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

We present a new partition-valued Markov chain for modeling latent temporal clustering. The family of Markov chains we consider satisfies notable statistical properties, including exchangeability, consistency under subsampling, and reversibility with respect to a tractable class of two-parameter partition models. These properties endow our model with a robustness to missing data, choice of labels, and changes in the sample over time. When combined with an appropriate model for response data, exchangeability and consistency give rise to the stronger model properties of label equivariance and non-interference, respectively. All of these properties are desirable for statistical applications, as they make model inferences easily interpretable and straightforward. We demonstrate these and other aspects with a detailed analysis of voting data in the Supreme Court over the period 1946–2012.