Efficient EM Estimation for the Pogit Model via Polya-Gamma Augmentation

The Poisson-logistic (pogit) model is widely used for count data with latent intensities, with applications including under-reporting correction and share-of-wallet estimation, yet existing estimation methods do not scale well to large datasets. We propose a new expectation-maximization (EM) algorithm for the standard pogit model based on Polya-Gamma data augmentation, which yields a conditionally Gaussian complete-data likelihood with closed-form EM-updates. The resulting EM algorithm has low per-iteration cost and naturally accommodates computational enhancements, including quasi-Newton acceleration and mini-batch implementations. These features enable efficient inference on datasets with millions of observations. Simulation studies and real-data applications demonstrate substantial computational improvements without loss of statistical accuracy, and comparisons with direct maximum-likelihood optimization routines show that the proposed method provides a scalable and competitive alternative for large-scale pogit estimation.