6.3.1Anchor Points

Within an activity space are anchor points or bases, the most important places in one’s spatial life (Coucelis, Golledge, Gale, & Tobler, 1987). The main anchor point for the vast majority of people is their residence, but other bases may exist such as a work site or close friend’s home. Some street criminals do not have a fixed address, basing their activities out of a bar, pool hall, or some other social activity location (Rengert, 1990). They can also be transient, homeless, living on the street, or mobile to such a degree that their anchor point constantly shifts. Offender anchor points are important in the understanding of crime patterns.

Especially significant are the “anchor points” which focus the routine activities of criminals on specific sites in our urban environments .... If a criminal routinely visits the same location nearly every day, this location may serve as an “anchor point” about which other activities may cluster. This proposition is implicitly recognized when we document that most crime occurs near the home of the criminal (Brantingham and Brantingham, 1984). The home is the dominant anchor point in the lives of most individuals. However, other anchor points also are important influences on the spatial behavior of criminals. (Rengert, 1990, pp. 4–5)

Criminals, to the extent that they live in everyday society, are bound by the normal limitations on human activity, shaped by the dictates of work, families, sleep, food, finances, transportation, and so forth. Canter (1994) suggests that environmental psychology and an understanding of offenders’ mental maps (“criminal maps”) can assist in the investigation of violent crime. Offenders operate within the confines of their experience, habits, awareness, and knowledge. “Like a person going shopping, a criminal will also go to locations that are convenient” (p. 187).

Criminal predators may be stable or nomadic. Stable offenders possess a permanent anchor point during their period of criminal activity. Nomadic offenders are transient, lacking a fixed address or anchor point. Albert DeSalvo, for example, resided in the same dwelling throughout his killing period, while Ottis Toole lived on the road, travelling from city to city, and state to state. Other offenders fall somewhere between these two positions. David Berkowitz resided in two different locations in New York City during his crimes, while Ted Bundy, though not nomadic, moved several times during his murder spree (Terry, 1987; U.S. Department of Justice, 1992).

6.4 Centrography

The spatial mean (sometimes referred to as the centroid or mean centre) is a univariate measure of the central tendency of a point pattern (Taylor, 1977),

© 2000 by CRC Press LLC

and has been used to analyze crime site patterns. This geographic “centre of gravity” minimizes the sum of the squared distances to the various points in a pattern. It provides a single summary location for a series of points and has a variety of geostatistical uses collectively referred to as centrography.

The spatial mean is defined as:

It is possible to determine a weighted mean centre if certain points are more important in a centrality analysis than others. The median centre – also known as the centre of minimum travel – is another measure of central tendency in point patterns and is found by locating the position from which travel to all points in a spatial distribution (i.e., the sum of the distances) is minimized. There is no general method for its calculation and the median centre must be calculated through an iterative process.

Changes over time in the location of the spatial mean allow for the calculation of the geographic equivalents of concepts of velocity (rate of spatial change), acceleration (rate of change in velocity), and momentum (velocity multiplied by number of points) (LeBeau, 1987b). The spatial mean is the basis for calculating the standard distance of a point pattern, a measure of spatial dispersion analogous to the standard deviation (Taylor, 1977). When used with the mean centre it can help describe two-dimensional distributions, and through the concept of relative dispersion (the ratio of two standard distances), allow for comparisons of spread between different sets of points. Similarly, the median distance is the radius which encompasses one half of the points in a spatial distribution.

The standard distance is defined as:

© 2000 by CRC Press LLC

Centrography has been used in a variety of criminological studies and investigative contexts. The spatial mean and changes in its location over time were calculated for rape incidents in San Diego (LeBeau, 1987b). An investigative review team helped locate the hometown of the Yorkshire Ripper from the geographic centre of the murder sites (Kind, 1987a). A similar approach in a blackmailing case used cash withdrawal points from automated teller machines (ATMs) to determine the offender’s residence area east of London (Britton, 1997). Such techniques were also employed in a retrospective analysis of the Hillside Stranglers (Newton & Swoope, 1987). The FBI and ATF analyze serial arson cases by determining the spatial mean of fire sites (Icove & Crisman, 1975). Traditionally, centrography has been the primary form of geographic analysis used to support criminal investigations.

As helpful as centrographic analysis may be in certain cases, the spatial mean suffers from three serious methodological difficulties: (1) it generally provides only a single piece of information; (2) it is distorted by spatial outliers; and (3) theory suggests the intersection between offender activity space and target backcloth (the distribution of crime targets across the physical landscape) may produce crime locations unrelated to measures of central tendency. If the activity space of an offender is not centred around his or her home, or if the target backcloth is highly variable, then the spatial mean of the crime sites and offender residence are not correlated.

A study of the spatial patterns in a sample of British serial rapists revealed the limitations in centrographic analysis (Canter & Larkin, 1993). The study plotted maximum distance from residence to crime site against maximum distance between crime sites, producing the following regression equation:

where:

y is the maximum distance in miles from residence to crime site; and x is the maximum distance in miles between crime sites.

