A Sparse Factor-Analytic Probit Model for Congressional Voting Patterns

This paper adapts sparse factor models for exploring covariation in multivariate binary data, with an application to measuring latent factors in U.S. Congressional roll call voting patterns. This straightforward modification provides two advantages over traditional factor analysis of binary data. First, a sparsity prior can be used to assess the evidence that a given factor loading may be exactly zero, realizing a principled unification of exploratory and confirmatory factory analysis. Second, incorporating sparsity into existing factor-analytic probit models effects a favorable bias–variance tradeoff in estimating the covariance matrix of the multivariate Gaussian latent variables. Posterior summaries from this model applied to the roll-call data provide novel metrics of partisanship of a given Senate.