Journal of Quantitative Criminology

, Volume 25, Issue 2, pp 181–200

Offender as Forager? A Direct Test of the Boost Account of Victimization

Authors

    • UCL Jill Dando Institute of Crime ScienceUniversity College London
  • Lucia Summers
    • UCL Jill Dando Institute of Crime ScienceUniversity College London
  • Ken Pease
    • UCL Jill Dando Institute of Crime ScienceUniversity College London
Original Paper

DOI: 10.1007/s10940-008-9060-8

Cite this article as:
Johnson, S.D., Summers, L. & Pease, K. J Quant Criminol (2009) 25: 181. doi:10.1007/s10940-008-9060-8

Abstract

Recent research has demonstrated that burglary clusters in space and time, resulting in temporal changes in crime hotspot patterns. Offender foraging behavior would yield the observed pattern. The offender as forager hypothesis is tested by analyzing patterns in two types of acquisitive crime, burglary and theft from motor vehicle (TFMV). Using a technique developed to detect disease contagion confirms that both crime types cluster in space and time as predicted, but that the space–time clustering of burglary is generally independent of that for TFMV. Police detections indicate that crimes of the same type occurring closest to each other in space and time are those most likely to be cleared to the same offender(s), as predicted. The implications of the findings for crime forecasting and crime linkage are discussed.

Keywords

Acquisitive crimeCrime hotspotsSpace–time clusteringForagingDetection

Introduction

Interviews with convicted burglars reveal clear targeting preferences. Salient features include likely occupancy, accessibility, and neighbourhood type. There is a substantial literature on offender ranges, i.e. travel to crime distances. Information about targeting strategies for crimes other than burglary is quite meagre. Temporal rhythms in respect of all crime types have been especially neglected.

The former England soccer player Gary Lineker opined that commentators who describe a player as being in the right place at the right time are foolish, since a player who is in the right place at the wrong time is, in fact, in the wrong place. Time is as important as space in understanding crime concentration. They must be considered together. A nightclub which is the most troublesome spot in town on Saturday night may be the quietest at first light on Sunday morning. The environs of a soccer ground which is a hotspot for vehicle crime during a match may not be a problem at other times.

In this paper we examine the space–time patterns of two types of acquisitive crime—burglary and theft from motor vehicle—using data for crimes recorded and detected by the police. First, we review previous research and outline the theoretical framework that informed the hypotheses tested. We then present analyses of recorded crime data concerned with space–time patterns of victimization. In the third section, we consider crimes detected by the police, and how emergent patterns in the crime data can illuminate putative offender targeting strategies. We conclude by discussing implications for criminological understanding and operational policing.

Patterns of Crime Concentration

Research consistently demonstrates that crime is concentrated in space across a range of scales. A small fraction of areas typically account for a disproportionate volume of crime (Block et al. 1995; Ratcliffe 2004; Sherman et al. 1989); a small number of street segments determine a city’s crime rate (Weisburd et al. 2004); and, a small fraction of victims account for a large proportion of events (Johnson et al. 1997; Pease 1998; Polvi et al. 1991). Explanations of crime clustering will be briefly noted. While it is contended that variation in clustering over time has not been explicitly accorded the attention it merits, the work reported here builds upon theories of spatial clustering of crime, in which temporal factors are implicit. Routine activity theory, drawing on human ecology (Hawley 1950), suggests that for a crime to occur, a motivated offender must come into contact with an opportunity for crime in the absence of a capable guardian (Cohen and Felson 1979). This convergence is likely to be episodic, being a function of the daily routine activities of offenders, potential victims and guardians against crime. Pattern theory (e.g. Brantingham and Brantingham 1993, 1995) considers the role of offender routine activities and the configuration of the environmental backcloth in the generation and distribution of criminal opportunity. The environmental backcloth determines the location of offenders’ routine activity nodes (e.g. home, school, pubs and shops) and how they travel between them. In turn, this influences awareness of criminal opportunities. Of course, offenders may commit crimes at locations outside of their routine activity space, but extensive exploration seems the exception (Cromwell et al. 1991; Rengert and Wasilchick 2000; Wiles and Costello 2000; Hodgkinson and Tilley 2007). Individual nodes will be central at particular times of day and day of week, yielding temporal periodicities of risk at different locations.

For all crimes so far analyzed, aggregate patterns suggest that travel to crime journeys relative to the home conform to a distance decay model (Rossmo 2000). Where offender residences are concentrated in space (Shaw and McKay 1969; Wiles and Costello 2000) or the topology of their routine activities overlap, pattern theory provides an elegant explanation for why some places become hotspots of crime (see also, Ratcliffe 2003). Areas may also become crime hotspots if they are crime attractors (Brantingham and Brantingham 1993, 1995) offering good opportunities for crime. Such locations may attract offenders if they are within or on the edges of their routine activity spaces (Brantingham and Brantingham 1995). Crime attractors (for example drug markets, clubs and sports venues) also exhibit diurnal, weekly and seasonal variation in activity, and are likewise liable to generate temporal variation in crime occurring in and around them. In short, research demonstrates that crime clusters in space and theories which focus on offender mobility and spatial and temporal constraints (see Ratcliffe 2002, 2006) offer explanations for this. The work has clear application, showing the benefits of allocating operational resources to high crime areas (Sherman et al. 1989; Sherman and Weisburd 1995; Braga 2001).

Theories concerned with crime clustering at the area level are useful in themselves, and temporal concentration is implicit in all of them. However, to oversimplify, their starting point tends to be that area features determine the overall rate of crime whose occurrence will fluctuate by time of day and day of week. An alternative focus of investigation starts by assessing the stability of crime hotspots or the flux of crime (Barr and Pease 1990). A growing body of research has examined the stability of crime hotspots (Weisburd et al. 2004; Johnson et al. 2008) and found a degree of instability. This chimes with the demonstration of the transience of risks of (near) repeat burglaries discussed below. The question to consider is whether these findings can be explained by reference to adaptive target search by offenders.

