Chapter 4: Mapping Crime and Geographic Information Systems
Definition in geographic space
The term hot spot has become part of the crime analysis lexicon and has received a lot of attention. What are hot spots? How do we recognize them?
A hot spot is a condition indicating some form of clustering in a spatial distribution. However, not all clusters are hot spots because the environments that help
generate crimethe places where people arealso tend to be clusters. So any
definition of hot spots has to be qualified. Sherman (1995) defined hot spots "as small places in which the occurrence of crime is so frequent that it is highly
predictable, at least over a 1-year period." According to Sherman, crime is approximately six times more concentrated among places than it is among individuals, hence the importance of asking "wheredunit" as well as "whodunit."
(See the appendix for hot spot-related resources.)
A great deal of confusion surrounds the hot spot issue, including the distinction between spaces and places. Block and Block (1995) pointed out that a place could be a point (such as a building or a classroom) or an area (such as a census tract or a metropolitan region). However, the former generally are regarded as places, and the latter, with their greater area, are spaces.
Sherman's definition notwithstanding, there is currently no widely accepted
definition of a hot spot. Indeed, a rigid, absolute definition may not be possible. Except for programs with procedures that self-define hot spots, such as the Spatial and Temporal Analysis of Crime (STAC) program (Block, 1995), jurisdiction-
specific procedures to define hot spots may make the most sense because they will fit local conditions. In Baltimore County, Maryland, for example, hot spots are identified according to three criteria: frequency, geography, and time. At least two crimes of the same type must be present. The area is small, and the timeframe is a 1- to 2-week period. Hot spots are monitored by analysts until they become inactive (Canter, 1997).
In many cases, analysts may not be able to define hot spots but may know one when they see it. This makes comparisons difficult both within and between jurisdictions.3 Furthermore, meaningful time-based analyses are problematic, because hot spot definition criteria may not be used consistently over time.
Wide interjurisdictional and intrajurisdictional variations in environments also make the application of absolute definition criteria tricky. For example, the size and shape of city blocks vary widely. West of the Appalachian Mountains, city layouts are usually dictated by the rectangular land survey system, and blocks tend to be fairly regular and rectangular. In the east, where metes-and-bounds surveys prevailed, blocks are more likely to be irregular in shape and size. Densities also vary greatly. Can the same definition criteria
be applied in low-density areas as in high-density areas? Crime-prone populations are found in both environments. Can hot spots exist in very low-density suburbs? Residents would probably think so.
Hot spots and scale
Are hot spots purely a function of scale? Some argue that any set of points in
geographic space can be made into a
hot spot if the scale is modified enough.
At extremely small scale,4 all the crime incidents in an entire metropolitan area appear to be a hot spot (figure 4.15, upper left). As scale increases, points become more dispersed (figure 4.15, upper right and lower left) until, at the largest scale, individual points can be isolated (figure 4.15, lower right). The level of resolution in the absence of absolute criteria makes it possible to manipulate the presence or absence of hot spots. However, absolute criteria are difficult to apply in urban environments (Brantingham and Brantingham, 1995).
Generally, the hot spot concept is applied to street crime rather than white-collar crime, organized crime, or terrorist crime. That a few white-collar crimes might
overwhelm street crime in their economic impact tends to be ignored. This may be because white-collar crime does not cause the same kind of community fear and anxiety as street crime. Similarly, if a city experienced several terrorist bombings or school shootings within 1 year, it is considered a hot spot that defies the normal hot spot definition. There is a qualitative aspect to hot spots; they refer only to
limited crime types.
Hot spots in time
Just as hot spots can be described geographically, they can also be defined using time-related criteria. An important question is: How long is a hot spot "hot"?
The answer requires defining an incident accrual rate within the spot, based on units of time. Related decisions are needed to determine whether the hot spot's "temperature" is measured according to all confirmed crimes, all calls for service, specific crimes, or other conditions. In a GIS framework, hot spots (and/or incidents within hot spots) can be color coded or otherwise symbolized according to their age.
An approach to monitoring hot spots over time is shown in figure 4.16. This map shows Devil's Night arson hot spots in Detroit in 1994 and 1997, using the STAC program developed by the Illinois Criminal Justice Information Authority. Although not a mapping program itself, STAC can
be used with most popular GIS packages. (For additional details on STAC, see the appendix and figure 4.20.)
Definition and measurement
What is a hot spot? Perceptions and definitions vary widely. Some analysts may see a hot spot as any cluster that looks interesting. Others define hot spots using rigid, detailed criteria. A study by Buerger, Cohn, and Petrosino (1995) found that the latter group initially used the following relatively formal criteria:
The Buerger group further identified three principal definition-related issues:
- Not more than one standard linear street block (one side of the street only).
- Not more than half a block from an intersection.
- No closer to another hot spot than one block.
