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Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach

  • Michael Bailey (a1)


Many conventional ideal point estimation techniques are inappropriate when only a limited number of votes are available. This paper presents a covariate-based random-effects Bayesian approach that allows scholars to estimate ideal points based on fewer votes than required for fixed-effects models. Using covariates brings more information to bear on the estimation; using a Bayesian random-effects approach avoids incidental parameter problems. Among other things, the method allows us to estimate directly the effect of covariates such as party on preferences and to estimate standard errors for ideal points. Monte Carlo results, an empirical application, and a discussion of further applications demonstrate the usefulness of the method.



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Anderson, E. 1972. “The Numerical Solution of a Set of Conditional Estimation Equations.” Journal of the Royal Statistical Society, Series B 34: 4254.
Bailey, Michael. 2001. “Quiet Influence: The Representation of Diffuse Interests on Trade Policy, 1983–1994.” Legislative Studies Quarterly 26: 4580.
Bailey, Michael, and Chang, Kelly. 2000. “Mimicry and Extremism: The Inter-Institutional Politics of Supreme Court Appointments.” Paper presented at the Annual Meeting of the Political Methodology Association, Los Angeles.
Bailey, Michael, and Rivers, Doug. 1997. “Ideal Point Estimation: A Survey.” Paper presented at the Midwest Political Science Association Annual Meeting, Chicago.
Baker, Frank. 1992. Item Response Theory. New York: Marcel Dekker.
Birnbaum, A. 1968. “Some Latent Trait Models and Their Use in Inferring an Examinee's Ability.” In Statistical Theories of Mental Test Scores. eds. Lord, Frederic and Novick, M. R. Reading, MA: Addision-Wesley.
Bock, R. Darrell, and Aitkin, M. 1981. “Marginal Maximum Likelihood Estimation of Item Parameters: An Application of an EM Algorithm.” Psychometrika 46: 443459.
Chamberlain, Gary. 1980. “Analysis of Covariance with Qualitative Data.” Review of Economic Studies 47: 225238.
Clinton, Joshua, Jackman, Simon, and Rivers, Doug. 2000. “The Statistical Analysis of Legislative Behavior: A Unified Approach.” Paper presented at the Summer Methodology Meetings, Los Angeles.
Dempster, A. P., Laird, N. M., and Rubin, Donald. 1977. “Maximum Likelihood from Incomplete Data via the EM Algorithm (with Discussion).” Journal of the Royal Statistical Society, Series B 39: 138.
Drasgow, Fritz. 1989. “An Evaluation of Marginal Maximum Likelihood Estimation for the Two-Parameter Logistic Model.” Applied Psychological Measurement 13: 7790.
Greene, William. 1997. Econometric Analysis, 3rd ed. New York: Macmillan.
Groseclose, Timothy, Levitt, Steven, and Snyder, James. 1999. “Comparing Interest Group Scores Across Time and Chambers: Adjusted ADA Scores for the U.S. Congress.” American Political Science Review 93: 3350.
Haberman, S. J. 1977. “Maximum Likelihood Estimates in Exponential Response Models.” Annals of Statistics 5: 815841.
Heckman, James, and Snyder, James. 1997. “Linear Probability Models of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” RAND Journal of Economics 28 (Special Issue): S142S189.
Herron, Michael. 2000. “Cutpoint-Adjusted Interest Group Ratings.” Political Analysis 8: 346366.
Jackman, Simon. 2000a. “Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8: 307332.
Jackman, Simon. 2000b. “Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.” American Journal of Political Science 44: 369398.
King, Gary, Honaker, James, Joseph, Anne, and Scheve, Kenneth. 2001. “Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation.” American Political Science Review 95: 4970.
Krehbiel, Keith. 1993. “Constituency Characteristics and Legislative Preferences.” Public Choice 76: 2137.
Krehbiel, Keith, and Rivers, Douglas. 1988. “The Analysis of Committee Power.” American Journal of Political Science 32: 11511174.
Lewis, Jefrey. 1998. “Estimating Voter Preference Distributions from Individual-Level Voting Data (with Application to Split-Ticket Voting).” Paper presented at the Annual Meeting of the American Political Science Association, Boston.
Londregan, John. 2000. “Estimating Legislators’ Preferred Points.” Political Analysis 8: 3556.
Maddala, G. S. 1987. “Limited Dependent Variable Models Using Panel Data.” Journal of Human Resources 22: 305348.
McLachlan, Geoffrey, and Krishnan, Thriyambakam. 1997. The EM Algorithm and Extensions. New York: Wiley-Interscience.
Mislevy, Robert. 1987. “Exploiting Auxiliary Information About Examinees in the Estimation of Item Parameters.” Applied Psychological Measurement 11: 8191.
Mislevy, Robert, and Darrell Bock, R. 1990. “BILOG 3: Item Analysis and Test Scoring with Binary Logistic Models” [computer program]. Mooresville IN: Scientific Software, Inc.
Mislevy, Robert, and Sheehan, Kathleen. 1989. “The Role of Collateral Information About Examinees in Item Parameter Estimation.” Psychometrika 54: 661679.
Neyman, J., and Scott, Elizabeth. 1948. “Consistent Estimates Based on Partially Consistent Observations.” Econometrika 16: 132.
Poole, Keith. 2000. “The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call Voting.” Paper presented at the Annual Meeting of the Midwest Political Science Association, Chicago.
Poole, Keith, and Rosenthal, Howard. 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35: 228278.
Poole, Keith, and Rosenthal, Howard. 1997. Congress: A Political-Economic History of Roll Call Voting. Oxford: Oxford University Press.
Smith, Alastair, and McGillivray, Fiona. 1996. “Senate Voting on NAFTA: The Power and Limitations of MCMC Methods for Studying Voting Across Bills and Across States.” Paper presented at the Summer Methodology Meeting, Ann Arbor, MI.
Snyder, James. 1992. “Artificial Extremism in Interest Group Ratings.” Legislative Studies Quarterly 17: 319345.
Tsutakawa, Robert, and Lin, Hsin Ying. 1986. “Bayesian Estimation of Item Response Curves.” Psychometrika 51: 251267.
Wu, C. F. Jeff. 1983. “On the Convergence Properties of the EM Algorithm.” Annals of Statistics 11: 95103.
Zorn, Christopher. 2001. “Generalized Estimating Equation Models for Correlated Data: A Review with Applications.” American Journal of Political Science 45: 470490.
Zwinderman, Aeilko. 1991. “A Generalized Rasch Model for Manifest Predictors.” Psychometrika 56: 589600.
Zwinderman, Aeilko. 1997. “Response Models with Manifest Predictors. In Handbook of Modern Item Response Theory, eds. van der Linden, and Hambleton, . New York: Springer-Verlag.
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Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach

  • Michael Bailey (a1)


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