Uncertainty-Aware Ideal Point Estimation via Variational EM

TL;DR

This paper introduces a fast, likelihood-based variational EM method for estimating legislators' ideal points and their uncertainties from roll-call data, improving computational efficiency over existing Bayesian and resampling approaches.

Contribution

It develops a novel variational EM algorithm using the Pólya--Gamma identity for efficient ideal point and standard error estimation, addressing computational challenges in large datasets.

Findings

Accurate ideal point estimates comparable to existing methods.

Reliable standard errors approximating Fisher information.

Significantly reduced computational time on large datasets.

Abstract

Roll-call data analysis aims to estimate legislators' ideal points and quantify the associated uncertainty. Existing approaches either rely on Bayesian methods implemented via Markov chain Monte Carlo sampling or focus primarily on point estimation, with uncertainty typically assessed through resampling procedures such as the bootstrap. Consequently, the computational burden of these approaches can become substantial when applied to large roll-call datasets. To address this challenge, we propose a computationally efficient likelihood method for estimating ideal points and their standard errors. Leveraging the P\'{o}lya--Gamma identity, we develop a variational expectation--maximization algorithm for estimating ideal points and introduce a variational Louis' method to approximate the observed Fisher information for standard error estimation. Numerical studies and applications to U.S. congressional roll-call data demonstrate that the proposed method produces accurate ideal point estimates and reliable standard errors while being substantially more computationally efficient than existing approaches.