Crime Mapping and Spatial Data Analysis using R

Hot spots of crime are simply a convenient perceptual construct. As Ned [Levine (2013)] (chapter 7, p. 1) highlights, "Hot spots do not exist in reality, but are areas where there is sufficient clustering of certain activities (in this case, crime) such that they get labeled such. There is not a border around these incidents, but a gradient where people draw an imaginary line to indicate the location at which the hot spot starts." Equally, there is not a unique solution to the identification of hot spots. Different techniques and algorithms will give you different answers. He further emphasises: "It would be very naive to expect that a single technique can reveal the existence of hot spots in a jurisdiction that are unequivocally clear. In most cases, analysts are not sure why there are hot spots in the first place. Until that is solved, it would be unreasonable to expect a mathematical or statistical routine to solve that problem" (chapter 7, p. 7).

So, as with most data analysis exercises, one has to try different approaches and use professional judgment to select a particular representation that may work best for a particular use. Equally, we should not reify what we produce and, instead, take the maps as a starting point for trying to understand the underlying patterns that are being revealed. Critically, you want to try several different methods. You will be more persuaded a location is a hot spot if several methods for hot spot analysis point to the same location. Keep in mind as well the points we raised about the problems with police data in earlier chapters. This data presents limitations. There is reporting bias, recording bias, and issues with geocoding quality. [Briz-Redón et al. (2020)], specifically, highlight that the common standard of a 85% match in geocoding is not good enough if the purpose is detecting clusters. What we see in our data may not be what it is, because of the quality of this data.

A more advanced approach at considering space time interactions and exploration of highly clustered even sequences than the one assumed by the Knox test relies on the idea of self-exciting points that are common in seismology. For details on this approach, see [Mohler et al. (2011)]. [Kulldorff et al. (2005)] also developed a space time permutation scan statistic for detecting disease outbreaks that may be useful within the context of crime analysis (see, for example, [Uittenbogaard and Ceccato (2012)] use to study spatio-temporal clusters of crime in Stockholm or [Cheng and Adepeju (2014)] use of the prospective scan statistic in London). [Gorr and Lee (2015)] discuss an alternative approach to study and respond to chronic and temporary hot spots. Of interest as well is the work by [Adepeju et al. (2021)], and the associated R package Akmedoids ([Adepeju et al., 2020]), for classifying longitudinal trajectories of crime at micro-places.

Also, as noted in previous chapters, we need to acknowledge the underlying network structure constraining the spatial distribution of our crime data. [Shiode et al. (2015)] developed a hot spot detection method that uses a network-based space-time search window technique (see also [Shiode and Shiode (2020)] for more recent work). However, the software implementation of this approach has not yet seen the light as of this writing despite the authors mentioning a "GIS plug-in tool" to be in development in their 2015 paper. Also relevant is the work by [Briz-Redón et al. (2019)] that developed an R package (DRHotNet) for differential risk hot spots on a linear network. This is a procedure to detect whether specific type of event is over-represented in relation to the other types of events observed (say, for example, burglaries in relation to other crimes). There is a detailed tutorial for this package in [Briz-Redón et al. (2019)].