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Multidimensional Analysis of Roll Call Data via Bayesian Simulation: Identification, Estimation, Inference, and Model Checking

Published online by Cambridge University Press:  04 January 2017

Simon Jackman
Simon Jackman*
Affiliation:
Department of Political Science, Stanford University, Stanford, California 94305-6044. e-mail: [email protected]
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Abstract

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Vote-specific parameters are often by-products of roll call analysis, the primary goal being the measurement of legislators' ideal points. But these vote-specific parameters are more important in higher-dimensional settings: prior restrictions on vote parameters help identify the model, and researchers often have prior beliefs about the nature of the dimensions underlying the proposal space. Bayesian methods provide a straightforward and rigorous way for incorporating these prior beliefs into roll call analysis. I demonstrate this by exploiting the close connections among roll call analysis, item-response models, and “full-information” factor analysis. Vote-specific discrimination parameters are equivalent to factor loadings, and as in factor analysis, they (1) enable researchers to discern the substantive content of the recovered dimensions, (2) can be used for assessing dimensionality and model checking, and (3) are an obvious vehicle for introducing and testing researchers' prior beliefs about the dimensions. Bayesian simulation facilitates these uses of discrimination parameters, by simplifying estimation and inference for the massive number of parameters generated by roll call analysis.

Type
Research Article
Information
Political Analysis , Volume 9 , Issue 3 , January 2001 , pp. 227 - 241
Copyright
Copyright © 2001 by the Society for Political Methodology 

References

Albert, James. 1992. “Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling.” Journal of Educational Statistics 17: 251–269.CrossRefGoogle Scholar
Bock, R. D., and Aitken, M. 1981. “Marginal Maximum Likelihood Estimation of Item Parameters: Application of An EM Algorithm.” Psychometrika 46: 443–59.CrossRefGoogle Scholar
Bock, R. D., Gibbons, R., and Muraki, E. J. 1988. “Full Information Item Factor Analysis.” Applied Psychological Measurement 12: 261–280.Google Scholar
Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. New York: Wiley.Google Scholar
Chang, H. H., and Stout, W. 1993. “The Asymptotic Posterior Normality of the Latent Trait in an IRT Model.” Psychometrika 58: 37–52.CrossRefGoogle Scholar
Clinton, Joshua D., and Mierowitz, Adam. 2001. “Agenda Constrained Legislator Ideal Points and the Spatial Voting Model.” Political Analysis 9: 242–259.CrossRefGoogle Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2000. “The Statistical Analysis of Legislative Behavior: A Unified Approach,” Paper presented to the Southern California Area Methodology Program, University of California, Santa Barbara, May 12–13.Google Scholar
Enelow, J., and Hinich, M. 1984. The Spatial Theory of Voting: An Introduction. New York: Cambridge University Press.Google Scholar
Heckman, James J., and Snyder, James M. 1997. “Linear Probabilty Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” RAND Journal of Economics 28: S142–S189.CrossRefGoogle Scholar
Hyndman, Rob J. 1996. “Computing and Graphing Highest Density Regions.” American Statistician 50: 120–126.Google Scholar
Jackman, Simon. 2000. “Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8: 307–332.CrossRefGoogle Scholar
Johnson, Valen E., and Albert, James H. 1999. Ordinal Data Modeling. New York: Springer-Verlag.Google Scholar
Loader, C. 1999. Local Regression and Likelihood. New York: Springer.Google Scholar
Londregan, John. 2000a. “Estimating Legislators’ Preferred Points.” Political Analysis 8: 35–56.Google Scholar
Londregan, John. 2000b. Legislative Institutions and Ideology in Chile's Democratic Transition. New York: Cambridge University Press.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35: 228–278.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
Reckase, Mark D. 1997. “The Past and Future of Multidimensional Item Response Theory.” Applied Psychological Measurement 21: 25–36.CrossRefGoogle Scholar
Takane, Yoshio, and de Leeuw, Jan. 1987. “On the relationship between item response theory and factor analysis of discreteized variables.” Psychometrika 52: 393–408.CrossRefGoogle Scholar
Weisberg, Herbert F. 1978. “Evaluating Theories of Congressional Roll-Call Voting.” American Journal of Political Science 22: 554–577.Google Scholar