Diffusion in homicide: Exploring a general method for detecting spatial diffusion processes

This article proposes a new method for examining dynamic changes in the spatial distribution of a phenomenon. Recently introduced exploratory spatial data analysis (ESDA) techniques provide social scientists with a new set of tools for distinguishing between random and nonrandom spatial patterns of events (Anselin, 1998). Existing ESDA measures, however, are static and do not permit comparisons of distributions of events in the same space but across different time periods. One ESDA method-the Moran scatterplot-has special heuristic value because it visually displays local spatial relationships between each spatial unit and its neighbors. We extend this static cross-sectional view of the spatial distribution of events to consider dynamic features of changes over time in spatial dependencies. The method distinguishes between contagious diffusion between adjoining units and hierarchical diffusion that spreads broadly through commonly shared influences. We apply the method to homicide data,:looking for evidence of spatial diffusion of youth-gang homicides across neighborhoods in a city. Contagious diffusion between neighboring census tracts is evident only during the year of peak growth in total homicides, when high local rates of youth-gang homicides are followed by significant increases in neighboring youth-nongang rates. This pattern is consistent with a spread of homicides from gang youth to nongang youth. Otherwise, the increases in both youth-gang and youth-nongang homicides generally occur simultaneously in nonneighboring tracts.