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Journal of Environmental Psychology 32 (2012) 37e42

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Journal of Environmental Psychology

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Criminal directionality and the structure of urban form

Richard Frank, Martin A. Andresen*, Patricia L. BrantinghamSchool of Criminology, Institute for Canadian Urban Research Studies, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6 Canada

a r t i c l e i n f o

Article history:Available online 10 October 2011

Keywords:DirectionalityGeometrySpatial analysis of crime

* Corresponding author. Tel.: þ1 778 782 7628; faxE-mail address: andresen@sfu.ca (M.A. Andresen).

1 See Sherman, Gartin, and Buerger (1989), Eck a(1997), Smith, Frazee, and Davidson (2000), Weisbu(2004) and Weisburd, Bernasco, and Bruinsma (2009

0272-4944/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.jenvp.2011.09.004

a b s t r a c t

Spatial criminology has three interrelated elements: place, distance, and direction. Though directionalityhas had theoretical support for many years, very few empirical verifications of this component of crimehave emerged. In this article, we investigate the strength of directionality by comparing a simulatedrandomized dataset and a large incident-based dataset of repeat offenders. We find strong evidence fora strong presence of directionality in criminal spatial decision-making. This aspect of the spatiality ofcrime must be considered in any attempts to understand the aetiology of crime.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Spatial criminology has a history dating back 175 years to themoral statistics of Quetelet (1831, 1842) and Guerry (1833). Withsubsequent interest in the spatial dimensions of crime in 19thcentury England (Glyde, 1856), early 20th century North Americansocial disorganization theory (Burgess, 1916; Shaw & McKay, 1931,1942), and current environmental criminology (Brantingham &Brantingham, 1981; Clarke & Cornish, 1985; Cohen & Felson,1979), one cannot deny the importance of spatial criminology tounderstand the aetiology of crimedsee Wortley, Mazerolle andRombouts (2008) for a recent collection of essays. These spatialcriminological theories have proven successful in explaining crimepatterns, helpful in understanding individual victimization, andrelevant to crime prevention/reduction activities. As such, investi-gations into the fundamental concepts of these theories areimportant for academics and practitioners to better understand thespatial nature of criminal activity. Indeed, our understanding of thespatial dimension of crime has made great advances in recent years(Ratcliffe, 2002).

Within the spatial analysis of crime, the decision-makingprocess of individuals involves three interconnected and funda-mental elements: place, distance, and direction. The first two ofthese elements (place and distance) are well-researched withincriminology. Recent developments for place form a “crime at pla-ces” literature.1 The crime at places literature argues that micro-

: þ1 778 782 4140.

nd Weisburd (1995), Taylorrd, Bushway, Lum, and Yang).

All rights reserved.

places such as street segments or street corners are key to under-standing criminal activity. The journey to crime (distance)continues as a focus in spatial criminology. Assuming the decision-making process to commit a crime begins at the home location, the“journey to crime” can be relatively short. This assumption may beproblematic because the journey to crime may start from placeother than the home (Townsley & Sidebottom, 2010). If this is thecase, much of the inference based on this research may bemisleading. However, this assumption is made because of datalimitations. Police records that have information on offenders willonly have their home address. Only detailed interview data wouldbe able to contain such details. With this criticism in mind, thejourney to crime being short has been supported in number studiesfor locations in both the United States and Europe. The trip(distance from home) varies from crime type to crime type, by ageof the offender, by location of potential targets, by mode of transit,but tends to be short (Bernasco & Block, 2009; Castanzo, Halperin, &Gale, 1986; LeBeau, 1987; Phillips, 1980; Pyle et al., 1974; Wiles &Costello, 2000)dsee Bernasco (2006) for a comprehensive reviewin the context of burglary. Also, see van Koppen and De Keijser(1997) and Rengert, Piquero, and Jones (1999) for discussions onthe issue of distance decay function as a representation of the rateat which offending decreases as the distance from home increases.

