Dynamic Factor Models for Binary Data in Circular Spaces: An Application to the U.S. Supreme Court

TL;DR

This paper introduces a novel dynamic factor model with a circular latent space to analyze voting behaviors in the U.S. Supreme Court, revealing that a circular model better captures the data than traditional linear models.

Contribution

It proposes a new dynamic factor model using a circular latent space specifically designed for binary voting data in courts, improving the understanding of ideological alignments.

Findings

Circular latent space better fits Supreme Court voting data

Model captures complex ideological relationships among justices

Voting patterns show cyclical ideological shifts over time

Abstract

Latent factor models are widely used in the social and behavioral science as scaling tools to map discrete multivariate outcomes into low dimensional, continuous scales. In political science, dynamic versions of classical factor models have been widely used to study the evolution of justices' preferences in multi-judge courts. In this paper, we discuss a new dynamic factor model that relies on a latent circular space that can accommodate voting behaviors in which justices commonly understood to be on opposite ends of the ideological spectrum vote together on a substantial number of otherwise closely-divided opinions. We apply this model to data on non-unanimous decisions made by the U.S. Supreme Court between 1937 and 2021, and show that, for most of this period, voting patterns can be better described by a circular latent space.