Accounting for Immunity in Spatial Processes: The Spatial Susceptibility Model

Abstract

Political scientists frequently study spatially interdependent processes, such as policy diffusion, democratization, or the spread of violent conflict. Existing studies of such mechanisms typically rely on the spatio-temporal autoregressive (STAR) model, or simplified variants thereof, for quantitative inference. This paper argues that the STAR model is often a theoretically unsatisfying and empirically inappropriate choice, as it implies that a unit’s vulnerability to outside influences is determined conclusively by its location in space and a single global autorecorrelation parameter. In many settings, however, theory suggests that units differ inherently in their susceptibility to outside changes. In this situation, STAR-like models yield incomplete, or even misleading inference about the presence, intensity and form of spatial interdependence. Addressing this issue, we present an extension of the STAR model that replaces the standard global autocorrelation parameter with a vector of stochastic, unit-varying susceptibility parameters. This hierarchical setup allows capturing heterogeneity in units’ responses to outside influences, and permits investigating the causes of such variation by introducing a second-level regression model with unit-level predictors. We derive the model, as well as a Bayesian estimation procedure, for normally distributed and count outcomes. We apply the model to a yearly panel of civil war related events in Africa, showing that there exists considerable variation in the degree to which African countries are susceptible to spill-overs of armed conflict.