Diffusion in Homicide: Exploring a General Method for Detecting Spatial Diffusion Processes

This article proposes a new method for examining dynamic changes in thespatial distribution of a phenomenon. Recently introduced exploratoryspatial data analysis (ESDA) techniques provide social scientists with anew set of tools for distinguishing between random and nonrandom spatialpatterns of events (Anselin, 1998). Existing ESDA measures, however, arestatic and do not permit comparisons of distributions of events in the samespace but across different time periods. One ESDA method—the Moranscatterplot—has special heuristic value because it visually displayslocal spatial relationships between each spatial unit and its neighbors. Weextend this static cross-sectional view of the spatial distribution ofevents to consider dynamic features of changes over time in spatialdependencies. The method distinguishes between contagious diffusion betweenadjoining units and hierarchical diffusion that spreads broadly throughcommonly shared influences. We apply the method to homicide data, lookingfor evidence of spatial diffusion of youth-gang homicides acrossneighborhoods in a city. Contagious diffusion between neighboring censustracts is evident only during the year of peak growth in total homicides,when high local rates of youth-gang homicides are followed by significantincreases in neighboring youth- nongang rates. This pattern is consistentwith a spread of homicides from gang youth to nongang youth. Otherwise, theincreases in both youth-gang and youth- nongang homicides generally occursimultaneously in nonneighboring tracts.