Section 10.1 Introduction
Subsection 10.1.1 Clusters, hot spots of crime, and near repeat victimisation
There has been a great interest within criminology and crime analysis in the study of local clusters of crime or hot spots over the last 30 years. "Hot spots" is the term typically used within criminology and crime analysis to refer to small geographical areas with a high concentration of crime. [Weisburd (2015)] argues for a law of concentration of crime that postulates that a large proportion of crime events occur at relatively few places (such as specific addresses, street intersections, street blocks, or other small micro-places) within larger geographical areas such as cities. In one of the earlier contributions to this field of research, [Sherman et al. (1989)] noted how roughly 3% of all addresses in Minneapolis (USA) generated about 50% of all calls to police services. A number of subsequent studies have confirmed this pattern elsewhere. [Steenbeek and Weisburd (2016)] argue that, in fact, most of the geographical variability of crime (58% to 69% in their data from the Hague) can be attributed to micro-geographic units, with a very limited contribution from the neighbourhood level (see, however, [Ramos et al. (2021)]). This literature also argues that many crime hot spots are relatively stable over time ([Andresen and Malleson, 2011]; [Andresen et al., 2017]; [Andresen et al., 2017b]).
There is also now a considerable body of research evaluating police interventions that take this insight as key for articulating responses to crime. Hot spots policing, or place-based policing, assumes that police can reduce crime by focusing their resources on the small number of places that generate a majority of crime problems ([Braga and Weisburd, 2010]). Policing crime hot spots has become a popular strategy in the US and efforts to adopt this approach have also taken place elsewhere. Theoretically, one could use all sorts of proactive creative approaches to solve crime in these locations (using for example conceptual and tactical tools from [Goldstein’s (1990)] problem oriented policing approach); though too often in practice directed patrol becomes the default response. Recent reviews of the literature (dominated by the US experience) suggest the approach can have a small effect size ([Braga et al., 2019]), though some authors contend alternative measures of effect size (which are suggestive of a moderate effect) should be used instead ([Braga and Weisburd, 2020]). Whether these findings would replicate well in other contexts is still an open question (see, for example, [Collazos et al., 2020]).
Thus, figuring out the location of hot spots and how to detect clusters of crime is of great significance for crime analysis. In previous chapters we explored ways to visualise the concentration of crime incidents in particular locations as a way to explore places with an elevated intensity of crime. We used tesselation and kernel density estimation as a way to do this. But, as noted by [Chainey (2014)]:
Maps generated using KDE and the other common hot spot mapping methods are useful for showing where crime concentrates but may fail to unambiguously determine what is hot (in hot spot analysis terms) from what is not hot. That is, they may fail in separating the significant spatial concentrations of crime from those spatial distributions of less interest or from random variation.
Apparent clusters may indeed appear by chance alone ([Marshall, 1991]). There are a number of tools that have been developed to detect local clusters among random variation. It is not exaggerated to say that this has been a key concern in the field of spatial statistics with practical applications in many fields of study. In crime analysis, for example, it is common to use the local \(Gi^*\) statistic, which is a type of a local indicator of spatial association (LISA). Another popular LISA is the local Moran’s \(I\text{,}\) developed by [Anselin (1995)].
These LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of non-stationarity, to identify outliers. On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic ([Anselin, 1995]). [Anselin (1995)] suggests that any LISA satisfies two requirements (p. 94):
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the LISA for each observation gives an indication of the extent of significant spatial clustering of similar values around that observation;
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the sum of LISAs for all observations is proportional to a global indicator of spatial association.
These measures of local spatial dependence are available in tools often used by crime analysts (CrimeStat, GeoDa, ArcGIS, and also R). But it is important to realise that there are some subtle differences in implementation that reflect design decisions by the programmers. These differences in design may result on apparent differences in numerical findings generated with these different programs. The defaults used by different software may give the impression different results are achieved. [Bivand and Wong (2018)] offer an excellent thorough review of these different implementations (and steps needed for ensuring comparability). Our focus here will be in introducing the functionality of the
spdep packages.
Aside from these LISAs, in spatial epidemiology a number of techniques have been developed for detecting areas with an unusually high risk of disease ([Marshall, 1991]). Although originally developed in the context of clusters of disease, these techniques can also be applied to the study of crime ([Gomez-Rubio et al., 2005]). Most of the methods in spatial epidemiology are based on the idea of "moving windows", such as the spatial scan statistic developed by [Kulldorff (1997)]. Several packages bring these scan statistics to R. There are also other packages that use different algorithms to detect disease clusters, such as AMOEBA, that is based in the Getis-Ord algorithm. As we will see, we are spoiled for choice in this regard. Here we will only provide a glimpse into how to perform a few of these tests with R.
