Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation

Andrew GelmanDepartment of Statistics and Department of Political Science, Columbia University, New York, NY e-mail: gelman{at}stat.columbia.edu, www.stat.columbia.edu/~gelman/David K. ParkDepartment of Political Science, Washington University, St. Louis, MO e-mail: dpark{at}artsci.wustl.eduNoah KaplanDepartment of Political Science, University of Houston, Houston, TX e-mail: nkaplan{at}uh.edu Logistic regression models have been used in political sciencefor estimating ideal points of legislators and Supreme Courtjustices. These models present estimation and identifiabilitychallenges, such as improper variance estimates, scale and translationinvariance, reflection invariance, and issues with outliers.We address these issues using Bayesian hierarchical modeling,linear transformations, informative regression predictors, andexplicit modeling for outliers. In addition, we explore newways to usefully display inferences and check model fit.