Directionality, however, is an under-researched area in crimi-nology. White (1932), Brantingham and Brantingham (1981, 1984),Rengert and Wasilchick (1985) and Ratcliffe (2006) approach thedirections and paths people use to move from one activity node toanother. Because of the constrained nature of our (built) environ-ment, we normally develop routines between frequently visiteddestinations. The trips between home and work or work andentertainment areas have a directional orientation; we routinelytravel along routes that are directed towards our destinations.Despite this importanceof directional knowledge/information, there

R. Frank et al. / Journal of Environmental Psychology 32 (2012) 37e4238

are only two theories and a small number of empirical investigationsthat consider direction in the (spatial) criminological literature.

2. Directionality and crime: theory and evidence

The theoretical foundation for the presence of directionality incriminal activity is the geometric theory of crime (Brantingham &Brantingham, 1981, 1984, 1993) and temporal constraint theory(Ratcliffe, 2006). The theoretical work of the Brantinghams has itsroots in the work of Lynch (1960), who described the ways inwhichwe move through our (urban) environment. The most importantconcepts from this work for understanding directionality in crim-inal behaviour are nodes and paths. Simply put, nodes are thoseplaces in our environment that we travel to and from: home, work,school, recreation sites, entertainment, and shopping; paths are thevectors that we move along to get from one node to the next: mostoften, these paths are roads and walkways. Put together, nodes andpaths comprise the areas within our environment that constituteour activity and awareness spaces, because this is where we spendmost of our time.

Brantingham and Brantingham (1981, 1984, 1993) representthese spaces as maps that can then be used to illustrate why weshould expect directionality in criminal behaviour. Fig. 1 shows twocases: 1) strong directionality and 2) weak directionality. In the caseof strong directionality, the vast majority of a person’s activities arecontained within a 45� angle. As such, if crime is (partially) theresult of opportunities that arise because of non-criminal activities(Brantingham & Brantingham, 1981, 1984; Cohen & Felson, 1979;Felson & Cohen, 1980, 1981), such a person’s criminal activitieswill also be contained within a 45� angle. In the case of weakdirectionality, this person’s activities are in all directions such thata priori no directional bias can be expected.

A consequence of considering these two forms of activity spaceis that the strength of directionality, in general, is going to dependon the relative frequency of strong and weak directionality activityspaces in the general population. However, if the majority ofpeoples’ activities are concentrated along one particular vector(work or recreation, for example), directionality will be present.This, of course, is an empirical question.

Temporal constraint theory (Ratcliffe, 2006), as the namesuggests, outlines the important of timewhen trying to understandcriminal activity. Temporal constraint theory not only shows theimportance of time, but that time and space are intimately related:because of temporal constraints, we constrain our movementsthrough space. In fact, Ratcliffe (2006) develops maps based ontemporal constraints that are quite similar to the awareness spacemaps of Brantingham and Brantingham (1981, 1984, 1993). Conse-quently, in order to consider our temporal constraints, we mustchoose our direction carefully.

Rengert and Wasilchick (1985) is the first piece of research toinvestigate empirically the strength of directional bias in criminalbehaviour, specifically burglary.2 They find that more than 50percent of burglary crimes occur within a 45� angle from the homelocation of the offenderd12.5 percent of the potential use of space.Moreover, when burglars who also have legitimate employmentare considered, upwards of 75 percent of crimes are containedwithin a 45� angle; most of the burglaries are just beyond the workplace or along the pathway between work and home. When otherspatial knowledge of burglars is considered (location of fence,friend’s residence, or other recreation sites) the search pattern isless directional but a distinct directional bias is still present.

