Logistic Regression Based on Individual-Level Predictors and Aggregate-Level Responses

Abstract

We propose estimation methods to conduct logistic regression based on individual-level predictors and aggregate-level responses. We derive the likelihood of logistic models in this situation and proposed estimators with different optimization methods. Simulation studies have been conducted to evaluate and compare the performance of the different estimators. A real data-based study has been conducted to illustrate the use of our estimators and compare the different estimators.

Keywords

• Poisson binomial distribution
• logistic regression
• data aggregation
• likelihood
• numerical optimization