The risk of future household victimization is higher when prior victimization has been suffered (for a review, see Farrell 2005). Crucially, the elevation in risk conferred by a burglary event is transient, decaying exponentially over time (e.g. Johnson et al. 1997). Thus, at the individual household level at least, risk changes over short periods of time.

Recent research has applied to burglary events statistical techniques developed to detect disease contagion. Data from Australia (Townsley et al. 2003), the UK (Johnson and Bowers 2004a, b), the Netherlands, New Zealand and the USA (Johnson et al. 2007; Grubesic and Mack 2008) demonstrate that the risk of burglary is temporarily elevated for homes near (typically up to 400 m) to previously burgled households. In the UK at least, risk is greater for homes on the same side of the road as those burgled (Bowers and Johnson 2005) within the elevated risk area. Thus domestic burglary clusters in space and time to yield local burglary spates, superimposed on longer-term area differences (Johnson and Bowers 2004b).

Theories of Space–Time Clustering

How do patterns of space–time clustering (of which repeat victimization is a special case) emerge? Heterogeneity in target attractiveness at the household and small area level may be responsible; some homes and neighbourhoods are simply more at risk of victimization than others. This is the flag explanation of victimization (e.g. Pease 1998; see also Johnson 2008). It provides a simple explanation for spatial clustering at the household or neighbourhood level, but at first glance struggles with spatio-temporal variation in risk. This difficulty may be illusory. Analyses of patterns of victimization are typically conducted using data aggregated to the area level. The analysis of data for heterogeneous populations can produce unexpected results, not unlike those described for patterns of space–time clustering (for a discussion, see Vaupel and Yashin 1985; Johnson 2008). The potential problem is that the researcher may commit the ecological fallacy, erroneously assuming that the aggregate patterns reflect those for individual properties (or groups). For example, consider an area in which there are two classes of home; those with a stable high risk of victimization and those with a stable low risk. Even on a chance basis, some homes from each group would experience repeated victimizations. If the patterns of repeat victimization were generated by chance (e.g. if they were unrelated in terms of who committed the offenses), and analyses were performed independently for each class of home, the time course of repeat victimization would be uniform over time for each group. However, if the data for the two groups were analyzed together, a curve may be generated. The high risk homes would be victimized more and would be more likely to be re-victimized. For these homes, the time to repeat victimization would typically be fairly swift. However, as we are considering a stochastic model, a proportion of such homes would experience re-victimizations only after a longer period of time has elapsed. Considering the low risk group, they would be victimized less often, but they might still be re-victimized. When they are, the time to re-victimization would typically be longer than that for the high risk group. Again, as this is a stochastic model, some of these homes would experience repeat victimization within a short-medium interval of time. Mixing the patterns for the two groups would generate a curve for which the coefficient would be proportional to the difference in risk for the two populations; the greater the difference the more accentuated the curve. Given that research indicates considerable variation in burglary at the household level (e.g. Budd 1999) the flag theory provides a plausible rationale for the time-course of repeat victimization. The same explanation can be extended to patterns of space–time clustering more generally if there is sufficient variation in risk across neighbourhoods.

The alternative explanation is that space–time clustering is the consequence of offenders adopting optimal (or efficient) foraging strategies at least some of the time (Johnson and Bowers 2004b; Johnson et al. 2008). As discussed above, in criminology, the majority of research concerned with offender movement has focused on the journey to crime, largely neglecting the geography of inter-crime trips. In contrast, when considering foraging activity across species, researchers have not limited themselves to what they would refer to as central place foraging (for a review, see Pyke 1984), but consider other factors affecting the decision where to forage. These include the rate of food intake; variation in the distribution of resources within and across patches (places); time spent searching within and between patches; optimal patch identification rules; optimal patch departure rules; foraging strategies for patches that vary over time; angular direction (and how this might vary as a function of success), the distance travelled between movements; and the risk of predation. The theory developed in behavioural ecology is rich but has rarely been applied to offender targeting strategies.

Principally, the aim of the foraging burglar is to increase his resources, whilst limiting the amount of energy expended and the associated risks. The forager operates under spatial and temporal constraints. Potential targets are likely to be clustered in space. Within clusters there will be variation in target attractiveness—calorific value for the animal, and (for example) the likely yield and ease of access for the burglar—but targets nearest to each other are likely to be most similar, the association between propinquity and similarity reflecting the first law of geography. Finding locations that fulfil the forager’s requirements will involve search strategies and movement decisions. For the rational forager (e.g. Cornish and Clarke 1986), such decisions must be informed by what is learned during foraging.

Having targeted a particular home for the first time, a burglar acquires knowledge to inform future targeting decisions. This may concern the internal layout of a burgled property, the ease of access and escape, the products that may be found were the offender to return, the risks of identification, and so on. This knowledge is likely to reduce uncertainty about nearby homes. Just as flowers in a cluster are likely to share nutritional value (Pyke 1984), homes proximate to each other are likely to share architectural features, levels of natural surveillance, and occupant affluence and routine activities. A forager seeking a strategy affording an acceptable balance of rewards and risks might favour homes about which most is known. This may involve returning to previously burgled homes, and also to those nearby.

