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

Keith T. PooleCenter for Advanced Study in the Behavioral Sciences and Department of Political Science, University of Houston, Houston, TX 77204-3011 e-mail: kpoole{at}uh.edu Over the last 15 years a large amount of scholarship in legislativepolitics has used NOMINATE or other similar methods to constructmeasures of legislators' ideological locations. These measuresare then used in subsequent analyses. Recent work in politicalmethodology has focused on the pitfalls of using such estimatesas variables in subsequent analysis without explicitly accountingfor their uncertainty and possible bias (Herron and Shotts2003, Political Analysis 11:44–64). This presents a problemfor those employing NOMINATE scores because estimates of theirunconditional sampling uncertainty or bias have until now beenunavailable. In this paper, we present a method of forming unconditionalstandard error estimates and bias estimates for NOMINATE scoresusing the parametric bootstrap. Standard errors are estimatedfor the 90th U.S. Senate in two dimensions. Standard errorsof first–dimension placements are in the 0.03 to 0.08range. The results are compared with those obtained using theMarkov chain Monte Carlo estimator of Clinton et al. (2002,Stanford University Working Paper). We also show how the bootstrapcan be used to construct standard errors and confidence intervalsfor auxiliary quantities of interest such as ranks and the locationof the median senator.