Spatial Conflict Analysis

It is the matrix W that defines which units are neighbors and how strongly, based on contiguity, distance, or nearest neighbors. Every spatial test and model operates through W, so the choice is a substantive modeling assumption: different definitions of 'neighbor' can change the estimated spatial dependence and the conclusions. Best practice specifies W on theoretical grounds and checks robustness to alternatives.

A spatial lag (autoregressive) model includes the spatially weighted outcome of neighbors as a predictor (y = ρWy + Xβ + ε), representing genuine interdependence or diffusion — conflict next door raises conflict here. A spatial error model places the dependence in the disturbances (ε = λWε + u), representing spatially correlated unobserved factors rather than a causal spillover. Choosing between them shapes whether you interpret clustering as contagion or as shared context.

Because in a spatial-lag model a change in one unit's covariate affects its neighbors through Wy, which feeds back to the unit itself. The total impact therefore splits into a direct effect (on the unit) and indirect/spillover effects (transmitted across neighbors), and these must be computed from the model's reduced form. Reporting the raw β alone understates and mischaracterizes the covariate's influence.