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

Keith T. Poole Center 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.     

Pseudo-gunpowder stippling caused by fragmentation of a plated bullet

In this report we present a case of pseudo-gunpowder stippling caused by fragmentation of a plated bullet. Investigation of the incident revealed absence of an interposed target, no evidence of ricochet, and a normally functioning, undamaged weapon. Electroplated ("plated" or "coated") bullets are relatively uncommon. They look similar to jacketed bullets in that the lead core is covered by a copper-colored jacketlike material. However, the copper-colored plating material is thinner than the typical jacket material. In certain instances, the plating may strip away from the lead core during transit through the barrel of the weapon and can produce injuries that mimic gunpowder stippling. Forensic pathologists are advised to be aware of this phenomenon. Misinterpretation of such wounds could result in improper classification of range of fire or improper conclusions about the presence or absence of an interposed target or ricochet.     

The Structure of Utility in Spatial Models of Voting

Empirical models of spatial voting allow legislators' locations in a policy or ideological space to be inferred from their roll‐call votes. These are typically random utility models where the features of the utility functions other than the ideal points are assumed rather than estimated. In this article, we first consider a model in which legislators' utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. Across many roll‐call data sets, we find that legislators' utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result suggests that extremists are more ideologically rigid while moderates are more likely to consider influences that arise outside liberal‐conservative conflict.