Browsing by Subject "crime concentration"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Reducing Bias in Estimates for the Law of Crime Concentration
    (Springer, 2019) Mohler, George; Brantingham, P. Jeffrey; Carter, Jeremy; Short, Martin; Computer and Information Science, School of Science
    Objectives The law of crime concentration states that half of the cumulative crime in a city will occur within approximately 4% of the city’s geography. The law is demonstrated by counting the number of incidents in each of N spatial areas (street segments or grid cells) and then computing a parameter based on the counts, such as a point estimate on the Lorenz curve or the Gini index. Here we show that estimators commonly used in the literature for these statistics are biased when the number of incidents is low (several thousand or less). Our objective is to significantly reduce bias in estimators for the law of crime concentration. Methods By modeling crime counts as a negative binomial, we show how to compute an improved estimate of the law of crime concentration at low event counts that significantly reduces bias. In particular, we use the Poisson–Gamma representation of the negative binomial and compute the concentration statistic via integrals for the Lorenz curve and Gini index of the inferred continuous Gamma distribution. Results We illustrate the Poisson–Gamma method with synthetic data along with homicide data from Chicago. We show that our estimator significantly reduces bias and is able to recover the true law of crime concentration with only several hundred events. Conclusions The Poisson–Gamma method has applications to measuring the concentration of rare events, comparisons of concentration across cities of different sizes, and improving time series estimates of crime concentration.
  • Thumbnail Image
    Item
    Spatial Concentration of Opioid Overdose Deaths in Indianapolis: An Application of the Law of Crime Concentration at Place to a Public Health Epidemic
    (Sage, 2019-05) Carter, Jeremy G.; Mohler, George; Ray, Bradley; School of Public and Environmental Affairs
    The law of crime concentration at place has become a criminological axiom and the foundation for one of the strongest evidence-based policing strategies to date. Using longitudinal data from three sources, emergency medical service calls, death toxicology reports from the Marion County (Indiana) Coroner’s Office, and police crime data, we provide four unique contributions to this literature. First, this study provides the first spatial concentration estimation of opioid-related deaths. Second, our findings support the spatial concentration of opioid deaths and the feasibility of this approach for public health incidents often outside the purview of traditional policing. Third, we find that opioid overdose death hot spots spatially overlap with areas of concentrated violence. Finally, we apply a recent method, corrected Gini coefficient, to best specify low-N incident concentrations and propose a novel method for improving upon a shortcoming of this approach. Implications for research and interventions are discussed.