A Metric Comparison of Predictive Hot Spot Techniques and RTM

Abstract

There are numerous hot spot mapping techniques that can be used in research and in practice for predicting future crime locations. Due to differences in the varying techniques, metrics were developed to compare the accuracy and precision of these techniques. The predictive accuracy index (PAI) and recapture rate index (RRI) were used to assess six different hot spot techniques. Spatial and Temporal Analysis of Crime, Nearest Neighbor Hierarchical, Kernel Density Estimation, and Risk Terrain Modeling were the general techniques compared in relation to their PAI and RRI values for short-term and long-term prediction of robberies. The results of the study were discussed with an emphasis on the utility of using multiple techniques jointly for analysis.

Keywords:

• hot spots
• crime prediction
• crime analysis
• Predictive Accuracy Index
• Recapture Rate Index

Notes

¹ Levine (2005) discussed how the concentrations of crime create the label of a crime “hot spot” but these applications only take crime locations into context (phenotype). The cause of the formation of the hot spots needs to be examined, which Levine (2005) discussed could be a result of land-use patterns or behavioral patterns (genotype).

² Kennedy et al.’s (2011) study did not use the PAI and RRI measures for comparison of techniques.

³ Additionally, a one day prediction, 1 January 2009, was examined but no technique was able to predict the robberies that occurred on that one day.

⁴ The search radius and minimum number of points were altered numerous times in relation to the findings of the Monte Carlo simulations. For example, seven minimum points with a 1075 ft search radius resulted in clusters being found in the STAC technique but not in the Nnh technique. The parameters were altered until comparable significant findings were found. Additionally, smaller search radii resulted in convex hulls having an area equal to zero, suggesting a hotpoint rather than hot spot (see Ratcliffe, 2004b). Past research argued that there can be variation in crime from street to street so the current study sought to account for this by examining smaller search radii (see Weisburd et al., 2004, 2009).

⁵ For the Nnh technique, it is possible to have second- and third-order clusters. Levine (2010) stated that first-order ellipses could cluster in space, allowing for a second-order ellipse to encompass multiple first-order ellipses. The third-order ellipse would include multiple second-order ellipses which are the result of clustering of first-order ellipses. The current analysis did not indicate the presence of second-order ellipses. Levine (2010) discussed the usefulness of the different order levels, and if second-/third-order ellipses were found in the current analysis they would have been included for comparison of PAI and RRI values.

⁶ Van Patten et al. (2009) used the normal interpolation method in their hot spot technique comparison study using PAI and RRI values. Chainey et al. (2008) chose the quartic interpolation method, which Levine (2008) also used when supplementing the PAI with the RRI measure. Hart & Zandbergen (in press) recommended the triangular or quartic methods for prediction.

⁷ Limiting the KDE to the highest value hot spot cells could result in an increase in the PAI and RRI values because the area KDE initially indicated as a hot spot was restricted to encompass smaller areas for comparison.

⁸ RTM is designed to include social measures as well as physical measures. Caplan (2010) discussed how to include Census data into the RTM at the block level. RTMDx operates using point-based data and expressing the point data via proximity or density. Higher level of aggregate data (i.e. block, block group, and tract) are not usable currently within RTMDx. Dugato (2013), while not using RTMDx, used physical, point-data, establishments as proxies for social characteristics (RTMDx was not available when Dugato’s study was conducted).

⁹ That is not to say it is not possible to determine the spatial influence each risk factor has without RTMDx, RTMDx automates many of the steps that would determine the spatial influence and significance testing of risk factors (see Caplan et al., 2013).

¹⁰ Future research should examine the inclusion of protective factors that could affect the riskiness of an area. RTMDx only builds an aggravating or protective model. It would be beneficial to be able to include both types of measures within one analytic technique.

¹¹ For greater detail on the steps and processes of RTMDx, see Caplan et al.’s (2013) manual.

¹² The coding of the data grouped hotel, motels, and motor home parks together.

¹³ Ratcliffe (2012) discussed the use of changepoint regression to determine the spatial influence around criminogenic places. This is a different method than the one utilized in the current study, yet future research can be directed at comparing the two methodologies to determine if there are differences in the operationalization of spatial influence for specific crime generators and crime attractors.

¹⁴ Caplan et al. (2013) noted that there is a difference in the type of kernel density function used by RTMDx and that which is used in ArcMap. While there are differences, Caplan et al. (2013) stated that relative risk values could vary slightly but generally this should not affect most research utilizing RTMDx.

¹⁵ It would be inaccurate to say that cells given a value of zero indicate no risk because only the highest risk cells were given the value of one based on the operationalization of the risk factors. The RTMDx output suggested that the range was from 1 to 820.4, interpreted as odds, but because of differences in the kernel density functions the range was 1 to 941.7. The average cell risk was 4.580 with a standard deviation value of 53.509.

¹⁶ The top 23% of cells were taken because if the top 20% of cells were used, there would be multiple cells with the same risk value. That is, the use of cut-off value of the top 20% would have arbitrarily excluded cells with the same risk values. There were 10 cells with the same value at the 20% mark and including those would have increased the hot area to 61 cells, 23% of the cells with values greater than two standard deviations from the mean. Additionally, if the 264 cells were used, the area would have been over one square mile, which is double to triple the other techniques area. By using the 61 cells, the area was .406 square miles, comparable to the other areas.

¹⁷ In fairness to the Nnh technique, Nnh was designed to indicate clustering within small distances. Using the default random nearest neighbor distance as the search radius instead of the 1290ft, the Nnh convex hull resulted in an average PAI value of 65.014 and a RRI value of 0.537. This was the second highest PAI value, behind KDE, and the lowest RRI value observed in the study. In short, the Nnh technique is best at identifying small, concentrated clusters.

¹⁸ Additional maps are available for each technique and an overlay of all the techniques together to show similarities and differences; contact the corresponding author.

¹⁹ RTM is capable of using a hot spot technique such as KDE and supplementing the analysis with the density measure determined by KDE as a risk factor. Robberies from 2008, as a risk factor, were excluded from the pool of risk factors to keep from creating a biased model.

²⁰ Levine et al. (1986) suggested the incorporation of a “vice index” that would take into account a number of vice-related business establishments (i.e. liquor stores, strip clubs, and adult cinemas) in future research.

²¹ Felson (1995) expanded upon Eck’s (1994) concept of place managers in greater context in relation to different types of people who are capable of discouraging crime.

Additional information

Notes on contributors

Grant Drawve

Grant Drawve is a PhD candidate at the University of Arkansas at Little Rock. His research interests include: environmental criminology, crime analysis, neighborhoods and crime, GIS, micro-places, crime prevention, and the built environment.