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

## TL;DR

The paper introduces a new and efficient method for estimating parameters in the pogit model using a Polya-Gamma augmentation approach, enabling faster and scalable analysis of large count datasets.

## Contribution

A novel EM algorithm for the pogit model using Polya-Gamma augmentation, enabling efficient and scalable estimation for large datasets.

## Key findings

- The proposed EM algorithm has low per-iteration cost and supports computational enhancements like mini-batch implementations.
- Simulation and real-data applications show substantial computational improvements without loss of statistical accuracy.
- The method is a scalable and competitive alternative to existing maximum-likelihood optimization routines for large-scale pogit estimation.

## Abstract

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.