Targeting homes near those previously burgled could (but does not have to) lead to a drift in the places targeted. No drift would occur if the offender chose to commit crimes in the same area over time, but such a strategy is likely to be suboptimal for reasons which include the following: there will be a limited population of targets and resources would eventually be depleted if the offender did not move; there may be an increased risk of identification over time, which is something that ethnographic research consistently identifies as a fear expressed by offenders (Wright and Decker 1994; Cromwell and Olson 2006); and, continued offending in the same area is eventually likely to attract police attention even in the absence of any change in the vigilance of residents. Rather than targeting locations randomly, an optimal foraging model would predict that the offender would conserve the time and energy expended in searching for the next target, and make targeting decisions with information regarding risks and rewards. For these reasons, over time some drift in neighbourhoods targeted would be expected, but with a gravitational influence of the offender’s routine activity nodes. Just as grass grows and becomes succulent to the foraging cow, so insurance replaces stolen goods and the risk (to the offender) of returning to a previously foraged area declines. In time, the forager returns.

To rehearse the argument, the flag account of spatial clustering in burglary at household and place level is also capable of yielding the transient decay in household risk after an earlier crime. The alternative (or complementary) notion is that of offender as optimal forager. It differs in being based on the idea that what burglars learn in committing an offense shapes what they do next, and in the short-run this typically elevates local risk of victimization. Speculatively, in the middle term local risk may be diminished, only to rise again when the pressures leading the forager further afield have declined. The temporary elevation of burglary risk as a consequence of offender foraging activity is known as the boost hypothesis (Pease 1998). The optimal forager account yields the same predictions as the boost account only in the short run, and then only when circumstances are as they typically have been in the locales investigated. Where householders are present, vigilant and co-operative, one might expect an immediate decline in risk of victimization as these unfavourable conditions communicate themselves to the offender. Middle and long-term local fluctuations in either direction are likewise possible depending upon prevailing pressures. However, for the moment we are concerned with current short-run trends, and the short-term increase in risk experienced by those burgled has been found to be ubiquitous, so boost and optimal forager views seem indistinguishable. The term boost presumes a direction of effect which may in principle be contingent on circumstance, and should perhaps be discarded as anything more than a convenient shorthand for currently observed patterns. The point will be touched upon in the discussion section of this paper. For the moment it suffices to say that the optimal forager account of local trends depends upon changes in risk being the consequence of the behaviour of returning offenders rather than homes flagging their desirability to passing burglars indiscriminately.

The two types of account, forager and flag, are not incompatible and both are likely to play their part, but understanding the contribution of both is important for criminological theory and police practice. For example, the implications for crime detection are quite different if patterns of (near) repeat victimization are generated by the exploits of returning offenders than if they are not.

A number of methodological approaches may be taken to attempt to examine the contribution of the two processes. Interviews with offenders provide one source of information. Research so far conducted (Ashton et al. 1998; Ericsson 1995; Shaw and Pease 2000) suggests that burglars do commit repeats and their stated reasons for so doing are compatible with the forager explanation. Hitherto studies have not probed offenders about how they target neighbourhoods in space and time in a way that informs the research questions considered here.

A second approach has used simple mathematical models to predict future crime locations. The logic is that if the space–time distribution of crime can be explained by time-stable variation in risk, then crime hotspots generated using historic data sufficient to estimate such variation should provide a good idea of where crimes will next occur. However, if space–time patterns of crime are also the function of a foraging process, then the equations used to derive the forecasts should consider both the location and timing of events, with more recent crimes being considered most salient. Studies conducted using data for urban (Bowers et al. 2004; Johnson et al. 2008) and rural areas (Johnson et al. 2007) suggest that forecasts which include information on the timing of events significantly outperform those that do not.

A further recent approach to analysis involves computer simulation. For example, Johnson (2008) investigated whether patterns of repeat victimization—including the distinct time course—could be generated by a micro-simulation that modelled only target heterogeneity at the place and household level, or whether a boost process was required. The findings suggested that whilst a range of different models which varied population heterogeneity could generate realistic patterns of burglary concentration at the household level, only those that also included a boost process could generate the so-far ubiquitous time course of repeat victimization. Thus, the study provided support for both theories of repeat victimization.

Unusual in that they analyze personal rather than property crime, Tseloni and Pease (2003) apply a multilevel model to personal crime counts from the National Crime Victimization Survey. The study suggested that both measured and unmeasured heterogeneity contribute to repeat victimization risk, so the flag account has merit. However, the two types of heterogeneity combined do not exhaust the predictive power of past for subsequent victimization, so the boost account also has validity.

The analysis of crimes detected by the police provides a further avenue for research. That concerned with repeat burglary victimization (Everson and Pease 2001; Kleemans 2001) suggests that crimes committed at the same household are often the work of returning offenders. In a recent study, using data for detected burglaries in the Netherlands, Bernasco (2008) examined whether pairs of burglaries close to each other in space and time were more likely to be the work of the same offender than other pairs of events. The results indicated that burglaries that occurred swiftly at the same household or nearby were much more likely to be the work of the same offender than those that occurred close to each other in space but not time, or vice versa.

Thus, for burglary and personal crime at least, the available evidence provides support for the foraging explanation as at least contributing to short-run space–time clustering. Research on crimes detected by the police is in some ways most persuasive as it provides a direct test of the hypothesis. Only Bernasco’s study has so far used this kind of data to examine space–time patterns of burglary beyond direct repeats. Further research of the same kind is required. Shortcomings of Bernasco’s pioneering study are acknowledged by its author and include the following linked problems: 1) the detection rate for the study area was very low, with patterns of detected crime perhaps being in consequence unrepresentative; and, 2) identified patterns may have reflected a bias in police officers’ detection strategies with a perpetrator of an earlier crime being deemed the primary suspect in subsequent cases that occur nearby. An aim of the current study was to attempt to address these concerns. The literature extant has concentrated too much on domestic burglary. If foraging occurs as the writers suppose, it is important to establish whether it applies to acquisitive crime generally. Consequently, we examine space–time patterns of burglary and one other type of acquisitive crime that does not require direct contact with the victim, theft from a motor vehicle. Analyses are conducted using data for victims of crime and for the offenders who committed them in one police area in the UK. The following hypotheses are tested:

H1

In line with previous findings, burglary will cluster in space and time.

