Hostname: page-component-77f85d65b8-g4pgd Total loading time: 0 Render date: 2026-04-17T18:22:31.732Z Has data issue: false hasContentIssue false
  • English
  • Français

Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation

Published online by Cambridge University Press:  04 January 2017

Joseph Bafumi ,
Andrew Gelman ,
David K. Park  and
Noah Kaplan
Joseph Bafumi
Affiliation:
Department of Political Science, Columbia University, New York, NY. e-mail: jb878@columbia.edu
Andrew Gelman
Affiliation:
Department of Statistics and Department of Political Science, Columbia University, New York, NY. e-mail: gelman@stat.columbia.edu, www.stat.columbia.edu/~gelman/
David K. Park
Affiliation:
Department of Political Science, Washington University, St. Louis, MO. e-mail: dpark@artsci.wustl.edu
Noah Kaplan
Affiliation:
Department of Political Science, University of Houston, Houston, TX. e-mail: nkaplan@uh.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
Research Article
Information
Political Analysis , Volume 13 , Issue 2 , Spring 2005 , pp. 171 - 187
Copyright
Copyright © The Author 2005. Published by Oxford University Press on behalf of the Society for Political Methodology 

References

Bafumi, Joseph, Kaplan, Noah, McCarty, Nolan, Poole, Keith, Gelman, Andrew, and Cameron, Charles. 2002. “Scaling the Supreme Court: A Comparison of Alternative Measures of the Justices’ Idealogical Preferences, 1953–2001.” Presented at the 2002 Annual Meeting of the Midwest Political Science Association, Chicago, IL.Google Scholar
Clinton, Joshua. 2001. “Legislators and their Constituencies: Representation in the 106th Congress.” Presented at the 2001 Annual Meeting of the American Political Science Association, San Francisco, CA.Google Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2003. “The Statistical Analysis of Roll Call Data.” Technical Report: Political Methodology Working Papers.Google Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2004. “The Statistical Analysis of Roll Call Data.” American Political Science Review 98: 355–370.CrossRefGoogle Scholar
Fenno, Richard F. 1978. Home Style: House Members in Their Districts. Boston: Little, Brown.Google Scholar
Gelman, Andrew. 2003. Bugs.R: Functions for Calling Bugs from R. Available at http://www.stat.columbia.edu/∼gelman/bugsR.Google Scholar
Gelman, Andrew. 2004. “Exploratory Data Analysis for Complex Models (with Discussion).” Journal of Computational and Graphical Statistics 13: 755–779.Google Scholar
Gelman, Andrew, Carlin, John S., Stern, Hal S., and Rubin, Donald B. 2003. Bayesian Data Analysis. 2nd ed. Boca Raton: Chapman and Hall.Google Scholar
Gelman, Andrew, and Rubin, Donald B. 1992. “Inference from Iterative Simulation using Multiple Sequences with Discussion.” Statistical Science 7: 457–511.Google Scholar
Gilks, Wally R., Richardson, Sylvia, and Spiegelhalter, David J., eds. 1996. Markov Chain Monte Carlo in Practice. London: Chapman & Hall.Google Scholar
Jackman, Simon. 2000. “Estimation and Inference are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8: 307–332.Google Scholar
Jackman, Simon. 2001. “Multidimensional Analysis of Roll Call Data via Bayesian Simulation: Identification, Estimation, and Model Checking.” Political Analysis 9: 227–241.Google Scholar
Lahav, Gallya. 2004. Immigration and Politics in the New Europe. Reinventing Borders. London: Cambridge University Press.Google Scholar
Liu, Chuanahai. 2004. Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression. In Applied Bayesian Modeling and Casual Inference from an Incomplete-Data Perspective, ed. Gelman, Andrew and Meng, X. L. London: Wiley chapter 21.Google Scholar
Liu, Chuanhai, Rubin, Donald B., and Wu, Yingnian. 1998. “Parameter Expansion to Accelerate EM: The PX-EM Algorithm.” Biometrika 85: 755–770.Google Scholar
Loken, Eric. 2004. Multimodality in Mixture Models and Factor Models. In Applied Bayesian Modeling and Causal Inference from an Incomplete-Data Perspective, ed. Gelman, Andrew and Meng, X. L., London: Wiley, chap. 19.Google Scholar
Martin, Anderew D., and Quinn, Kevin M. 2001. “The Dimensions of Supreme Court Decision Making: Again Revisiting The Judicial Mind .” Presented at the 2001 meeting of the Midwest Political Science Association.Google Scholar
Martin, Andrew D., and Quinn, Kevin M. 2002a. “Assessing Preference Change on the U.S. Supreme Court.” Presented at the University of Houston, March 15, 2002.Google Scholar
Martin, Andrew D., and Quinn, Kevin M. 2002b. “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court, 1953–1999.” Political Analysis 10: 134–153.CrossRefGoogle Scholar
Park, David. 2001. “Representation in the American States: The 100th Senate and Their Electorate.” Unpublished working paper.Google Scholar
Poole, Keith T. n.d. “Spatial Models of Parliamentary Voting.” Unpublished manuscript.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1997. Congress: A Political-Economic History of Roll Call Voting. New York: Oxford University Press.Google Scholar
Pregibon, D. 1982. “Resistant Fits for Some Commonly Used Logistic Models with Medical Applications.” Biometrics 38: 485–498.CrossRefGoogle Scholar
R Development Core Team. 2003. R: A Language and Environment for Statistical Computing. Vienna, Austria: R. Foundation for Statistical Computing. Available at http://www.R-Project.org.Google Scholar
Rasch, George. 1980. Probabilistic Models for Some Intelligence and Attainment Tests. Chicago: University of Chicago Press.Google Scholar
Rivers, Douglas. 2003. “Identification of Multidimensional Spatial Voting Models.” Technical Report: Political Methodology Working Papers.Google Scholar
Spiegelhalter, David J., Thomas, Andrew, and Best, Nickey G. 1999. WinBugs Version 1.4. Cambridge: MRC Biostatistics Unit.Google Scholar