An expectation-maximization algorithm for logistic regression based on individual-level predictors and aggregate-level response

Logistic regression is widely used in complex data analysis. When predictors are at individual level and the response at aggregate level, logistic regression can be estimated using the Maximum Likelihood Estimation (MLE) method with the joint likelihood function formed by Poisson binomial distributions. When directly maximizing the complicated likelihood function, the performance of MLE will worsen as the number of predictors increases. In this article, we propose an expectation-maximization (EM) algorithm to avoid the direct maximization of the complicated likelihood function. Simulation studies have been conducted to evaluate the performance of our EM estimator compared to different estimators proposed in the literature. Two real data-based studies have been conducted to illustrate the use of the different estimators. Our EM estimator proves efficient f or t he l ogistic r egression problem with an aggregate-level response and individual-level predictors.