The Spatial Model and Speci cation of Choice Models

The spatial model has been in use in political science for close to 30 years, and in that period it has achieved a place of prime importance as our paradigm of the process of candidatechoice used by voters. For much of this time political scientists have estimated models of candidatechoice using binary logit or probit, even in cases where there were more than two choices facing voters. Recently discrete choices models beyond binary logit and probit have been making their way into use in political science with increasing frequency. The properties of these models, and their relationship to the spatial model, are frequently misunderstood. This paper demonstrates four essential points. First, the popular multinomial logit model is in fact equivalent to running a series of binary logit models. It involves nothing more than pairwise comparisons of the choices. Second, despite containing no information about the choices, the multinomial logit model provides reduced form estimates of the e ect of characteristics of choices that are equivalent to the estimates of such e ects provided by the conditional logit model which does utilize information about the characteristics of the choices. Third, the multinomial logit model cannot o er any inferences as to e ects of changing the characteristics of the choices, or introducing additional choices; whereas the conditional logit model can o er such inferences. Fourth, the classic spatial model has a aw in multi-candidate settings that has been overlooked, with more than two candidates the spatial model explicitly contradicts an aspect of voter behaviour widely believed to be prevalent: the tendency of voters to view certain candidates as `similar' alternatives, and thus for the presence of additional candidates to e ect asymettrically the probability of existing candidates being chosen. R. Michael Alvarez California Institute of Technology Jonathan Nagler University of California, Riverside