Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T03:59:07.138Z Has data issue: false hasContentIssue false
  • English
  • Français

Measuring Bias and Uncertainty in Ideal Point Estimates via the Parametric Bootstrap

Published online by Cambridge University Press:  04 January 2017

Jeffrey B. Lewis  and
Keith T. Poole
Jeffrey B. Lewis
Affiliation:
Department of Political Science, University of California, Los Angeles, Los Angeles, CA 90095. e-mail: jblewis@ucla.edu
Keith T. Poole
Affiliation:
Center for Advanced Study in the Behavioral Sciences and Department of Political Science, University of Houston, Houston, TX 77204-3011. e-mail: kpoole@uh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Over the last 15 years a large amount of scholarship in legislative politics has used NOMINATE or other similar methods to construct measures of legislators' ideological locations. These measures are then used in subsequent analyses. Recent work in political methodology has focused on the pitfalls of using such estimates as variables in subsequent analysis without explicitly accounting for their uncertainty and possible bias (Herron and Shotts 2003, Political Analysis 11:44–64). This presents a problem for those employing NOMINATE scores because estimates of their unconditional sampling uncertainty or bias have until now been unavailable. In this paper, we present a method of forming unconditional standard error estimates and bias estimates for NOMINATE scores using the parametric bootstrap. Standard errors are estimated for the 90th U.S. Senate in two dimensions. Standard errors of first—dimension placements are in the 0.03 to 0.08 range. The results are compared with those obtained using the Markov chain Monte Carlo estimator of Clinton et al. (2002, Stanford University Working Paper). We also show how the bootstrap can be used to construct standard errors and confidence intervals for auxiliary quantities of interest such as ranks and the location of the median senator.

Type
Research Article
Information
Political Analysis , Volume 12 , Issue 2 , Spring 2004 , pp. 105 - 127
Copyright
Copyright © Society for Political Methodology 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bollen, Kenneth A., and Stein, Robert A. 1992. “Bootstrapping Goodness-of-Fit Measures in Structural Equation Models.” Sociological Methods and Research, 21: 205–229.CrossRefGoogle Scholar
Brownstone, David, and Valletta, Robert G. 1996. “Modeling Earnings Measurement Error: A Multiple Imputation Approach.” Review of Economics and Statistics 78: 705–717.CrossRefGoogle Scholar
Clinton, Joshua, Jackman, Simon D., and Rivers, Douglas. 2002. “The Statistical Analysis of Roll Call Data.” Working paper. Stanford, CA: Stanford University.Google Scholar
Efron, Bradley. 1979. “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7: 1–26.Google Scholar
Efron, Bradley. 1982. “Maximum Likelihood and Decision Theory.” Annals of Statistics 10: 340–356.Google Scholar
Efron, Bradley, and Tibshirani, Robert J. 1993. An Introduction to the Bootstrap. New York: Chapman & Hall.CrossRefGoogle Scholar
Hall, Peter. 1985. “Resampling a Coverage Pattern.” Stochastic Processes and Their Applications 20: 231–246.Google Scholar
Hall, Peter. 1994. “Methodology and Theory for the Bootstrap.” In Handbook of Econometrics, Vol. IV, eds. Engle, R. F. and McFadden, D. L. New York: Elsevier, pp. 2342–2379.Google Scholar
Heckman, James J., and Snyder, James M. 1997. “Linear Probability Model s of the Demand for Attributes with an Empirical Application to Estimating the Preferences of Legislators.” Rand Journal of Economics 28: 142–189.Google Scholar
Herron, Michael C., and Shotts, Kenneth W. 2003. “Using Ecological Inference Point Estimates as Dependent Variables in Second-Stage Linear Regressions.” Political Analysis 11: 44–64.CrossRefGoogle Scholar
Jackman, Simon D. 2000a. “Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.” American Journal of Political Science 44: 375–404.Google Scholar
Jackman, Simon D. 2000b. “Estimation and Inference Are ‘Missing Data’ Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8: 307–332.Google Scholar
Jackman, Simon D. 2001. “Multidimensional Analysis of Roll Call Data via Bayesian Simulation: Identification, Estimation, Inference and Model Checking.” Political Analysis 9: 227–241.CrossRefGoogle Scholar
Londregan, John. 2000. “Estimating Legislator's Preferred Points.” Political Analysis 8: 35–56.CrossRefGoogle Scholar
Londregan, John, and Snyder, James M. 1994. “Comparing Committee and Floor Preferences.” Legislative Studies Quarterly 19: 233–266.Google Scholar
Lord, Frederic M. 1983. “Unbiased Estimates of Ability Parameters, of Their Variance, and of Their Parallel Forms Reliability.” Psychometrika 48: 477–482.CrossRefGoogle Scholar
McFadden, Daniel. 1976. “Quantal Choice Analysis: A Survey.” Annals of Economic and Social Measurement 5: 363–390.Google Scholar
Mooney, Chrisopher Z. 1996. “Bootstrap Statistical Inference: Examples and Evaluations of Political Science.” American Journal of Political Science 40: 570–602.Google Scholar
Poole, Keith T. 2000. “Non-Parametric Unfolding of Binary Choice Data.” Political Analysis 8: 211–237.CrossRefGoogle Scholar
Poole, Keith T. 2001. “The Geometry of Multidimensional Quadratic Utility in Models of Parliamentary Roll Call Voting.” Political Analysis 9: 211–226.CrossRefGoogle Scholar
Poole, Keith T., and Rosenthal, Howard. 1985. “A Spatial Model For Legislative Roll Call Analysis.” American Journal of Political Science 29: 357–384.Google Scholar
Poole, Keith T., and Rosenthal, Howard. 1991. “Patterns of Congressional Voting.” American Journal of Political Science 35: 228–278.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
Schonemann, Peter H. 1966. “A Generalized Solution of the Orthogonal Procrustes Problem.” Psychometrika 31: 1–10.Google Scholar
Young, G. Alastair. 1994. “Bootstrap: More than a Stab in the Dark?” Statistical Science 9(3: 382–415.Google Scholar