H2

Sharing similar motivations to burglary, theft from motor vehicle offenses (TFMV) will cluster in space and time.

For TFMV, the distribution of targets will be different to burglary as vehicles may be parked at residential locations, but also in car parks and within town centres. Thus, patterns of space–time clustering may be quite different. Understanding the dimensions of risk is important both for theories of offender foraging and to clarify implications for operational policing.

H3 and H4

Burglaries (or TFMV) offenses detected by the police occurring close in space and time are more likely to be cleared to the same offender(s) than other pairs of crimes of the same type.

Given well documented offender versatility (e.g. Piquero 2000), a further question concerned whether patterns of one type of crime might influence those of another. To elaborate, insofar as offenders typically commit more than one type of crime, then foraging activity may be a composite. In addition to identifying other homes to target during the commission of a burglary, an offender may identify good opportunities for TFMV, or vice versa. We therefore examine whether events of TFMV and burglary close to each other in space and time are more likely to be the work of the same offender(s) than other pairs of events. Hypotheses five and six are thus:

H5

If there is evidence of offender versatility across the two offense types of interest, incidents of burglary and TFMV will cluster in space and time.

H6

If H5 is supported, pairs of detected burglaries and TFMV offenses occurring close to each other in space and time will be those most likely to be cleared to the same offender(s). If H5 is unsupported but this hypothesised pattern is evident, this would suggest that the patterns are the result of a detection bias rather than offender foraging strategies.

The analyses that follow are presented in two sections. In the first, we present analyses of recorded victim data, in the second, crimes detected by the police.

Space–Time Clustering: Crimes Recorded by the Police

Data and Analytic Strategy

Recorded Crime Data

Recorded crime data for residential burglary and TFMV for the Bournemouth police basic command unit were obtained. Table 1 provides contextual information for the area studied, derived from a limited set of variables collected as part of the UK census. It also shows the volume and rate of crime experienced in the study area for the calendar year 2005 and, for the purposes of comparison, the county within which it is located. Comparing the rate of crime (for example) in Bournemouth and the county as a whole, it is evident that the risk is higher in the former than the latter.
Table 1

Demographic and crime related information for Bournemouth Unitary Authority and for the county of Dorset within which it is located

 

Bournemouth

Dorset

Demographic data

    Total population

163,444

692,712

    Population aged 16–74

117,345

490,818

    Population aged 16–74 in employment

72,296

308,954

    Total number of households

72,199

299,244

    Total number of cars/vans

79,936

374,787

    Area size (ha)

4,618

265,274

Police data (for the year 2005)

    Total number of burglaries

891

2,245

    Number of burglaries per 1,000 population

5.45

3.24

    Number of burglaries per 1,000 households

12.34

7.50

    Proportion of burglaries detected

0.25

0.23

    Total number of TFMV offenses

1,894a

5,021

    Number of TFMV offenses per 1,000 population

11.59

7.25

    Number of TFMV offenses per 1,000 cars/vans

23.70

13.40

    Proportion of TFMV offenses detected

0.18

0.13

Source: Demographic data obtained from the 2001 Census; crime data obtained from Dorset Police

aThis figure includes those crimes for which the address information was incomplete

For each crime, the data included the location of the offense, accurate to a resolution of 1 m; a unique identifier for individual households (to distinguish between flats in the same building); and, the date of the offense. Considering the date on which offenses took place, the majority of burglaries and effectively all TFMV offenses occur when the house or vehicle is unoccupied. When such crimes are reported to the police, victims indicate the likely interval of time during which the crime could have occurred. Crimes for which the interval was 48 h or more were excluded from analyses.1

For TFMV, it was necessary to establish the accuracy of the x and y coordinates provided. Unlike burglary, which occurs at a discrete address, vehicle crimes may occur outside a victim’s home, in a car park, on a street, and so on. A victim’s description of the location of the crime may be incomplete or erroneous. For example, a victim not parked outside of an easily identifiable building may be able to provide the police with only the name of the street. In such cases, the offense’s x and y coordinates will be approximate. Only those crimes for which there was a street name, street number, town name and/or postcode were included in the analysis. The exclusion of events not meeting this criterion (33%) yielded a data set for the year 2005 comprising 1,253 events.

Detected Offenses

Detected burglary and TFMV offenses that occurred between 1 January 2001 and 31 December 2005 were analyzed. Tables 1 and 2 provide descriptive statistics for the data used. As is evident from Table 1, detection rates for both residential burglary and TFMV are relatively high; around five times higher than those for the Bernasco (2008) study, in part since in the UK, crimes deemed detected include those that are taken into consideration (TICs); i.e. crimes that offenders bring to police attention at the point of being charged for other offenses. This removes the possibility of later being proceeded against for the admitted offenses and affects sentence trivially, if at all. Offenders are required to verify the details of the offense before they can be charged for them to avoid spurious confessions. Forty-six percent of detected burglaries and 61% of TFMV offenses were TICs.
Table 2

Descriptive statistics for crimes detected by the police for the period January 2001 to December 2005

 

