More Places than Crimes Implications for Evaluating the Law of Crime Concentration at Place

• Published in: Journal of quantitative criminology Vol. 33; no. 3; pp. 451 - 467
• Main Authors: Bernasco, Wim, Steenbeek, Wouter
• Format: Journal Article
• Language: English
• Published: New York Springer Science + Business Media 01.09.2017; Springer US; Springer Nature B.V
• Subjects: Bias; Concentration; Crime; Criminology; Criminology and Criminal Justice; Equality; Generalizations; Law and Criminology; Lorenz Curve; Methodology of the Social Sciences; ORIGINAL PAPER; Sociology; Statistics; Crime concentration; Lorenz curve; Gini coefficient; Criminology of place
• ISSN: 0748-4518; 1573-7799
• DOI: 10.1007/s10940-016-9324-7

Objectives The crime and place literature lacks a standard methodology for measuring and reporting crime concentration. We suggest that crime concentration be reported with the Lorenz curve and summarized with the Gini coefficient, and we propose generalized versions of the Lorenz curve and the Gini coefficient to correct for bias when crime data are sparse (i.e., fewer crimes than places). Methods The proposed generalizations are based on the principle that the observed crime concentration should not be compared with perfect equality, but with maximal equality given the data. The generalizations asymptotically approach the original Lorenz curve and the original Gini coefficient as the number of crimes approaches the number of spatial units. Results Using geocoded crime data on two types of crime in the city of The Hague, we show the differences between the original Lorenz curve and Gini coefficient and the generalized versions. We demonstrate that the generalizations provide a better representation of crime concentration in situations of sparse crime data, and that they improve comparisons of crime concentration if they are sparse. Conclusions Researchers are advised to use the generalized versions of the Lorenz curve and the Gini coefficient when reporting and summarizing crime concentration at places. When places outnumber crimes, the generalized versions better represent the underlying processes of crime concentration than the original versions. The generalized Lorenz curve, the Gini coefficient and its variance are easy to compute.