Comparing NOMINATE and IDEAL: Points of Difference and Monte Carlo Tests

Empirical models of spatial voting allow us to infer legislators' locations in an abstract policy or ideological space using their roll-call votes. Over the past 25 years, these models have provided new insights about the U.S. Congress, and legislative behavior more generally. There are now a number of alternative models, estimators, and software packages that researchers can use to recover latent issue or ideological spaces from voting data. These different tools usually produce substantively similar estimates, but important differences also arise. We investigated the sources of observed differences between two leading methods, NOMINATE and IDEAL. Using data from the 1994 to 1997 Supreme Court and the 109th Senate, we determined that while some observed differences in the estimates produced by each model stem from fundamental differences in the models' underlying behavioral assumptions, others arise from arbitrary differences in implementation. Our Monte Carlo experiments revealed that neither model has a clear advantage over the other in the recovery of legislator locations or roll-call midpoints in either large or small legislatures.