In crime analysis, the study of repeat victimisation is also relevant. This refers to the observed pattern of repeated criminal victimisation against the same person or target. The idea that victimisation presages further victimisation was first observed in studies of burglary, where the single best predictor of new victimisation was past victimisation. This opened up an avenue of research led by British scholars Ken Pease and Graham Farrell, who noticed that the risk of re-victimisation is much higher in the days immediate to the first offence and that repeat victimisation accounts for a non-trivial proportion of crime ([Pease, 1998]). There continues to be some debate as to whether this is to do with underlying stable vulnerabilities (flag hypothesis) or to increased risk resulting form the first victimisation (boost hypothesis), although likely both play a role. Subsequent research has extended the foci of application well beyond the study of burglary and the UK (for a review see [Pease and Farrell, 2017] and [Pease et al., 2018]). From the very beginning this literature emphasised the importance for crime prevention policy, for this helps to identify potential targets for it. The advocates of this concept argue that using insights from repeat victimisation is a successful approach to crime reduction ([Grove et al., 2014]; [Farrell and Pease, 2017]).
A related phenomenon is that of near repeat victimisation. [Townsley et al. (2003)], building in the epidemiological notion of contagion, proposed and tested the idea that "proximity to a burgled dwelling increases burglary risk for those areas that have a high degree of housing homogeneity and that this risk is similar in nature to the temporarily heightened risk of becoming a repeat victim after an initial victimisation" (p. 615). Or as, in a subsequent paper, [Bowers and Johnson (2004)] put it, "following a burglary at one home the risk of burglary at nearby homes is amplified" (p. 12). So if we combine the ideas of repeat victimisation and near repeats we would observe: (1) a heightened but short-lived risk of victimisation for the original victim following a first attack and (2) a heightened but also short-lived risk for those "targets" located nearby. Although most studies on near repeats have focused on studying burglary, there are some that have also successfully applied this concept to other forms of criminal victimisation. In 2006 and with funds from the US National Institute of Justice, Jerry Ratcliffe developed a free point-and-click interface to perform near repeat analysis ([Ratcliffe, 2020]). This software can be accessed from his personal home-page. But our focus in this chapter will be in a package (
NearRepeat) developed by Wouter Steenbeek in 2019 to bring this functionality into R [Steenbeek (2021)]. At the time of writing, this package is not yet available from CRAN but needs to be installed from its GitHub repository. This can be done by using the install_github() function from the remotes package, with the code below:
remotes::install_github("wsteenbeek/NearRepeat")
Additionally, for this chapter we will need the following packages:
# Packages for handling data and for geospatial carpentry
library(dplyr)
library(readr)
library(sf)
library(raster)
# Packages for detecting clusters
library(spdep)
library(rgeoda)
library(DCluster)
library(spatstat)
# Packages for detecting near repeat victimisation
library(NearRepeat) # Available at https://github.com/wsteenbeek/NearRepeat
# Packages for visualisation and mapping
library(tmap)
library(mapview)
library(RColorBrewer)
# Packages with relevant data for the chapter
library(crimedata)
Subsection 10.1.2 Burglaries in Manchester
We return to burglaries in Manchester for most of this chapter. The files we are loading include the geomasked locations of burglary occurrences in 2017, for the whole of Manchester city and separately for its city centre. Later in this chapter, we will look at the whole of Manchester and we will use counts of burglary per Lower Super Output Area (LSOA); so we will also load this aggregated data now.
# Create sf object with burglaries for Manchester city
manc_burglary <- st_read("data/manc_burglary_bng.geojson",
quiet=TRUE)
manc_burglary <- st_transform(manc_burglary , 4326)
# Create sf object with burglaries in city centre
cc_burglary <- st_read("data/manch_cc_burglary_bng.geojson",
quiet=TRUE)
cc_burglary <- st_transform(cc_burglary , 4326)
# Read the boundary for the Manchester city centre ward
city_centre <- st_read("data/manchester_wards.geojson",
quiet = TRUE) %>%
filter(wd16nm == "City Centre")
city_centre <- st_transform(city_centre, 4326)
# Read the boundary for Manchester city
manchester <- st_read("data/manchester_city_boundary_bng.geojson",
quiet = TRUE)
manchester <- st_transform(manchester , 4326)
# Read into R the count of burglaries per LSOA
burglary_lsoa <- st_read("data/burglary_manchester_lsoa.geojson",
quiet = TRUE)
# Place last file in projected British National Grid
burglary_lsoa <- st_transform(burglary_lsoa, 27700)
Now that we have all the data we need in our environment, let’s get started.
