A Bayesian Approach to Modeling Binary Data: The Case of High-Intensity Crime Areas

Abstract

This paper reports the fitting of a number of Bayesian logistic models with spatially structured or/and unstructured random effects to binary data with the purpose of explaining the distribution of high-intensity crime areas (HIAs) in the city of Sheffield, England. Bayesian approaches to spatial modeling are attracting considerable interest at the present time. This is because of the availability of rigorously tested software for fitting a certain class of spatial models. This paper considers issues associated with the specification, estimation, and validation, including sensitivity analysis, of spatial models using the WinBUGS software. It pays particular attention to the visualization of results. We discuss a map decomposition strategy and an approach that examines properties of the full posterior distribution. The Bayesian spatial model reported provides some interesting insights into the different factors underlying the existence of the three police-defined HIAs in Sheffield. High-intensity crime areas, or HIAs, are areas identified by urban police forces in England that experience high levels of violent, often drug-related, crime. Violence involves the use of knives and/or firearms. There may be further problems when bringing charges because of high levels of witness intimidation. The reason for this is that individuals or families resident in the neighborhood often perpetrate the crimes. HIAs therefore are more than simply areas with high levels of particular types of offenses (“hot spots”); they are areas with a particularly dangerous cocktail of violent crime perpetrated by offenders who are also resident in the area. They present particularly difficult policing problems. Craglia, Haining, and Signoretta (2001) reported the results of work into the spatial distribution of police-defined HIAs for a sample of English cities. The boundaries of HIAs were defined by senior police officers familiar with their cities. They first identified which of their basic command units (BCUs) had HIAs within them and