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

This article proposes a new method for examining dynamic changes in the spa tial 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 acr oss different time periods. One ESDA method-the Moran scatterplot-has speci al heuristic value because it visually displays local spatial relationships between each spatial unit and its neighbors. We extend this static cross-s ectional view of the spatial distribution of events to consider dynamic fea tures of changes over time in spatial dependencies. The method distinguishe s between contagious diffusion between adjoining units and hierarchical dif fusion that spreads broadly through commonly shared influences. We apply th e method to homicide data,:looking for evidence of spatial diffusion of you th-gang homicides across neighborhoods in a city. Contagious diffusion betw een neighboring census tracts is evident only during the year of peak growt h in total homicides, when high local rates of youth-gang homicides are fol lowed by significant increases in neighboring youth-nongang rates. This pat tern is consistent with a spread of homicides from gang youth to nongang yo uth. Otherwise, the increases in both youth-gang and youth-nongang homicide s generally occur simultaneously in nonneighboring tracts.