2 The second edition of their work, Rengert and Wasilchick (2000) performed thesame analysis.

Following this initial work by Rengert and Wasilchick (1985),there has been relatively little research on the issue of directionalityin criminological research; in fact, we are only aware of five otherpieces of research on this subject matter. Immediately following thework of Rengert and Wasilchick (1985), Castanzo et al. (1986) testwhether offenders who live near one another travel in the samedirection to commit their offences. They find that regardless of thecrime classification offenders that live close to one another move insimilar directions to commit their offences. Only considering serialhomicide, Godwin (2001) and Lundrigan and Canter (2001) findthat serial murderers are directionally biased for not only targetselection, but also the disposal of bodies. Goodwill and Alison(2005), investigating serial homicide, rape, and burglary, not onlyfind a strong directional bias, but the strength of this directionalbias varies by crime type: it is strongest for burglary, then rapists,and murderersdthe majority of burglars and rapists select theirtargets within a 90� angle.

The difficulty with this discussed research, particularly the veryearly work, is the size of their samples. Though the small samplesused in these papers may indeed be representative of criminaldirectionality, it is difficult to make any claims of generalizability.Wiles and Costello (2000) is the first paper to investigate the travelpatterns of offenders with a large sample of offenders, approxi-mately 19,000. They find that offenders do have a directional biastowards urban areas, but there is no indication of the strength ofthat bias.

In this paper, we contribute to the directionality literaturethrough an examination of directionality on a large number ofoffenders. We confirm a directional bias with this large data set andshow the strength of the directional bias through computersimulation.

3. Data and methods

3.1. Data

All crime data are provided by the Royal Canadian MountedPolice in British Columbia. British Columbia is Canada’s western-most province, bordering the U.S. states of Alaska, Washington,Idaho, and Montana and the Canadian province of Alberta. BritishColumbia has approximately 4 million residents and a total of 186police jurisdictions. The dominant police force in British Columbiais the Royal Canadian Mounted Police (RCMP), responsible forpolicing 174 of the 186 British Columbia police jurisdictions and 67percent of the provincial population, approximately 2.7 millionpersons.3 Because of the variety of jurisdictions, the RCMP patrolurban, suburban, and rural areas. The incident-based data used inthe analyses below are extracted from the RCMP Police InformationRetrieval System (PIRS). All data are extracted from August 1, 2001through July 31, 2006. The files contain for these five years thecomplete set of incidents dealt with by the RCMP. Within thesefiles, there are details regarding the offence event, such as locationand type of crime. Linked to the events are the people involved inthe event, their role, and home address, amongst others.

The PIRS database contains information for approximately 5million negative contacts with the police involving approximately 9million individuals (offenders, victims, complainants, andwitnesses) over the five available years. Despite the PIRS databasebeing so large and there being 174 different police jurisdictions

3 The remaining police jurisdictions include Abbotsford, Central Saanich, Delta,Esquimalt, Nelson, New Westminster, Oak Bay, Port Moody, Saanich, Vancouver,Victoria, and West VancouvereEsquimalt merged with Victoria after our data timeframe ended.

Home

Work

Entertainment

Shopping Home

Work

Entertainment

Shopping

a b

Fig. 1. Geometry of crime a) Strong directionality. b) Weak directionality.

R. Frank et al. / Journal of Environmental Psychology 32 (2012) 37e42 39

reporting to it, they are tabulated from one police agency orreporting body. Unlike the National Incident Based ReportingSystem (NIBRS) database that combines data from thousands ofenforcement agencies, the RCMP data minimize inconsistencies inreporting of criminal incidents. From this dataset, the details of allrepeat offenders who were charged or had charges recommendedagainst them in at least 2 burglaries were analyzed. This yielded2622 offenders and 8126 burglaries for the entire province. Thisdataset is hereafter referred to as the “real” dataset.

A breakdown of the percentages of offenders that had differentnumbers of crime trips is shown in Table 1. Immediately evidentfrom this Table is that the vast majority of offenders had beencharged with 2 or 3 burglaries. Though there are offenders withmore than 10 crime trips, these offenders consist of 2.2 percent ofthe data. Therefore, their inclusion or exclusion has little qualitativeimpact on the results below.

