Measuring bias and uncertainty in ideal point estimates via the parametric bootstrap

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.