Race, Space, Homicide, and Demographic Correlations
by John Sprague

John Sprague
Washington University in St. Louis

Race, Space, Homicide, and Demographic Correlations

My research interests relevant to this workshop have focused on crime distributions as structured by demography including race, especially the spatial distribution of homicide. Space plays a central role for both methodological and substantive reasons. Methodologically, the spatial organization of homicide as a point process can be aggregated to polygon coverages for which detailed demographic information, including race, can be obtained. Thus spatial organization enables the systematic statistical modeling of homicide distributions in space and the further study of their behavior over time. The data used in these analyses (in collaborative work with Carol Kohfeld, University of Missouri - St. Louis) have been assembled from police and census records for the City of St. Louis for a period of over 30 years. And the analyses have been conducted at coverages varying in detail from block groups (about 550) through voting precincts (about 350) to census tracts (about 111). St. Louis is nearly evenly divided between blacks and whites and because homicide occurs disproportionately within the black population a strong spatial correlation between homicide and race is observed corresponding to the strong individual level correlation between race and homicide. Many demographic predictors of homicide are also strongly correlated with race and the substantive and methodological problem becomes one of sorting out the separate influences of demographic predictors other than race compared with racial effects. Race has a bimodal distribution in these data at any level of aggregation and this frequently carries over into its correlates thus undermining the usual distribution assumptions of statistical models. Spatial analysis techniques allow some alternative structuring of these data in an attempt to isolate the separate effect of race when compared with other demographic predictors. An initial attempt to pursue this strategy is Kohfeld, Sprague, and Walker (1999) "Objective Bases for Racial Stereotypes: The Fundamental Irrelevance of the Correlation between Race and Homicide" (available as paper number 370 from http://artsci.wustl.edu/~polisci/papers.html).

In our research we have made extensive use of choropleth maps and somewhat less use of point maps, although point maps are crucial for assessing the stability in time of the spatial homicide distributions. We have also made extensive use of spatial correlograms based on Moran's I to assess spatial structure of homicides and predictors as polygons become removed from each other in space. Analysis of the spatial structure of model residuals using such correlograms and comparing these correlograms with the original correlograms of homicide rates has been a valuable strategy in analysis. The statistical packages we have used include, in recent years, ArcView with the Anselin enhancements, Anselin's SpaceStat, S-PLUS, and STATA. Of these programs the Anselin utilities for constructing contiguity matrices (now available in ArcView) for k nearest neighbors, and especially using the queen algorithm for our particular data, have been crucial. I have written a number of S-PLUS programs to facilitate the preparation of visual displays, to construct higher order contiguity matrices from first order matrices, to compute and display Moran's I correlograms, and to aid in the communication between the output from the spatial programs and statistical analyses in either STATA or S-PLUS. Because of the mechanism by which the basic measure of the dependent behavior, homicide, is generated, the principal statistical modeling strategy has been with multivariate event count models. Increasingly our written output has emphasized visualization. A presentation of our use of point process maps, multivariate graphs (Trellis graphs), spatial correlograms, choropleth maps, and multivariate statistical event count models is Kohfeld and Sprague (2000) "Visualizing Homicide" (available as paper number 392 from http://artsci.wustl.edu/~polisci/papers.html).

A superb example of statistical spatial analysis that touches on the interests of political scientists comes from William S. Cleveland's masterwork Visualizing Data (1993) at pages 304-319. At this point in his narrative Cleveland takes up a multiway analysis of count data on livestock distributions in European countries and concludes the analysis with a map display of residuals for the distribution of sheep showing their dependence on geographical location. That book, of course, belongs on every social scientist's shelf and I find this analysis of multiway data with fundamental visualization techniques particularly compelling.