For comparative purposes, a “baseline dataset” was generatedthrough a simulation using randomized data for each offender’shome location and crime locations. This dataset consisted of100,000 simulated offenders, each having a randomly generated XYcoordinate for the home location. In this baseline dataset, eachoffender had c crimes associated to them, where c was randomlydetermined but was between 4 and 21. Finally, each crime had

Table 1Number of trips, offenders, and burglaries.

Number oftrips

Offenders Burglaries Percentoffenders

Percentburglaries

2 1618 3236 61.7 39.83 482 1446 18.4 17.84 223 892 8.5 11.05 87 435 3.3 5.46 56 336 2.1 4.17 34 238 1.3 2.98 28 224 1.1 2.89 17 153 0.6 1.910 19 190 0.7 2.311 11 121 0.4 1.512 5 60 0.2 0.713 9 117 0.3 1.414 4 56 0.2 0.715 1 15 0.0 0.216 2 32 0.1 0.417 5 85 0.2 1.018 1 18 0.0 0.219 3 57 0.1 0.720 1 20 0.0 0.221 1 21 0.0 0.322 3 66 0.1 0.823 6 138 0.2 1.724 1 24 0.0 0.325 2 50 0.1 0.628 1 28 0.0 0.331 1 31 0.0 0.437 1 37 0.0 0.5Total 2622 8126 100 100

a randomly generated XY coordinate associated to it to determinethe location of the event. Though it is possible for the location of theevent to be placed in an unrealistic location such as in the middle ofa lake or on top of a mountain, this is not problematic for theanalysis at hand. This is because we are concerned with the direc-tion the offenders move, not the location itself. In total 1,000,000simulated offence locations were generated.

Because our simulated baseline dataset was created randomly,we know that there is no directionality preference present.Therefore, if the results of the analysis on this baseline dataset aresimilar to the real dataset, it would imply that directional prefer-ence does not exist in offender activity. However, if significantdifferences do exist, then we can conclude that actual offenderactivity does exhibit directionality preferences.

In addition to the data for all of British Columbia, we include theanalysis of two municipalities within the Metro Vancouver region(Coquitlam and Surrey) and one municipality outside the MetroVancouver region (Prince George)ethe selection of these munici-palities is primarily because they contain a large number of crim-inal incidents. Coquitlam is a city of approximately 115,000persons, whereas Surrey is a city of approximately 400,000 personsand Prince George is a city of 71,000 persons. Aside from their size,these three municipalities each have very different urban forms.

Both municipalities within Metro Vancouver have urban sprawl,light industry, strip development and malls, apartments, and singlefamily dwellings, but the locations of these facilities are quitedifferent for each municipality. Coquitlam essentially has onecommercial district centred on a large shopping area. The area alsocontains a major transportation hub, and direct train-line todowntown Vancouver, a library, a college campus and a sportscomplex. This commercial district not only attracts residents ofCoquitlam, but residents from neighbouringmunicipalities becauseof its size. In contrast, Surrey has multiple commercial districts andregional shopping areas, each large enough to attract residentsfrom neighbouring municipalities as well. Of course, this is in partbecause of Surrey’s greater population. However, the importance ofthis comparison is to investigate the impact of urban form ondirectionality. Prince George is included to provide a more ruralexample of the importance of directionality. A priori, we expect thatoffender residents of Coquitlam will exhibit a stronger degree ofdirectionality than their counterparts in Surrey and Prince Georgebecause there is essentially only one place to go in Coquitlam. InSurrey, offender residents may have just as strong a directionalitypreference if they consistently select one area for their criminalactivities. However, with greater choice in targets we expecta weaker directionality preference, in the aggregate.

