Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation

Logistic regression models have been used in political science for estimating ideal points of legislators and Supreme Court justices. These models present estimation and identifiability challenges, such as improper variance estimates, scale and translation invariance, reflection invariance, and issues with outliers. We address these issues using Bayesian hierarchical modeling, linear transformations, informative regression predictors, and explicit modeling for outliers. In addition, we explore new ways to usefully display inferences and check model fit.