Burglary

TFMV

Total offenses

1,410

815

Total number of offenders

628

306

Crimes per offender

    Mean

2.60

3.29

    SD

5.03

9.58

    Range

1–54

1–99

Offenders per crime

    Mean

1.16

1.23

    SD

0.47

0.63

    Range

1–7

1–6

With respect to offender versatility, of the 875 offenders, 59 committed crimes of both types. A more systematic way of describing offender versatility is to compute an index of heterogeneity (Blau 1977) for each offender. This index, which represents the probability of any two crimes randomly selected from an offender’s series being of the same type, is derived using Eq. 1.
$$ {\text{Index}}_{i} = 1 - \sum\limits_{j = 1}^{n} {\left( {\frac{{{\text{crimetype}}_{ij} }}{{{\text{totalcrime}}_{i} }}} \right)^{2} } $$
(1)
where, i is the ith offender and j is the type of crime considered

A value of zero so derived would indicate that an offender was entirely consistent, a value of 0.5 that an offender committed equal numbers of crimes of each type. For the group as a whole, the index of heterogeneity was 0.03 (SD = 0.11, range = 0–0.50, N = 875) indicating that the majority of offenders were specialists. Of course, offenders who commit only one crime will be entirely consistent and so the index was recomputed for those who committed two or more crimes (M = 0.08, SD = 0.17, range = 0–0.50, N = 276), and those who committed at least one crime of each type (M = 0.38, SD = 0.15, range = 0.03–0.50, N = 59). Thus, even those offenders who committed crimes of each type, tended to favor one crime over the other. Of course, the indices are crude in that some offenders will have committed both offense types but, being charged with only one type, will not (indeed cannot by UK law) ask for offenses of the other type to be taken into consideration.

The fact that there was evidence of only modest offender versatility for the sample studied suggests that Hypotheses H5 and H6 should be unsupported by the results that follow. On the one hand this may be considered unfortunate, on the other, this means that a more selective pattern of results should emerge across the analyses if the general hypothesis has any validity and the methods used are robust. Offender specialisation provides a more stringent test of the theory articulated.

Identifying Space–Time Clustering

Analyses were conducted to determine whether (for each crime type) events occurred close to each other in space and time more than would be expected if timing and location were independent. The method used was a variant of that developed in epidemiology to test for disease contagion (see Knox 1964; Besag and Diggle 1977). As it has been detailed elsewhere (Johnson et al. 2007), only an overview will be provided here.

For a given data set, each crime is compared to every other, and the geographic distance and time elapsed between each pair of events computed. This generates ½ n(n − 1) comparisons. A contingency table summarizing the results (e.g. how many events occurred within 100 m and 14 days of each other) is populated. The dimensions (i.e. the spatial and temporal bandwidths used) of the contingency table are selected to provide a sensitive analysis of the hypothesis tested, whilst ensuring that the observed cell frequencies are adequate for reliability. One might select a temporal bandwidth of one day to provide detail, but at this level of resolution, the cell frequencies are likely too small. To ensure validity of inferences made, a range of space–time bandwidths was used.2 Since the same pattern emerged for each combination, only those using intervals of 14 days and 100 m are reported.

The contingency table generated to summarize the observed distribution is then compared with what would be expected if the timing and location of events were independent. To do this, the process described is repeated but using permutations of the data set in which the date on which the crimes occurred is randomized (or shuffled) across events.3 As a full permutation is virtually impossible for even a moderately sized data set, a Monte Carlo (MC) simulation is used to draw a random sample of (say 999) permutations. The results of the MC simulation are then compared with the observed distribution, and the frequency with which each cell value for the observed distribution exceeds those for the permutation test recorded. The number of times that the observed cell frequency exceeds those generated by the MC simulation provides an estimate of the statistical significance of the results for that cell. For example, if an observed cell frequency exceeds those generated by the MC simulation only 50% of the time, this would indicate that the observed value would be expected roughly 50% of the time even if the location and timing of crimes were independent. However, if the observed frequency for a particular cell exceeds the values generated during the MC simulation 95% of the time, then this would indicate that the observed result would be unlikely to occur under the null hypothesis. Formally, the statistical significance (see North et al. 2002) of an observed value for any particular cell is computed using Eq. 2.
$$ p = \frac{{{\text{rank}} + 1}}{n + 1} $$
(2)
where n is the number of simulations, and rank is the position of the observed value in a rank ordered array for that cell

An indication of the size of the observed effect (or Knox ratio) can be derived by dividing the cell frequency for any particular cell by the median value generated by the MC simulation. To illustrate, a value of one so derived would indicate that the observed frequency for a cell was that expected under the null hypothesis. A value of two would indicate that twice as many events occurred within a given space–time proximity of each other as would be expected according to the null hypothesis. In the event that crimes are clustered in space and time, the Knox ratios of the cells in the top left corner of the table will be above one, indicating that relative to chance expectation, there is an over-representation of events close in space and time.

Decisions regarding the data used in analyses of the kind reported here involve a number of considerations. The use of more data may increase the reliability of the analysis (if the patterns are time stable), but larger data sets increase the time required for analysis. For the type of permutation test conducted, doubling the number of records increases the number of comparisons by a factor of four. A data set of 2,000 records, and 999 iterations of the MC simulation requires just under four billion comparisons. For this reason, a decision taken was to use between 1,000 and 2,000 records for each analysis. To ensure that seasonal effects did not generate patterns inviting errors of inference, data for complete years were used. Data for a 2 year period (January 2004–December 2005) were required for burglary (1,735 events), and for 1 year (January–December 2005) for TFMV (1,253 events).