3.2. Measuring directionality

In order to measure the degree of directionality preference of anindividual, all c crime locations of the individual are mapped. From

R. Frank et al. / Journal of Environmental Psychology 32 (2012) 37e4240

these mapped locations an angle, called the Crime Activity Angle(CAA), is enclosed around the locations. In an effort to eliminateoutliers from the analysis, a parameter p (where 0 < p < 100) isused to denote the percentage of crimes that must be included inthe CAA. The CAA is positioned such that the vertex of the CAA iscentred on the home location and oriented such that the size of theangle is as small as possible, while still capturing p percent of theoffences by that individual. The larger the value of p, the larger theCAA has to be in order to accommodate the larger percentage ofoffence locations it needs to capture.

The smaller the angle that is created, the larger that the direc-tionality preference exhibited by the individual. If there is nodirectionality preference and all crime locations are scatteredequally around the home location, then the expected size of theCAA can be calculated mathematically using Eq. (1):

size of CAA ¼ 360ðpc� 1Þc

(1)

For example, in order to enclose 50 percent of 20 crime locationsthat are randomly distributed, the expected size of the angle is162�. However, if the crime locations are not randomly distributedand they show clustering, then the actual size of the CAA cannot bemodelled as it will be smaller than the randomized model.

4. Results

In order to establish that there is directionality preferenceevident for offenders, the results for all of British Columbia arecompared to the randomized model. Following this, two munici-palities (Coquitlam and Surrey) within the Metro Vancouver andone outside of Vancouver (Prince George) are compared to see howthe urban form impacts this directionality preference.

4.1. Is there directionality preference?

In order tomeasure the effect of directionality preference for theentire population of offenders, the p value was initially set to 50percent, then the size of the CAA for each individual was computed.The cumulative number of offenders, from both datasets, who havea CAA less than an angle of specific size was then plotted (Fig. 2).

Crime activity angle (degrees)

351301251201151101511

Per

cent

of

crim

es c

aptu

red

(cum

ulat

ive)

1.00

0.80

0.60

0.40

0.20

0.0050 PercentPrince GeorgeCoquitlamSurreyBritish ColumbiaRandom

Angle needed to capture 50% of crime locations

Fig. 2. CAA of individual versus size of angle, p ¼ 50.

Evident from Fig. 2, the curves produced for the two datasets aredifferent. For half the population a CAA size of 20� is required inorder to capture 50 percent (p ¼ 50) of their crimes. If no direc-tionality preference is present, as is the case for the randomizeddataset, the size of the CAA turned out to be 40�. This is a differenceof a factor of two. From another perspective, if there was nodirectionality preference, based on the randomized dataset, itwould be expected that about 55 percent of the population havea CAA less than 45 percent; however, 78 percent of the populationsatisfy this constraint. This clearly indicates that there is a signifi-cant difference between the expected directionality preference forindividuals, and what is seen in actual offender activity. Conse-quently, half of all criminal activity of those in the present sample iscaptured by a very small CAA. In fact, only 5.5 percent of thepotential directions available to offenders are used by the offenderswhen committing crimes.

We then increased the p value to 75 percent in order for the CAAto enclose a greater portion of the crime locations. As shown inFig. 3, for half the population, there is a difference of 31� betweenthe expected and actual CAA sizes. For this same population, it isexpected that 16 percent of the population has a CAA size of 45�.However, approximately 34 percent has that CAA size. Again,a notable difference between what was expected and what ismanifest.

Lastly, Fig. 4 shows the results for p ¼ 100, in order to considerall of the offenders’ crime locations. As expected, the CAA hasincreased substantially, but the same patterns remain: for half thepopulation there is a difference of 30� between the expected andactual CAA sizes. And it is expected that 15 percent of the pop-ulation has a CAA size of 45�, but approximately 29 percent havethat CAA size.

Overall, these results are typical. Similar differences betweenactual and expected CAA sizes were found as the p value was variedbetween 50 and 100. Clearly, a strong directionality preference ispresent for offenders in this dataset as the two graphs were verydistinct for all p values tested.

