Estimating Vote Choice in U.S. Elections with Approximate Poisson-Binomial Logistic Regression

We develop an approximate method for maximum likelihood estimation in Poisson-Binomial Logistic regression. The resulting approximate log-likelihood is generally non-convex but easy to optimize in practice. We investigate the geometry of the likelihood and propose simple but effective optimization procedures. We use these methods to fit logistic regressions in all statewide U.S. elections between 2016 and 2020, a total of 544 offices and over 1.75 billion votes.