Results

Burglary

Table 3 shows results for the crime of burglary. The columns divide the table into increments of 14 day intervals up to 112 days (roughly 4 months) and, finally, for 112 days or more. The first row of the table shows the results for events which occurred at the same household (a unique identifier was used to distinguish flats at the same location). The final row shows the results for pairs of events that occurred over 1 km from each other.
Table 3

MC simulation results for recorded Burglaries in Bournemouth (values in bold statistically significant, p < 0.05)

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

4.00

1.50

2.00

1.67

0.83

1.00

0.83

1.17

0.74

0–100 m

1.63

1.24

1.22

0.87

1.07

0.97

1.02

1.01

0.95

101–200 m

1.26

1.17

1.23

1.01

1.04

1.15

0.95

0.94

0.96

201–300 m

1.14

1.04

1.11

0.99

1.01

1.00

1.03

1.02

0.98

301–400 m

1.11

1.08

1.16

1.01

1.02

0.96

1.00

1.01

0.98

401–500 m

1.04

1.01

1.02

0.96

1.05

0.97

1.02

0.99

1.00

501–600 m

1.07

0.99

1.08

1.03

1.06

0.97

1.08

1.05

0.98

601–700 m

1.05

1.05

1.03

1.03

1.02

1.02

0.99

0.96

0.99

701–800 m

1.09

1.01

1.03

0.99

1.01

1.02

0.98

1.05

0.99

801–900 m

1.06

1.00

1.06

1.01

1.08

1.01

0.97

0.95

0.99

901–1 km

0.96

0.99

1.01

1.00

0.96

1.00

1.01

1.01

1.00

1 km+

0.99

1.00

0.99

1.00

1.00

1.00

1.00

1.00

1.00

In line with previous research, there was clear evidence of space–time clustering; the highest Knox ratios are to be found in the top left of the table, and the pattern observed conforms to one of spatial and temporal decay. The ratios at the right of the table were also statistically significant. In this case, they were less than would be expected; the precise pattern observed—which is the reverse of that observed in the left hand side of the table—is consistent with Hypothesis 1. There are five further cells for which the Knox ratio was statistically significant. Considering these, the Knox ratios are smaller than most of those in the top left of the table and, even on a chance basis (0.05 * 108=) five cells would have statistically significant results. For these reasons, we interpret the results as supporting the hypothesis that for this area, burglaries cluster in space and time in the way expected.

To summarize, it would appear that more burglaries occur near to each other in space and time than would be expected if there were no relationship between when and where they took place (e.g. if they were only the consequence of risk heterogeneity). In particular, it appears that this is true for events that occur within 400 m and 42 days of each other.

Theft from Motor Vehicle (TFMV)

The results shown as Table 4 confirm that offenses of TFMV also cluster in space and time. In this case, the pattern extends over a greater distance but for a much shorter time. As for burglary, the Knox ratios on the right hand of the table are statistically significant and show that relative what would be expected if the distribution of TFMV offenses clustered only in space, fewer events occur near to each other after 4 months or more has elapsed. The Knox ratios for five other cells were statistically significant. These results could have occurred on the basis of chance and, importantly the Knox ratios for these cells are weak and fail to exhibit any systematic pattern.
Table 4

MC simulation results for recorded TFMV in Bournemouth (values in bold statistically significant, p < 0.05)

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

2.22

1.05

1.38

1.00

1.00

1.29

0.82

0.75

0.73

0–100 m

1.74

0.87

0.95

0.90

0.92

1.21

1.11

0.92

0.90

101–200 m

1.46

0.91

1.07

0.91

0.98

0.91

1.12

1.10

0.93

201–300 m

1.22

0.93

1.11

0.91

1.00

0.98

1.07

0.99

0.97

301–400 m

1.21

0.90

1.05

0.93

1.07

1.13

1.03

1.01

0.95

401–500 m

1.13

0.96

1.05

0.98

0.97

0.99

1.11

1.04

0.97

501–600 m

1.11

0.98

1.03

0.92

0.96

1.06

1.04

0.94

0.99

601–700 m

1.19

0.96

1.05

0.97

0.91

1.10

1.00

0.97

0.98

701–800 m

1.09

1.01

0.99

0.98

0.94

1.07

1.01

1.05

0.98

801–900 m

1.03

1.00

0.98

0.98

0.96

1.16

1.03

1.06

0.97

901 m–1 km

1.03

1.12

0.96

1.02

0.96

1.06

1.07

1.03

0.97

1 km+

0.99

1.00

1.00

1.00

1.00

0.99

1.00

1.00

1.00

Thus, as for burglary, TFMV events cluster in space and time.4 The pattern observed differs. For both crime types the effect decays in space and time, but for TFMV the distance over which the effect is observed is greater, whilst the duration of the effect appears to be shorter. Interpreted in the context of the forager explanation, this would suggest that TFMV offenders forage over greater distances than burglars. This would be consistent with studies which have examined the journey to crime for burglary and vehicle offenses which indicate that the average crime trip is shorter for the former than the latter (e.g. Wiles and Costello 2000).

Burglary and Theft from Motor Vehicle (TFMV)

To see if there was a correlation between space–time patterns of burglary and those of TFMV we use a modification of the approach described above. Rather than generating a contingency table summarizing how distant events of one type of crime occurred from each other in space and time, we consider how far apart events of one type of crime occurred from those of the other. Thus, for each burglary the time elapsed and distance between that event and all incidents of TFMV was computed, and a contingency table populated. To generate the expected distribution, a MC simulation was again used. In this case, the dates on which one type of crime5 occurred were shuffled followed by those for the other, and the analysis repeated.

