Spatiotemporal Modeling of Correlated Small‐Area Outcomes: Analyzing the Shared and Type‐Specific Patterns of Crime and Disorder

Abstract

This research applies a Bayesian multivariate modeling approach to analyze the spatiotemporal patterns of physical disorder, social disorder, property crime, and violent crime at the small‐area scale. Despite crime and disorder exhibiting similar spatiotemporal patterns, as hypothesized by broken windows and collective efficacy theories, past studies often analyze a single outcome and overlook the correlation structures between multiple crime and disorder types. Accounting for five covariates, the best‐fitting model partitions the residual risk of each crime and disorder type into one spatial shared component, one temporal shared component, and type‐specific spatial, temporal, and space–time components. The shared components capture the underlying spatial pattern and time trend common to all types of crime and disorder. Results show that population size, residential mobility, and the central business district are positively associated with all outcomes. The spatial shared component is found to explain the largest proportion of residual variability for all types of crime and disorder. Spatiotemporal hotspots of crime and disorder are examined to contextualize broken windows theory. Applications of multivariate spatiotemporal modeling with shared components to ecological crime theories and crime prevention policy are discussed.

A Bayesian spatial shared component model for identifying crime-general and crime-specific hotspots

“…While this has been observed in past social disorganization and routine activity research that compares the results of many univariate analyses (Ceccato, Haining, and Signoretta 2002;Andresen 2006;Chamberlain and Hipp 2015), this study provides quantitative evidence that the local patterns of violent crime and property crime were relatively more similar than different at the study region scale. Note that, while including risk factors is not common in hotspot analyses, this multivariate shared component model can be extended to include covariates (Quick, Li, and Brunton-Smith 2018;Quick, Li, and Law 2019) and future research focused on explaining the differences between crimegeneral and crime-specific patterns should look to include covariates that operationalize social disorganization, routine activity, and crime pattern theories, and examine how these risk factors influence the location of crime-general and crime-specific hotspots.…”

“…Focusing on crime-specific hotspots, routine activity theory, in particular, highlights how the distribution of crime targets may lead to some locations being hotspots for only one crime type. For example, routine activity theory contends that property crime-specific hotspots may be located in non-residential areas that have many attractive targets, such as in shopping districts where there are many stores with physical goods suitable for theft offences but relatively fewer features likely to facilitate aggressive and violent behaviours (LaGrange 1999;Quick, Li, and Law 2019). Violent crime-specific hotspots, in contrast, may be more likely to occur in residential neighbourhoods that have low informal social control, weak social ties, and few attractive property crime targets.…”

“…Both of these studies observe that accounting for the between-crime type correlation structures improves model fit compared to separate type-specific analyses. Identifying crime-general spatial patterns using a shared component modelling approach similar to the method applied in this study, Quick, Li, and Brunton-Smith (2018) show that burglary, robbery, vehicle crime, and violent crime share two distinct crimegeneral patterns, one that is common to all crime types and a second that is common to the theft-related crimes, and Quick, Li, and Law (2019) show that physical disorder, social disorder, property crime, and violent crime share a crime-general spatial pattern and a crimegeneral time trend.…”

“…One explanation for this is that both property crime and violent crime were analysed as standardized ratios and had similar scales centred near one (see Appendix A). If the crimes were analysed as counts without expected counts used as offsets or as rates with a common population at risk or denominator, for example, then the more frequent crime type could have a larger scaling parameter and a greater relative influence on the crime-general pattern (Quick, Li, and Law 2019).…”

“…Common hotspot methods applied to area-based crime data include local Moran's I, the Getis-Ord G Ã i statistic, and the spatial scan statistic, for example (Murray et al 2001;Ratcliffe and McCullagh 1999;Andresen 2009; Nakaya and Yano 2010; Shiode 2011; Ceccato and Dolmen 2011; Li and Radke 2012; Wang 2012). However, because univariate hotspot identification methods focus on only one outcome, they do not account for the underlying data-generating processes shared amongst multiple crime types and do not distinguish between crime-general hotspots, or areas where there are unusually high levels of two or more crime types, and crime-specific hotspots, or locations with unusually high levels of only one crime type (Knorr- Held and Best 2001;Quick, Li, and Law 2019;Yue et al 2017). Differentiating the spatial patterns of crime-general and crime-specific hotspots advances understanding of the possible risk factors associated with all, some, or only one type of crime, and provides policy-relevant information for the location, design, and implementation of comprehensive crime prevention initiatives that focus on many crime types and/or specialized initiatives that focus on a single crime type (Weisburd et al 1993;Haberman 2017).…”