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

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 justice's 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 the U.S. Supreme Court between 1937 and 2021, and show that there are at least two periods (1949-1952 and 1967-1970) when voting patterns can be better described by a circular latent space. Furthermore, we show that, for periods for which circular and Euclidean models can explain the data equally well, key summaries such as the ideological rankings of the justices coincide.