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.

翻译：潜在因子模型在社会科学和行为科学中被广泛用作缩放工具，将离散的多变量结果映射到低维连续尺度上。在政治学中，经典因子模型的动态版本已被广泛用于研究多法官法庭中法官偏好的演变。本文提出一种新的动态因子模型，该模型基于潜在圆形空间，能够容纳一种投票行为——即通常被视为处于意识形态光谱两端的法官，在大量分歧意见投票中共同投票。我们将该模型应用于1937年至2021年间美国最高法院非一致裁决的数据，并证明在至少两个时期（1949-1952年和1967-1970年），圆形潜在空间能更好地描述投票模式。此外，我们表明，在圆形模型与欧几里得模型能同等解释数据的时期，关键总结指标（如法官意识形态排名）具有一致性。