Modeling the Social and Spatial Proximity of Crime: Domestic and Sexual Violence Across Neighborhoods

Objectives: Our goal is to understand the social dynamics affecting domestic and sexual violence in urban areas by investigating the role of connections between area nodes, or communities. We use innovative methods adapted from spatial statistics to investigate the importance of social proximity measured based on connectedness pathways between area nodes. In doing so, we seek to extend the standard treatment in the neighborhoods and crime literature of areas like census blocks as independent analytical units or as interdependent primarily due to geographic proximity. Methods: In this paper, we develop techniques to incorporate two types of proximity, geographic proximity and commuting proximity in spatial generalized linear mixed models (SGLMM) in order to estimate domestic and sexual violence in Detroit, Michigan and Arlington County, Virginia. Analyses are based on three types of CAR models (the Besag, York, and Mollié (BYM), Leroux, and the sparse SGLMM models) and two types of SAR models (the spatial lag and spatial error models) to examine how results vary with different model assumptions. We use data from local and federal sources such as the Police Data Initiative and American Community Survey. Results: Analyses show that incorporating information on commuting ties, a non-spatially bounded form of social proximity, to spatial models contributes to better deviance information criteria scores (a metric which explicitly accounts for model fit and complexity) in Arlington for sexual and domestic crime as well as overall crime. In Detroit, the fit is improved only for overall crime. The distinctions in model fit are less pronounced when using cross-validated mean absolute error as a comparison criteria. Conclusion: Overall, the results indicate variations across crime type, urban contexts, and modeling approaches. Nonetheless, in important contexts, commuting ties among neighborhoods are observed to greatly improve our understanding of urban crime. If such ties contribute to the transfer of norms, social support, resources, and behaviors between places, they may then transfer also the effects of crime prevention efforts.