4.2. Variations in directionality preference

Turning to the results for the three individual municipalities(Coquitlam, Surrey, and Prince George), the results are notably

Crime activity angle (degrees)

351 301 251 201 151 101 51 1

Per

cent

of

crim

es c

aptu

red

(cum

ulat

ive)

1.00

0.80

0.60

0.40

0.20

0.00 50 Percent Prince George Coquitlam Surrey British Columbia Random

Angle needed to capture 75% of crime locations

Fig. 3. CAA of individual versus size of angle, p ¼ 75.

Crime activity angle (degrees)

351 301 251 201 151 101 51 1

Per

cent

of

crim

es c

aptu

red

(cum

ulat

ive)

1.00

0.80

0.60

0.40

0.20

0.00 50 Percent Prince George Coquitlam Surrey British Columbia Random

Angle needed to capture 100% of crime locations

Fig. 4. CAA of individual versus size of angle, p ¼ 100.

R. Frank et al. / Journal of Environmental Psychology 32 (2012) 37e42 41

different. Immediately apparent is that Surrey tends to follow thesame general pattern as British Columbia as a whole. In fact, whenp ¼ 75, British Columbia and Surrey almost perfectly coincide, witha directionality preference being somewhat stronger in Surreywhen p ¼ 100. Prince George, on the other hand, exhibits a lesser,though significantly different from random, directionalitypreference.

As expected because of its urban form, Coquitlam does exhibita much stronger directionality preference (smaller CAA) thanSurrey, Prince, George, and British Columbia, in general. Specifi-cally, when p ¼ 50 the CAA required to capture half of those crimelocations is approximately two-thirds of the CAA for BritishColumbia and Surrey. However, despite this notable decrease in theCAA, the entire curve for Coquitlam (Fig. 2) follows the samepattern as for British Columbia and Surreyethe curve is morejagged, simply because there are fewer repeat offenders in Coqui-tlam. When p is increased to 75, Fig. 3, not only does Coquitlamcontinue to have a significantly smaller CAA than British Columbiaand Surrey, but the pattern of the curve is different. As thepercentage of the repeat offender population is increased (y-axis),the CAA required to capture 75 percent of their crimes does notincrease proportionately as with British Columbia and Surrey. Andwhen p ¼ 100, Fig. 4, all of the curves follow the same generalpattern, with a brief exception. In Coquitlam, a CAA of 80� isrequired to capture 50 percent of all their crime locations; in Surreyand British Columbia, those CAAs are approximately 100 and 93�,respectively. This result shows a very strong directionality prefer-ence for a significant portion of repeat offenders in Coquitlam.

As discussed above, this stronger directionality preferencewithin Coquitlam is expected, but the magnitude (lower CAA) is ofparticular interest. This result implies that despite the presence ofa directionality bias, the availability of more target areas (Surrey)does lead to more spatial diversification in repeat offender activity.Consequently, spatial behaviour is a function of the urban form itoperates within (Horton & Reynolds, 1971).

5. Discussion and conclusion

Directionality matters. This claim has been easy to justify froma theoretical standpoint for this element of spatial criminology, but

has largely evaded empirical verification. Though, as noted above,a small number of studies have investigated the importance ofdirectionality. However, these studies have either been based onsmall samples or little detail is garnered from the data.

This paper is the first analysis of the strength of directionality inoffending based on a large incident-based dataset and varyingurban forms. Through the use of a simulation of randomized data,we are able to quantify the magnitude of directionality preferencefor repeat offenders in British Columbia, Canada. We find a signifi-cant difference between the randomized data and actual criminalactivity. We also find significant differences in the strength ofdirectionality preference within different urban forms. Therefore,when considering spatial decision-making for crime, directionalitymust be given asmuch consideration as place and distance if we areto understand the spatiality of criminal incidents.

