Exploiting autoregressive properties to develop prospective urban arson forecasts by target

Municipal fire departments responded to approximately 53,000 intentionally-set fires annually from 2003 to 2007, according to National Fire Protection Association figures. A disproportionate amount of these fires occur in spatio-temporal clusters, making them predictable and, perhaps, preventable. The objective of this research is to evaluate how the aggregation of data across space and target types (residential, non-residential, vehicle, outdoor and other) affects daily arson forecast accuracy for several target types of arson, and the ability to leverage information quantifying the autoregressive nature of intentional firesetting. To do this, we estimate, for the city of Detroit, Michigan, competing statistical models that differ in their ability to recognize potential temporal autoregressivity in the daily count of arson fires. Spatial units vary from Census tracts, police precincts, to citywide. We find that (1) the out-ofsample performance of prospective hotspot models for arson cannot usefully exploit the autoregressive properties of arson at fine spatial scales, even though autoregression is significant in-sample, hinting at a possible bias-variance tradeoff; (2) aggregation of arson across reported targets can yield a model that differs from by-target models; (3) spatial aggregation of data tends to increase forecast accuracy of arson due partly to the ability to account for temporally dynamic firesetting; and (4) arson forecast models that recognize temporal autoregression can be used to forecast daily arson fire activity at the Citywide scale in Detroit. These results suggest a tradeoff between the collection of high resolution spatial data and the use of more sophisticated modeling techniques that explicitly account for temporal correlation. Published by Elsevier Ltd. 3 TheFederalBureauof Investigation’sUniformCrimeReportsclassifycrimes into two categoriesdmore serious, ‘Part I’, and less serious, ‘Part II’, crimes. Part I crimes are Introduction Law enforcement organizations are increasingly using automated crime mapping tools that endeavor to produce shortand medium-term predictions of altered criminal activity (e.g., Bowers, Johnson, & Pease, 2004). These tools have been developed for alternative spatial and temporal scales but have typically not been subject to assessment of forecast accuracy, with few exceptions (e.g., Chainey, Tompson, & Uhlig, 2008; Gorr, 2009). A central challenge with such mapping is that hotspot identification requires abundant data, but at fine spatial or temporal scales such abundance is lacking, so coarse scale data are instead used; yet, it is not clear how this aggregation of data affects forecast results, or the ability to leverage information describing the dynamic process of emon), [email protected] r Ltd. crime (e.g., Bowers et al., 2004; Johnson, 2013; Lottier, 1938; Prestemon & Butry, 2005). Some modelers report advances in hotspot mapping (e.g., Cohen, Gorr, & Olligschlaeger, 2007); however, these efforts are focused on categories of relatively frequent more serious ‘Part I’ crimes (United States Department of Justice, 2004) such as robbery, aggravated assault, burglary, larceny, or motor vehicle theft, but rarely on less frequent Part I crimes such as murder (see Groff & McEwen, 2007), rape, and arson, or the many categories of less reliably reported less serious (‘Part II’) crimes (but see Kakamu, Polasek, & Wago, 2008).3 Furthermore, while much criminal homicide, forcible rape, robbery, aggravated assault, burglary, larceny-theft, motor vehicle theft, and arson. Part II crimes are other assault, forgery and counterfeiting, fraud, embezzlement, stolen property, vandalism, weapons, prostitution and commercial vice, sex offenses, drug abuse violations, gambling, offenses against the family and children, driving under the influences, liquor laws, drunkenness, disorderly conduct, vagrancy, all other state and local laws not included in Part I or II (traffic laws excluded), suspicion, curfew and loitering laws, and runaways. 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% Nonresidential: Left Axis Residential: Left Axis Vehicle: Left Axis Outside and Other: Right Axis Total: Right Axis Fig. 1. Percent of total national arson by type by day of week, National Fire Incident Reporting System 2002e2006. J.P. Prestemon et al. / Applied Geography 44 (2013) 143e153 144 effort has been devoted to developing static (backward-looking) crime mapping tools, few have been developed that are designed for forecastingdprospective hotspotting. The hotspot maps generated by the static tools are updated on a relatively frequent basis (e.g., weekly or monthly), but little is known about the value of more frequently updated or short time-step reliability. This is in spite of the recognition that such tools have potential high value in terms of tactical police response (e.g., Bowers et al., 2004) and in the planning of a built environment resilient to crime (e.g., Nelson, Bromley, & Thomas, 2001). In addition to the lack of progress in developing prospective mapping tools for less common crimes at fine temporal scales, there is an under-appreciation of the negative effects of aggregation bias. Broad-scale analysis of crime may obscure patterns found at the micro-scale (Nelson et al., 2001), and the appropriateness of aggregating crimes by type may depend on spatial scale used (Andresen & Linning, 2012). For example, crime maps showing aggregates of Part I crimes do not always recognize subcategories within these crime categoriesdsuch as burglaries of commercial targets versus burglaries of residences. Lack of recognition of the within-category heterogeneity may lead to statistical biases and inconsistencies in the estimates of the model parameters embedded in the mapping toolsdthis is the Modifiable Unit Areal Problem (e.g., see Ratcliffe & McCullagh, 1999). It may also lead to the use of inappropriate (ineffective) mitigation strategies (e.g., Haworth, Bruce, & Iveson, 2013). For example, arson focused on residential structures may have a different amount of temporal, spatial, or spatio-temporal clustering or respond differently to law enforcement efforts compared to vehicular or outdoors arson (e.g., see Groff & McEwen, 2007). The objective of this research is to evaluate how the aggregation of data across space and target types (residential, non-residential, vehicle, outdoor and other) affects daily arson forecast accuracy for several target types of arson, and the ability to leverage information quantifying the autoregressive nature of intentional firesetting. To do this, we estimate, for the city of Detroit, Michigan, competing statistical models that either recognize or do not recognize potential temporal autoregressivity in the arson counts. The spatial units that we study vary fromCensus tracts, police precincts, to citywide.We do not vary the temporal unit from daily, although the results of the modeling potentially can be used to design strategies that account for the regular variations in arson frequencies over time (e.g., those linked to days of theweek or seasons of the year). Four specific target types for arson are modeled: residential structures, commercial structures, vehicles, and vegetation and outdoor targets (e.g., trash fires). Two aggregations are modeled separately and compared with the individual types: aggregation of structures (residential plus commercial) and aggregation of all arson (all structures plus vehicles plus outdoors and other). A contribution of this research is that we find that temporal autoregressivity found for smaller spatial units is not beneficially exploited to improve forecast accuracy, whereas this temporal autoregressivity found at large spatial units is beneficially exploited to improve forecast accuracy, compared to alternative forecasting approaches. We conjecture that the lack of additional forecast accuracy provided by the autoregressive models for our smaller spatial units derives from the inappropriateness of the model specification for a count process occurring at low temporal frequency. The remainder of this paper is organized as follows. First, we describe the arson crime data generating processes for alternative targets, tying these to crime theory. Second, we outline empirical predictive models that may be useful for forecasting arson by target. Third, we apply the estimated predictive models and describe and compare their performance across spatial scales and targets. The paper concludes with recommendations for further research and development of forward-looking crime hotspotting tools that could be useful for law enforcement and fire agencies.