A Bayesian Probit Model with Spatial Dependencies

A Bayesian probit model with individual effects that exhibit spatial dependencies is set forth. Since probit models are often used to explain variation in individual choices, these models may well exhibit spatial interaction effects due to the varying spatial location of the decision makers. That is, individuals located at similar points in space may tend to exhibit similar choice behavior. The model proposed here allows for a parameter vector of spatial interaction effects that takes the form of a spatial autoregression. This model extends the class of Bayesian spatial logit/probit models presented in LeSage (2000) and relies on a hierachical construct that we estimate via Markov Chain Monte Carlo methods. We illustrate the model by applying it to the 1996 presidential election results for 3,110 US counties.