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Latent factor models are widely used in the social and behavioral science asscaling tools to map discrete multivariate outcomes into low dimensional,continuous scales. In political science, dynamic versions of classical factormodels have been widely used to study the evolution of justice's preferences inmulti-judge courts. In this paper, we discuss a new dynamic factor model thatrelies on a latent circular space that can accommodate voting behaviors inwhich justices commonly understood to be on opposite ends of the ideologicalspectrum vote together on a substantial number of otherwise closely-dividedopinions. 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 twoperiods (1949-1952 and 1967-1970) when voting patterns can be better describedby a circular latent space. Furthermore, we show that, for periods for whichcircular and Euclidean models can explain the data equally well, key summariessuch as the ideological rankings of the justices coincide.

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