The gradient of 0.84 in Equation 6.5 indicates an eccentric placement of the residence vis-à-vis the crime sites (a perfect centric placement would yield a gradient of 0.5). Similar regressions for U.S. and British serial murder crime location data yield values of 0.81 and 0.79, respectively (Canter & Hodge,

© 2000 by CRC Press LLC

1997), and an Australian study found gradients of 0.77 for rape, 0.60 for arson, and 0.65 for burglary (Kocsis & Irwin, 1997). This eccentricity suggests the spatial mean is limited in its ability to predict offender residence location.

Additionally, the spatial mean lacks real world significance. The geographic centre of Canada is in the Northwest Territories which tells one little about the demographic, economic, or political patterns of that country. LeBeau (1987b) notes “an important property about the mean center to remember is that it is a synthetic point or location representing the average location of a phenomenon, and not the average of the characteristics of the phenomenon at that location” (pp. 126–127; see also Taylor, 1977).

Studies of journey-to-crime trips, particularly those that are offence specific, help determine the most likely radius within which offenders search for victims. For example, research has consistently shown targets are typically located within one or two miles of offender residence (see McIver, 1981). When utilized in conjunction with the spatial mean, such information may be of investigative value.

6.5 Nearest Neighbour Analysis

While the spatial mean provides a way to measure central tendency in a point pattern, nearest neighbour analysis, first developed by plant ecologists, supplies a way to quantify spacing between points (Taylor, 1977; see Boots & Getis, 1988; Garson & Biggs, 1992). Distances between points and their closest neighbours provides important information concerning a pattern’s degree of randomness and underlying evolution. It is also possible to calculate other proximity pattern measures including centroid, k-nearest neighbour, mean interpoint, and furthest neighbour distances (Garson & Biggs).

The random allocation of points to a map can be described by the Poisson process (Taylor, 1977). The Poisson probability function is defined as:

where:

p(x) is the probability that a given small area will contain x points; and

λis the expected probability of finding a point within that area.

Connecting nearest neighbour analysis to the Poisson probability function allows the degree of clustering, dispersion, or randomness in a given independent point pattern to be calculated. The R scale, the ratio between the actual average nearest neighbour distance and that expected under an

© 2000 by CRC Press LLC

assumption of randomness, provides a simple index for measuring divergence from randomness. It is calculated as follows:

Theoretically the R scale can fall between the limits of 0 to 2.149, though real world patterns tend to range between 0.33 and 1.67 (Taylor, 1977). A value of 1 (meaning that ra = re) indicates a random pattern, values smaller than 1, a clustered pattern, and values larger than 1, a dispersed pattern. Problems result in the interpretation of the R scale if boundary placement is distorted (Garson & Biggs, 1992).

It is possible by chance for a randomly produced pattern to appear aggregated or dispersed, therefore it is necessary to determine the significance of the R scale value (Taylor, 1977). This can be accomplished through the Z-score calculated from the standard error of the expected average nearest neighbour distance. The associated two-tailed probability may then be determined from a table of normal distribution values (e.g., Blalock, 1972). The standard error (SE) is estimated as follows:

While the R scale provides a measure of spatial randomness, it says nothing about the actual evolution of the point pattern. More than one distinct process can be operating as might be found with a series of chaotic binary points (Boots & Getis, 1988). Statistical tests are only inferential, and it may be necessary to corroborate results over time or examine higher-order or k-nearest (e.g., second-nearest) neighbour distances.

© 2000 by CRC Press LLC

“Murder Alley” was the name given to an unpaved lane near downtown Kenosha, Wisconsin, where seven bizarre homicides took place between 1967 and 1981 (Newton, 1990a). The frequency and unusual nature of the crimes

— including a corpse found in a hearse, another buried beneath a rose garden, and a triple homicide — prompted investigators to publicly comment that something strange was happening in this “Bermuda Triangle of murder.” During its early years, Los Angeles was a violent frontier town. In 1850, the year California joined the Union, “Los Diablos” experienced a murder a day; with a population of 4000, this translates into a homicide rate of 1 murder per 11 residents (Blanche & Schreiber, 1998). Most of these murders took place close to the central plaza in a narrow alley slum named Calle de los Negros (“Nigger Alley”), a collection of shabby buildings, housing saloons, brothels, and gambling dens. Shootings, riots, lootings, and lynch-

ings were common activities.

“What surfaces in terrible places... is a rapport between persons and places such that the techniques of the habitat and forms of personation become indistinguishable” (Seltzer, 1998, p. 233). Routine activity and ecology of place theories provide an explanation for the phenomena of dangerous places or “dreadful enclosures.” The related concepts of “fishing holes” and “trap lines” — used by serial killers and rapists in the hunt for victims — also help explain the clustering of predatory murders and rapes. The geography of crime encompasses the study of the spatial and temporal distribution of criminal offences.

The methodological and theoretical approaches developed in a variety of disciplines are often adopted to the study of crime and criminals, and the fields of geography and urban analysis provide several analytical tools for criminologists. Perspectives that make particular use of geographic techniques include the social ecology of crime, environmental criminology, geography of crime, routine activity approach, situational crime prevention, and

© 2000 by CRC Press LLC