The results, shown as Table 5, reveal no association between the timing and locations of incidents of burglary and TFMV other than that which could be explained by their general distribution in space or time. For the area studied, incidents of burglary with TFMV did not cluster in space and time. Insofar as offenders committed both types of crime, their targeting decisions in space and time for one crime were not influenced by those for the other.
Table 5

MC simulation results for recorded TFMV and Burglary in Bournemouth (values in bold statistically significant, p < 0.05)

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

1.01

1.05

0.96

0.93

1.04

0.99

1.16

1.07

0.96

0–100 m

1.01

0.97

1.01

0.95

0.97

1.01

0.96

1.03

0.97

101–200 m

1.03

1.00

1.03

1.01

0.93

1.04

1.00

1.05

1.00

201–300 m

0.98

1.00

1.01

1.01

0.96

1.02

0.95

1.03

1.04

301–400 m

1.00

1.02

0.98

0.96

1.02

1.05

0.98

1.04

1.02

401–500 m

1.03

0.98

1.05

0.99

1.02

1.02

1.00

0.98

1.00

501–600 m

1.00

0.99

1.04

1.01

1.03

1.01

1.02

1.04

0.98

601–700 m

0.96

0.99

1.00

1.00

1.00

1.01

1.01

1.02

0.98

701–800 m

0.99

0.98

1.03

0.98

1.03

1.03

1.04

1.00

1.03

801–900 m

0.98

0.98

1.01

1.01

1.04

1.01

1.01

1.02

0.99

901 m–1 km

0.99

0.97

1.02

1.01

1.05

1.02

1.02

1.01

1.01

1 km+

0.98

0.99

1.04

1.00

1.01

1.00

0.98

1.00

0.98

Patterns of Offending

The analyses that follow examine the extent to which detected offenses occurring near in space and time are the work of the same offender(s). According to the foraging hypothesis, crimes that occur closest to each other in both dimensions should be the most likely to be committed by, and hence cleared to the same offender(s). Given the above findings, this should be true within but not across crime types.

Analytic Strategy

For each crime type, every detected offense was compared to every other and the distance and time between event pairs recorded. A contingency table like that used in the previous section was then populated to indicate how many detected offenses occurred within the various space–time intervals considered. For each pair of detected crimes, the number of times at least one offender was involved in both crimes was computed, and the data summarized in the contingency table. Finally, for each space–time interval considered, the percentage of pairs for which at least one offender was involved in both crimes was derived. Thus, a percentage of 100 in a cell would indicate that pairs of crimes which occurred within that space–time interval of each other were always cleared to the same offender(s), a percentage of 50 that this was the case for one-half of the detected crime pairs. To simplify interpretation, the dimensions of the contingency tables were as used in the previous section.

Results

Burglary

Table 6 shows that for repeat burglary victimization, detected events were almost always cleared to the same offender. Moreover, events that occurred closest to each other in space and time were those most likely to involve one or more of the same offenders. An alternative way of framing the analysis is to compare the likelihood that any two (detected) crimes close to each other in space and time will have been the work of the same rather than different offender(s), and to then contrast this with the same calculation for pairs of events that occurred far apart in space or time. To illustrate, the number of pairs of events that occurred within 100 m and 14 days and linked to the same offender(s) was divided by the number of false alarms that would result from linking events of this kind to each other. This was then compared to the same ratio for pairs of events that occurred more than 100 m or 14 days apart from each other. Dividing the two gave a ratio of 702. Simply put, events which occurred within 100 m and 14 days of each other were massively more likely to have been committed by the same offender(s) than more distant events. For repeat victimizations that occurred within 14 days of each other, the ratio of correct links to false alarms was 9,787 times that observed for non-repeats that occurred more than 14 days later.
Table 6

Fraction of burglary pairs for each space–time interval for which one or more offenders were involved in both offenses

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

99

88

90

83

100

100

50

25

24

0–100 m

76

40

27

26

16

6

15

21

2

101–200 m

64

40

21

7

4

4

23

24

1

201–300 m

52

31

15

7

4

6

10

4

1

301–400 m

46

24

16

12

5

5

3

7

1

401–500 m

39

21

10

3

5

2

5

4

1

501–600 m

36

12

9

11

2

1

4

6

<1

601–700 m

33

13

13

6

9

3

3

4

1

701–800 m

27

13

16

2

5

3

3

5

<1

801–900 m

23

18

11

5

4

2

2

2

<1

901 m–1 km

25

15

12

2

5

3

2

1

<1

1 km+

8

6

4

3

2

2

1

1

<1

Theft from Motor Vehicle (TFMV)

The results for TFMV, shown as Table 7, reveal a similar pattern to that for burglary. The proportion of detected TFMV offenses cleared to the same offender(s) is clearly a function of how far apart the events occurred to each other in space and time. However, compared to burglary, a higher proportion of detected TFMV offenses which occurred further apart in space and time were cleared to the same offenders. This is in line with the pattern observed in Table 3 and suggests that the results are unlikely to be the result of a detection bias.
Table 7

Fraction of pairs of incidents of TFMV for each space–time interval for which one or more offenders were involved in both offenses

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

99

97

100

67

60

40

0

0

17

0–100 m

94

64

63

64

22

0

30

29

23

101–200 m

92

63

62

39

37

50

33

38

15

201–300 m

77

63

56

59

30

20

17

4

11

301–400 m

78

43

66

48

34

21

29

9

9

401–500 m

74

47

46

45

31

19

8

13

7

501–600 m

72

51

41

45

20

20

5

13

8

601–700 m

65

64

40

43

16

23

15

27

8

701–800 m

72

47

41

37

28

16

18

19

7

801–900 m

70

49

40

33

27

15

15

15

8

901 m–1 km

68

40

35

33

19

20

13

19

6

1 km+

27

15

11

8

8

6

5

6

2

Considering the ratio of the number of detected events that could be correctly linked to the same offenders and those that would represent false alarms, for events that occurred within 100 m and 14 days of each other, this was 683 times higher than that for events that occurred more than 100 m or 14 days apart. For events that occurred at the same location within 14 days of each other, the same ratio was 1,546.

