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Political Analysis Advance Access originally published online on March 1, 2005
Political Analysis 2005 13(2):171-187; doi:10.1093/pan/mpi010
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Political Analysis Vol. 13 No. 2, © The Author 2005. Published by Oxford University Press on behalf of the Society for Political Methodology. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation

Joseph Bafumi

Department of Political Science, Columbia University, New York, NY
e-mail: jb878{at}columbia.edu

Andrew Gelman

Department 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. Park

Department of Political Science, Washington University, St. Louis, MO
e-mail: dpark{at}artsci.wustl.edu

Noah Kaplan

Department of Political Science, University of Houston, Houston, TX
e-mail: nkaplan{at}uh.edu

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.


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