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Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation

Published online by Cambridge University Press:  04 January 2017

Simon Jackman
Simon Jackman*
Affiliation:
Department of Political Science, Stanford University, Stanford, California 94305-2044. e-mail: jackman@stanford.edu, http://jackman.stanford.edu
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Abstract

Bayesian simulation is increasingly exploited in the social sciences for estimation and inference of model parameters. But an especially useful (if often overlooked) feature of Bayesian simulation is that it can be used to estimate any function of model parameters, including “auxiliary” quantities such as goodness-of-fit statistics, predicted values, and residuals. Bayesian simulation treats these quantities as if they were missing data, sampling from their implied posterior densities. Exploiting this principle also lets researchers estimate models via Bayesian simulation where maximum-likelihood estimation would be intractable. Bayesian simulation thus provides a unified solution for quantitative social science. I elaborate these ideas in a variety of contexts: these include generalized linear models for binary responses using data on bill cosponsorship recently reanalyzed in Political Analysis, item—response models for the measurement of respondent's levels of political information in public opinion surveys, the estimation and analysis of legislators' ideal points from roll-call data, and outlier-resistant regression estimates of incumbency advantage in U.S. Congressional elections

Information

Type
Research Article
Information
Political Analysis , Volume 8 , Issue 4 , 18 July 2000 , pp. 307 - 332
Copyright
Copyright © 2000 by the Society for Political Methodology 

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References

Albert, James H., and Chib, Siddhartha. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” Journal of the American Statistical Association 88: 669–679.CrossRefGoogle Scholar
Albert, James H., and Chib, Siddhartha. 1995. “Bayesian Residual Analysis for Binary Response Regression Models.” Biometrika 82: 747–759.CrossRefGoogle Scholar
Alvarez, R. Michael, and Brehm, John. 1995. “American Ambivalence Towards Abortion Policy: Devlopment of a Heteroskedastic Probit Model of Competing Values.” American Journal of Political Science 39: 1055–1082.CrossRefGoogle Scholar
Bailey, Michael, and Rivers, Douglas. 1997. “Ideal Point Estimation: A Survey.” Paper presented at the Annual Meetings of the Midwest Political Science Association, Chicago.Google Scholar
Bartels, Larry M. 1993. “Messages Received: The Political Impact of Media Exposure.” American Political Science Review 87: 267–285.CrossRefGoogle Scholar
Beck, Nathaniel, and Jackman, Simon. 1998. “Beyond Linearity by Default: Generalized Additive Models.” American Journal of Political Science 42: 596–627.CrossRefGoogle Scholar
Bock, R. D., and Aitken, M. 1981. “Marginal Maximum Likelihood Estimation of Item Parameters: Application of An EM Algorithm.” Psychometrika 46: 443–459.CrossRefGoogle Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2000. “The Statistical Analysis of Legislative Behavior: A Unified Approach.” Paper presented at the Southern California Area Methodology Program, University of California, Santa Barbara, May 12–13, 2000.Google Scholar
Gelman, Andrew, and King, Gary. 1990. “Estimating Incumbency Advantage Without Bias.” American Journal of Political Science 34: 1142–1164.CrossRefGoogle Scholar
Geweke, J. 1993. “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 8: S19–S40.CrossRefGoogle Scholar
Herron, Michael C. 1999. “Postestimation Uncertainty in Limited Dependent Variable Models.” Political Analysis 8: 83–98.CrossRefGoogle Scholar
Jackman, Simon. 1994. ”Measuring Electoral Bias: Australia, 1949–1993.” British Journal of Political Science 24: 319–357.CrossRefGoogle Scholar
Jackman, Simon. 2000. “Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.” American Journal of Political Science 44: 375–404.CrossRefGoogle Scholar
Johnson, Valen E., and Albert, James H. 1999. Ordinal Data Modeling. New York: Springer-Verlag.CrossRefGoogle Scholar
Katz, Jonathan N., and King, Gary. 1999. “A Statistical Model for Multiparty Electoral Data.” American Political Science Review 93: 15–32.CrossRefGoogle Scholar
King, Gary. 1989. Unifying Political Methodology. New York: Cambridge University Press.Google Scholar
King, Gary, Honaker, James, Joesph, Anne, and Scheve, Kenneth. 1998. “Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation,” Typescript. Cambridge, MA: Department of Government, Harvard University. http://GKing.Harvard.Edu/preprints.shtml.Google Scholar
King, Gary, Tomz, Michael, and Wittenberg, Jason. 2000. “Making the Most of Statistical Analysis: Improving Interpretation and Presentation.” American Journal of Political Science 44: 341–355.CrossRefGoogle Scholar
Krehbiel, Keith. 1995. “Cosponsors and Wafflers from A to Z.” American Journal of Political Science 39: 906–923.CrossRefGoogle Scholar
Ladha, Krishna. 1991. “A Spatial Model of Voting with Perceptual Error.” Public Choice 78: 43–64.Google Scholar
Londregan, John. 2000. “Estimating Legislator's Preferred Points.” Political Analysis 8: 35–56.CrossRefGoogle Scholar
Lord, F. M. 1975. Evaluation with Artificial Data of a Procedure for Estimating Ability and Item-Characteristic Curve Parameters. Princeton, NJ: Educational Testing Service.Google Scholar
Metropolis, N., and Ulam, S. 1949. “The Monte Carlo Method.” Journal of the American Statistical Association 44: 335–341.CrossRefGoogle ScholarPubMed
Mondak, Jeffrey J. 2000. “Reconsidering the Measurement of Political Knowledge.” Political Analysis 8: 57–82.CrossRefGoogle Scholar
Mooney, Christopher Z. 1997. Monte Carlo Simulation. Thousand Oaks, CA: Sage.CrossRefGoogle Scholar
Poole, Keith T., and Rosenthal, Howard. 1997. Congress: A Political-Economic History of Roll Call Voting. New York: Oxford University Press.Google Scholar
Rubin, Donald B. 1987. Multiple Imputation for Nonresponse in Surveys. New York: Wiley.CrossRefGoogle Scholar
Schafer, J. L. 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall.CrossRefGoogle Scholar
Sniderman, Paul M., and Theriault, Sean M. 1999. “The Structure of Political Argument and the Logic of Issue Framing.” Presented at the International Society of Political Psychology, Amsterdam.Google Scholar
Venables, William N., and Ripley, Brian D. 1999. Modern Applied Statistics with S-PLUS, 3rd ed. New York: Springer-Verlag.CrossRefGoogle Scholar
Western, Bruce. 1995. “Concepts and Suggestions for Robust Regression Analysis.” American Journal of Political Science 39: 786–817.CrossRefGoogle Scholar
Zaller, John R. 1992. The Nature and Origins of Mass Opinion. New York: Cambridge University Press.CrossRefGoogle Scholar