Place has been clearly shown to matter for predicting actualcrime locations. Whether an analysis considers place attributessuch as hot spots, routine activity nodes, or the pathways betweenthem we know that crime is neither randomly nor uniformlydistributed across space. We also know that offenders, on average,commit their crimes close to home, especially violent crimes. Withregard to distance, understanding directionality may be used toidentify suspects: not only is the offender likely to live “close by”,but also from a particular direction. This potentially allows inves-tigators to use their local knowledge of the built environment topredict where the offender came from. In the context of place,directionality may also be used to identify the establishment ofdeveloping crime generators and crime attractors (Brantingham &Brantingham, 1995). If the directional bias of offenders is moni-tored, places that are developing as crime generators and crimeattractors may become the targets of crime prevention initiatives toprevent these places from becoming hot spots. Such crimeprevention initiatives are classified as “secondary” according to theprimary-secondary-tertiary (PST) model of crime prevention(Brantingham & Faust, 1976) because they identify and intervene atplaces before they become a problem.

As with any analysis, ours has its limitations. First and foremost,our analysis is based on police data. Though, because of the natureof the crime, burglary has a high reporting rate to the police, it alsohas a low clearance ratedapproximately 8e9 percent over ourstudy period with little variation year to year. Consequently, ourdata contain a small fraction of the actual number of burglars. Wemust assume they are representative. Second, as briefly discussedabove, we must assume that the journey to crime begins from thehome. This common assumption is made because we only havegeographic data for the crime locations and the home addresses ofthe burglars. Last, we are only able to identify a directional bias withregard to the journey to crime. This is not problematic, but limitsour ability to further inform theory. Both the geometric theory ofcrime (Brantingham & Brantingham, 1981, 1984, 1993) andtemporal constraint theory (Ratcliffe, 2006) predict a directionalbias that is rooted in peoples’ awareness space, more generally, notjust the journey to crime.

Now that we have shown empirically what we have knowntheoretically for decades, there are a number of implications andfuture research directions. First, both individual and collectivedirectionality may be used in geographic profiling (Rossmo, 2000)to further narrow down suspects, not just proximity. Second, ifmultiple offenders move towards the same location, crimeprevention through environmental design (CPTED) methods maybe better focused. And third, knowledge of offender residences andrelevant directions may be applied to explaining and predictingwhere crime is higher.

With regard to future research, a number of issues are imme-diately apparent. First, does the strength of directionality vary with

R. Frank et al. / Journal of Environmental Psychology 32 (2012) 37e4242

crime type? Similar to the element of distance, we should notexpect directionality to be the same for all crime types. Second,where/what are offenders attracted to? The distribution of oppor-tunities will certainly influence direction of travel. All offenders ina relatively large area may be attracted to one location such asa shopping mall (global convergence), or offender attractors mayvary across relatively small areas (local convergence). Thirdly, howmany “directions” do offenders use? The geometric theory of crimeposits multiple nodes. If a significant portion of offenders only haveone direction and there is a pattern to that direction (most oftentowards a drug dealer, for example), this information may be usefulfor investigative purposes. Is directionality preference related tothe prolific nature of repeat offenders? In other words, do repeatoffenders becomemore or less directionally biased as their numberof offences increases? There is also the question of directionality forco-offending. The common meeting grounds probably have themajor orientation for the direction of travel. Research on way-finding supports increased directionality inwell known areas. Withoffenders returning to their original targets or near them as crim-inality of place and with crime attractiveness, it is possible thatdirectionality is more pronounced with clustering of criminalevents. Understanding the street structure, the mode of movement(pedestrian, public transit, by motor vehicle) will likely influencethe directionality/distance interaction.

Needless to say, in our confirmation of a directionality prefer-ence using a large incident-based data set, we pose more questionsthan we answer. However, it should be clear that direction is animportant aspect when considering the spatial dimension ofcriminal activity.

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