Crime hotspots

Nearest neighbor distances, also known as the nearest neighbor index (NNI), was an area of interest of two botanists in the early 1950s, Philip Clark and Francis Evans. The two botanists began designing a formula to distinguish patterns of plants and animals and their distributions in their environment. Clark & Evans (1954) proposed a formula that would measure the spacing between plants and animals in a population that have a random distribution. If it was randomly distributed, a mean distance to the nearest neighbor could be developed. They defined a random distribution as “a set of points on a given area that have the same chance of occurring in any sub-area as any other point” (Clark & Evans 1954, p. 446).

The methodology has been adapted into CrimeStat, a computer program built to analyze crime data. This program uses nearest neighbor index (NNI) to test for clustering to determine if there is a “hotspot” of crime. CrimeStat uses Clark's and Evans' theory and assumes that the distribution of crime used to perform global statistics have a random distribution (Eck et al. 2005). NNI compares observed distances between each point on a map and its nearest neighbor, or in other terms between each crime incident. The distances are then computed to create an average distance to determine if a crime pattern is randomly dispersed (Ratcliffe 2004).

The following will explain in full detail the steps to calculate NNI according to Eck et al. (2005). First, crime incidents are geocoded on a map, and then the distance between one crime incident and its neighbor is calculated. Following that all the distances are added up and divided by the number of crime incidents on the map. According to Eck et al. (2005) this value is called the observed average nearest neighbor distance. Then a map of random incidents needs to be made covering the same area being analyzed. The same process of calculations needs to be made to make the average random nearest neighbor distance. These two numbers then create a ratio that compares the observed incidents to the random incidents that is called the nearest neighbor index.

Eck et al. (2005) further explain that if the results generated are less than 1.0 the crime incident data are considered clustered. If the results are equal to 1.0, the crime incident data are randomly distributed on the map. Finally a nearest neighbor index that is greater than 1.0, the data set shows a significant uniform crime pattern in then data set. Using the nearest neighbor index tests for complete randomness in a set of data points. This is useful for analysts because it is a technique that can measure changes of density over periods of time (Ratcliffe 2004)

The development of spatial and temporal analysis of crime ellipses, or STAC ellipses, started off as a program to determine a “hot circle” of crime incidents on crime maps (Block 1995). Samuel Bates created a formula that used a grid, rectangular or triangular, to create boundaries around an area. A radius then would be defined, and a circle would be created around a pinpoint of each crime incident. Following this, another grid is created that creates circles that are half of the original radius defined. This grid is then combined with the first grid to create a circle that contains the highest number of incidents, creating the “hot circle” (Block 1995). This method created the foundation of what is now used to create hot spot ellipses.

Bate’s original formula did not answer if the “hot circle” represented an area that clearly had a higher density of crime incidents or not. The formula had other problems as some “hot circles” would overlap and share same crime incidents. The “hot circles” also sometimes became elongated creating ovals (Block 1995). These problems led to the creation of the hot spot ellipses.

Ellipses are created now to show different levels of dispersion of crime incidents. They are always used in analysis to examine if there are any directional trends in the data set. First a user sets the size of the ellipses, typically for a crime data set on a map, miles are used. Following this, the user defines the standard deviation amount they want to use; this determines the number of data points wanted to be included in the ellipse. Typically one or two standard deviations are used; one standard deviation includes sixty-eight percent of the data, and two includes ninety-five percent of the data (Mitchell 2005).

An example of STAC ellipses using two standard deviations. The black ellipse is a hotspot containing bars in the city of Kenosha, WI. The yellow ellipse is hotspot of DUI crimes for the city.

STAC ellipses have become an essential tool for analysts because of its efficiency and quickness. Studies typically use STAC ellipses to compare different data sets. Usually, areas of crime over periods of time are examined using the ellipses (Levine 2005). Ellipses are called first-order statistics because they give analyst a starting point in examining a data set, while looking at the global statistics. Ellipses create a firm boundary for the data set that does not necessarily follow streets or neighborhood outlines. Therefore, when examining these ellipses, more statistical analyses should be used on top of the ellipses (Eck et al. 2005).

