constrained by fixed asymptotes at 0 and 1, limiting their ability to capture complex relationships between responses and covariates as well as dependencies among binary outcomes. This work proposes a composite logistic regression model that constructs a more flexible mean response structure by combining multiple logistic functions. The approach retains model interpretability while overcoming the restrictive asymptotic boundaries inherent in standard logistic regression. By naturally incorporating covariates and effectively modeling correlated binary responses, the proposed method substantially extends the applicability and expressive capacity of logistic regression in practical settings.
📝 Abstract
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.