Uncertainty-Aware Ideal Point Estimation via Variational EM with Pólya-Gamma identity
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 Pólya-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.
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BibTeX
@misc{seo2026uncertaintyaware,
title = {{Uncertainty-Aware Ideal Point Estimation via Variational EM with Pólya-Gamma identity}},
author = {Kwangok Seo and Youngjo Lee and Jong Hee Park and Xinlei Wang and Johan Lim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.19591},
eprint = {2605.19591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19591},
}
RIS
TY - UNPB
TI - Uncertainty-Aware Ideal Point Estimation via Variational EM with Pólya-Gamma identity
AU - Kwangok Seo
AU - Youngjo Lee
AU - Jong Hee Park
AU - Xinlei Wang
AU - Johan Lim
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2605.19591
UR - https://arxiv.org/abs/2605.19591
AB - 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 Pólya-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.
ER -