A study that uses nearest neighbor index (NNI), and STAC Ellipses was completed for the City of Roanoke, Virginia. The study focuses on data reported to police on robberies that occurred between January 1, 2004 and December 31, 2007, with a total of 904 robberies reported (Van Patten, McKeldin-Coner & Cox 2009). The purpose of this study was to determine if there were localized areas of robberies using hotspot analysis. The project first began by geo-coding all data onto a pinpoint map. The records of all robbery data came from the cities records and management system. After receiving satisfying results from geocoding the data, the data was then tested for global and spatial clustering (Van Patten, McKeldin-Coner & Cox 2009). To test for spatial randomness, NNI was employed. For each year, 2004-2007, NNI was calculated and compared to a set of random points. Each year presents a NNI value of less than one (Van Patten, McKeldin-Coner & Cox 2009). A value less than one, according to Eck et al. (2005) signifies that the clustering in the data set is consistent in its distribution. (Van Patten, McKeldin-Coner & Cox 2009). concluded that the data set has significant global spatial clustering that applies to the entire study population.

Following the testing of random clustering, using NNI hotspot analysis, was employed in the study. The study examined hotspot using many different spatial analysis techniques. The study used nearest neighbor hierarchal clustering (NNH) and other kernel density estimation (KDE). The following will look at the analysis of STAC ellipses in further details for the purpose of this section. Ellipses were developed for each year and then were further examined using different techniques. To create the ellipses, parameter settings were made based on the distance a person can travel on foot in approximately five minutes before looking for another form of transportation. A search radius of a quarter-mile was set for the data (Van Patten, McKeldin-Coner & Cox 2009). Ellipses were made for the total number of robbery incidents, 904. Fifteen offenses per ellipse were used. Offenses were dropped to seven incidents per ellipse for a single year, and for two-year increments 7, 10, and 15 incidents were evaluated (Van Patten, McKeldin-Coner & Cox 2009).

With all the different techniques employed in this study, it was concluded that STAC ellipses had the greatest reliability rate. It was determined that ellipses tend to be less accurate than other methods utilized; but, by far were more consistent. Van Patten, McKeldin-Coner & Cox (2009) concluded in this study that all methods utilized converge around the same areas of the city. This indicated there is random spatial clustering and agreement between the different methods employed. Using the hotspot analysis, different areas in the city were identified as “problem areas.” There were areas that were determined to be crime generators and others attractors. Van Patten, McKeldin-Coner & Cox (2009) recommend that for areas of attractors increase in guardianship, and better place management should be the area of focus. Areas that contain crime generators would require more strategic approaches by police to make an impact (Van Patten, McKeldin-Coner & Cox 2009, p. 27).

In the early 1990s, crime began to rise in Chicago, Illinois at a significant rate. Many social groups asked the Community Safety Project to analyze relationships between alcohol selling establishments and crime in the city (Block & Block 1995) harv error: no target: CITEREFBlockBlock1995 (help). To analyze data for the city, STAC ellipses were utilized. Location data of establishments with liquor licenses were retrieved from the City of Chicago Department of Revenue. Three types of liquor licenses were utilized: taverns, packaged goods, and incidental consumption (Block & Block 1995, p. 151) harv error: no target: CITEREFBlockBlock1995 (help). In 1993, there were a total 5,947 liquor licenses, with some establishments holding several. This data was then geocoded to create a pinpoint map of the respected locations. The study period of incidents was a six-month period from January–June 1993. There were 3,364 crime incidents reported to police over this period of time that occurred in or around the liquor establishments. These crimes included property crimes, drug offenses, and misdemeanors, but they were not limited to these categories (Block & Block 1995, p. 152) harv error: no target: CITEREFBlockBlock1995 (help). This data was also geo-coded into a pinpoint map for analysis.

In order to examine the concentration of liquor establishments and crime incidents, STAC ellipses were utilized. Five ellipses were generated that contained the densest areas of the liquor establishments. It was concluded that all ellipses were contained in the northern area of the city, centered on nightlife areas, a fashionable singles area, and shopping centers (Block & Block 1995, p. 158) harv error: no target: CITEREFBlockBlock1995 (help). Six ellipses were generated for the crime incident hotspots. Two of the ellipses were concentrated in areas of hotspots of liquor establishments, whereas four of them resided in areas of low-income census tracts. C. Block and R. Block concluded from these ellipses that hotspots of liquor establishments do not necessary attract the most crime.

This study further examined the statistics of crime related to liquor establishments by dissecting the number of each category that were included in each ellipse. It was determined that crimes of homicide were typically committed in low-income areas of the city that were not located near the liquor establishment hotspots. It was also determined that hotspot areas of crime in the liquor establishment hotspot were typically located on main streets of the city that attracted tourism, and also near rapid transit and singles' neighborhoods (Block & Block 1995) harv error: no target: CITEREFBlockBlock1995 (help). Block & Block (1995) harvp error: no target: CITEREFBlockBlock1995 (help) concluded the study by stating that density of liquor licenses and density of crime are not strongly related. These areas do attract crime, but they are not necessarily always the cause of crime.