A hidden Markov model for latent temporal clustering with application to ideological alignment in the U.S. Supreme Court

Abstract

An alternative approach to modeling latent time-varying sequences of clusters demonstrates certain benefits over existing methods for analyzing Supreme Court voting data. The family of Markov chains presented here satisfies important statistical properties, including exchangeability, consistency under subsampling, and reversibility with respect to a tractable class of two-parameter partition models. These properties make the model robust to missing data, choice of labels, and changes in the sample over time. When combined with an appropriate model for the response, exchangeability and consistency give rise to the stronger model properties of label equivariance and non-interference, respectively, which together make inferences readily interpretable. These and other aspects of the approach are illustrated with a detailed analysis of voting data in the Supreme Court over the period 1946–2012. The results of this analysis agree with what is known about the Court’s behavior during this period of time. In some cases, this approach detects aspects of the Court that other quantitative analyses, such as Martin–Quinn scores, do not.