Risk Terrain Modeling: Brokering Criminological Theory and GIS Methods for Crime Forecasting

Abstract

The research presented here has two key objectives. The first is to apply risk terrain modeling (RTM) to forecast the crime of shootings. The risk terrain maps that were produced from RTM use a range of contextual information relevant to the opportunity structure of shootings to estimate risks of future shootings as they are distributed throughout a geography. The second objective was to test the predictive power of the risk terrain maps over two six‐month time periods, and to compare them against the predictive ability of retrospective hot spot maps. Results suggest that risk terrains provide a statistically significant forecast of future shootings across a range of cut points and are substantially more accurate than retrospective hot spot mapping. In addition, risk terrain maps produce information that can be operationalized by police administrators easily and efficiently, such as for directing police patrols to coalesced high‐risk areas.

Keywords:

• GIS
• risk
• shootings
• crime
• modeling

Notes

1. Data was provided by the NJ State Police through the Regional Operations Intelligence Center and the many datasets they maintain, validate and update regularly to support internal crime analysis and police investigations.

2. A 1,000 foot bandwidth was selected because it seemed a reasonable sphere of influence for shooters—the average blockface is approximately 350 feet (Felson, 1995; Taylor, 1997; Taylor and Harrell, 1996). 100 × 100 foot cells were the smallest area that our computers could process reasonably fast and, for this proof of concept of RTM, if a Risk Terrain could predict locations of shootings at the smallest (but reasonable) geographic units, it would best exemplify the utility of RTM for operational policing compared to larger, less specific, units of analysis.

3. Moran’s I is an area‐wide analysis that was used to measure spatial autocorrelation in the distributions of shootings within cells of the Period 1 and Period 2 risk terrains of Irvington, NJ. Distributions among geographical units, such as grid cells, are usually not independent, meaning that values found in a particular cell are likely to be influenced by corresponding values in nearby cells (Anselin, Cohen, Cook, Gorr, & Tita, 2000). Moran’s I measures this autocorrelation, with values approaching 1 when geographical units are situated near other similar geographical units, and approaching −1 when geographical units are situated near dissimilar geographical units. A Moran’s I value of 0 indicates the absence of autocorrelation, or independence, among geographical units. GeoDa, a freestanding software application, was used to calculate Moran’s I values for each risk terrain with a Queen Contiguity Weight matrix (Anselin, 2003). A permutation process “in which a reference distribution is calculated for spatially random layouts with the same data (values) as observed” permitted generating pseudo p‐values for assessing the statistical significance of the Moran’s I values (Anselin, 2003, p. 91). The value of the global Moran’s I score for the Period 1 Risk Terrain was 0.014; the value of the Moran’s I score for the Period 2 Risk Terrain was 0.011. These values near 0 indicate that no spatial autocorrelation was present in the distributions of shootings across cells in either risk terrain. Though, neither value was statistically significant (p > 0.05 after running 999 permutations).

4. Random numbers were necessary to randomize the sorting of cells with the same risk values. For example, if 11 out of 100 cells had a risk value of eight, and they were sorted in descending order, the top 10% of cells to be designated as “high risk” would all have values of eight. But, the 11% cell would be excluded due to a rather arbitrary sorting algorithm. The random number ensured that every cell had an equal chance of being sorted above or below each cut point.

5. This test is an alternative to Chi‐square for 2 × 2 tables when predicted cell counts are low, which is the case with shootings. The lack of spatial autocorrelation means that assumptions of independence of spatial units are legitimate in this case.