Estimating heterogeneous graphical models for discrete data with an application to roll call voting

TL;DR

This paper introduces a joint estimation method for multiple discrete graphical models that captures shared and unique structures across different categories, demonstrated on U.S. Senate voting data.

Contribution

The paper develops a novel group-penalized Markov graphical model for estimating heterogeneous networks with shared structure in discrete data.

Findings

Successfully applied to U.S. Senate voting data revealing issue-specific and bipartisan networks.

Proven consistency in parameter estimation and model selection.

Performed well in simulations, demonstrating numerical robustness.

Abstract

We consider the problem of jointly estimating a collection of graphical models for discrete data, corresponding to several categories that share some common structure. An example for such a setting is voting records of legislators on different issues, such as defense, energy, and healthcare. We develop a Markov graphical model to characterize the heterogeneous dependence structures arising from such data. The model is fitted via a joint estimation method that preserves the underlying common graph structure, but also allows for differences between the networks. The method employs a group penalty that targets the common zero interaction effects across all the networks. We apply the method to describe the internal networks of the U.S. Senate on several important issues. Our analysis reveals individual structure for each issue, distinct from the underlying well-known bipartisan structure common to all categories which we are able to extract separately. We also establish consistency of the proposed method both for parameter estimation and model selection, and evaluate its numerical performance on a number of simulated examples.