- Public space. Hot spots were initially limited to one side of the street, raising the question of how street curtilage (public space in front of private properties) would be treated. Common sense dictated that if a patrol car was across the street, technically outside the hot spot, it should be considered in the hot spot, so the definition was modified to include both sides of the street.
- Intersections. Ambiguities surrounded the definition of an intersection. The term eventually came to include not only the street, but also adjacent sidewalks and buildings. Even when a hot spot did not technically include all four corners of an intersection, it was found that the best viewpoint for seeing around a corner might be on the other side of the street, outside the hot spot. Thus, all four corners of intersections came to be included in hot spots.
- One-block exceptions. Irregular blocks with large open spaces contained some hot spots, making exceptions to the one-block rule.
In practice, hot spots are defined in numerous ways, some with rigid criteria, like those above, and others with a more flexible approach. None is right or wrong. Both approaches have pros and cons, and an informal cost-benefit analysis can determine the ideal criteria in individual locations. The sharply defined criteria may omit many commonsense exceptions (but allow greater comparability in space and time); softer rules permit easy adaptation to local variation (but make comparisons difficult).
Hot spot mapping
A detailed presentation of hot spot mapping methods is beyond the scope of this guide. However, an investigation sponsored by the Crime Mapping Research Center at the National Institute of Justice in 1998 can offer some tips. This assessment found that most hot spot analysis methods fall into one of five categories: visual interpretation, choropleth mapping, grid cell analysis, cluster analysis, and spatial autocorrelation (Jefferis, 1999; see also Canter, 1995).
All methods of hot spot mapping should produce similar maps if there are underlying and recognizable point clusters. Something is wrong if a method produces clusters where visual inspection indicates there are none. However, analysis should recognize that some methods involve user-defined search criteria, and variations in those criteria, such as differences in cell sizes or search radii, can affect outcomes.
- Visual interpretation. The survey showed that, of the police departments that do computer mapping, 77 percent conducted hot spot analyses. Of these, 86 percent identified hot spots visually, and 25 percent used a program to perform this task (Mamalian and La Vigne et al., 1999). The problems presented by the visual approach include overlapping points, points stacked on top
of one another, making it impossible to see how many incidents are represented5 (that is, only one appears at any given location). Most serious, perhaps, is that readers' interpretations of point data vary, resulting in different interpretations of the same patterns.
- Choropleth mapping. Areas are shaded according to their data values, by either rate or frequency. The caveats mentioned in chapter 2 still applyclass interval selection methods will affect the appearance and interpretation of the map (see figures 2.15 and 2.16), as will color choices, shading levels, and size variation among the polygons. The latter elements tend to draw attention to the largest areas, particularly when they have higher data values.
- Grid cell analysis. A grid is superimposed over a map. Points within cells, or within a designated radius from the centers of the cells, are assigned to the cells. The size of cells is variable and affects the outcome of the analysis. Small cells present higher resolution,
at the cost of more computer resources. With larger cells, resolution suffers,
but computation is easier. What is the advantage of grid cell analysis over a pin map? First, adding points to the grid solves the problem of "stacked" data points, which occurs when multiple incidents occur at the same location or nearby locations. Second, the points are transformed into a smooth surface, generalizing the data. (For related methods, see the appendix: ArcView Spatial Analyst Extension, Idrisi, Vertical Mapper, the U.S. Department of Justice Criminal Division Hot Spot Slider.) Several examples of grid cell analysis have been illustrated in figures 4.11, 4.12, and 4.13. Another map of this type is shown in figure 4.17, which depicts hot spots in the United Kingdom city of Nottingham and police perceptions of hot spots. This map was produced using the custom program known as SPAM (Spatial Pattern Analysis Machine), which links to MapInfo for the finished map (see appendix). Variations of surface mapping include three-dimensional renditions, as noted in chapter 1. One key to readers' perception of three-dimensional maps is the degree of vertical exaggeration in the map. In the examples shown in figures 4.18 and 4.19 of Salinas, California, quite different types of data (firearm crimes and gangs) are shown in three dimensions.
- Cluster analysis. Cluster analysis methods depend on the proximity of incident points. Typically, an arbitrary starting point ("seed") is established. This seed point could be the center of the map. The program then finds the data point statistically farthest from there and makes that point the second seed, thus dividing the data points into two groups. Then distances from each seed to other points are repeatedly calculated, and clusters based on new seeds are developed so that the sums of within-cluster distances are minimized. (For related methods, see the appendix: STAC, SaTScan, SpaceStat, and Geographic Analysis Machine (GAM.) Figure 4.20 illustrates hot spots derived from the STAC method, which performs the functions of radial search and identification of events concentrated in a given area (Levine, 1996).
- Spatial autocorrelation. This concept relies on the idea that events that happen in different locations may be related. In a crime hot spot, for example, underlying social and environmental processes generate crimes in a small area. Multiple events, such as the presence of drug markets, may have similar causes. This means that statistical measures of this condition, known as autocorrelation, can serve as hot spot indicators (Roncek and Montgomery, 1995).