Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace

This article demonstrates how spatially dependent data witha categorical response variable can be addressed in a statisticalmodel. We introduce the idea of an autologistic model wherethe response for one observation is dependent on the value ofthe response among adjacent observations. The autologistic modelhas likelihood function that is mathematically intractable,since the observations are conditionally dependent upon oneanother. We review alternative techniques for estimating thismodel, with special emphasis on recent advances using Markovchain Monte Carlo (MCMC) techniques. We evaluate a highly simplifiedautologistic model of conflict where the likelihood of war involvementfor each nation is conditional on the war involvement of proximatestates. We estimate this autologistic model for a single year(1988) via maximum pseudolikelihood and MCMC maximum likelihoodmethods. Our results indicate that the autologistic model fitsthe data much better than an unconditional model and that theMCMC estimates generally dominate the pseudolikelihood estimates.The autologistic model generates predicted probabilities greaterthan 0.5 and has relatively good predictive abilities in anout-of-sample forecast for the subsequent decade (1989 to 1998),correctly identifying not only ongoing conflicts, but also newones.