Burglary and Theft from Motor Vehicle (TFMV)

One concern with the findings with respect to burglary already discussed is that the patterns observed could either reflect offender foraging strategies, or a bias in the way that police officers prioritize the investigation of and link crimes, or the ease with which pairs of crimes are likely to be detected and processed via TICs. However, if the patterns observed in the detected crime data were simply the result of bias, we would expect that the analyses of the detected TFMV offenses to have revealed the same pattern of results. While the general patterns were similar, the precise patterns varied in a way that suggests that the patterns of detected events reflect the space–time distribution of events rather than a simple detection bias.

A more direct test of this hypothesis can be provided by examining patterns in the data for the two crimes considered together. Recall that there was no evidence of space–time clustering for pairs of TFMV and burglary offenses. Thus, if the patterns observed for burglary and TFMV were simply the results of a detection bias, we would predict that the probability of detecting a pair of TFMV–burglary events would be a function of how far apart they occurred from each other in space and time. If they instead reflect the targeting behavior of offenders, no discernable pattern should emerge. The general profile of results shown in Table 8 chimes with that shown in Table 5, revealing little or no pattern. That said, the reader will notice that events at the same location and within 14 days were highly likely to have been cleared to the same offender(s). Unlike the other cells in the contingency table, only two detected offenses occurred at the same location and within 14 days of each other, rendering this particular result unreliable.
Table 8

Fraction of pairs of incidents of TFMV and Burglary for each space–time interval for which one or more offenders were involved in both offenses

Distance between events

Days between events

14

28

42

56

70

84

98

112

112+

Same

50

0

0

0

0

0

0

0

0

0–100 m

0

5

4

0

0

0

0

0

0

101–200 m

4

2

4

4

0

1

0

0

0

201–300 m

3

2

2

0

1

0

1

1

0

301–400 m

3

3

2

3

1

0

1

0

0

401–500 m

3

1

4

1

0

2

1

1

0

501–600 m

6

4

3

2

1

1

2

0

0

601–700 m

2

2

4

2

1

1

0

2

0

701–800 m

1

1

1

1

0

0

0

1

0

801–900 m

2

2

0

0

1

1

1

0

0

901 m–1 km

1

2

3

0

2

2

2

0

0

1 km+

0

0

0

0

0

0

0

0

0

Discussion

The general aim of this paper was to see if spatial and temporal patterns of acquisitive crime are consistent with the idea that offenders engage in foraging activity. The patterns which mark out such activity are the temporal variation in crime locales, and the attribution of such variation to patterns in the behavior of particular offenders. That is, rather than crimes consistently being more likely to occur in some places (hotspots) than others, there is dependency in the data such that a crime is more likely to occur at a particular location if another took place recently and nearby.

The findings reported here are consistent with those reported elsewhere for burglary (e.g. Johnson et al. 2007), and extend to TFMV, inviting further extension to other types of acquisitive crime (see also Grubesic and Mack 2008). One caveat should be entered. Around one-third of TFMV events had incomplete address information which would mean that there would be an error associated with the geographic grid coordinates assigned. While exclusion of these events ensures the reliability of the data used it also means that the results may not apply to the totality of such crimes.

The findings have clear implications for the forecasting of crime locations and detection strategies. Earlier work (see Bowers et al. 2004; Johnson et al. 2007; Johnson et al. 2008) has shown that the generation of crime forecasts that take account of when and where crimes occurred in the past improves predictive accuracy relative to standard methods of crime hot-spotting. The finding that TFMV conforms to the same pattern as burglary suggests that this approach of prospective mapping may be useful for this type of crime also.

A related aim of the study was to determine if the space–time distribution of one type of crime was linked to that of the other, with the hypothesis being that foraging offenders would commit different types of crime in parallel as they moved through different neighborhoods. If this were the case, we would expect to find that pairs of burglary–TFMV events clustered in space and time above and beyond what would be expected on the basis of the spatial distribution of the two types of crime. No support for this hypothesis was found, but further research on this point is clearly warranted to see if such patterns exist in other locations or for other types of crime. The method developed here to detect the patterns discussed provides researchers with a framework for analysis.

As already discussed, hypotheses other than that tested here could explain the basic space–time patterns and so a more direct test of the foraging hypothesis was attempted through the analysis of crimes detected by the police. In line with this hypothesis, for both burglary and TFMV it was clear that most crimes which occurred close in space and time were cleared to the same offender(s). Rarely were crimes close in space but a long time apart cleared to the same offender(s). As discussed, one potential problem with interpretation of these results is that the data concerned with detected crimes could represent a biased sample. That the data only represent a sample of crimes committed is unquestionable, but this is an issue for all studies that consider detected crimes. For the current data, the detection rate was considerably higher than for other studies, which alleviates the problem to some degree but imperfections in the data are acknowledged, not least the underestimation of offender versatility by dint of the rule that offenses TIC have to be similar to the offense charged. An equally serious concern is that crimes which cluster in space and time might simply be more likely to be detected than other crimes. This would mean that the results observed here and elsewhere (Bernasco 2008) may merely reflect the characteristics of the sample. If this were true it would not suggest that offenders do not adopt foraging strategies of the kind discussed, but that the use of such strategies is less common than might be inferred from the results here presented. At this point it is important to be very clear about what we are and are not suggesting. We do not suggest that offenders are a homogeneous group, all of whom adopt optimal foraging strategies all of the time, but rather that enough of them do so for a sufficient proportion of crimes to generate detectable patterns in the space–time distribution of crime events. For the current study, we interpret the findings as suggesting that a detection bias alone is unlikely to have generated the results. If this were the case, then the same patterns should have been observed for burglary and TFMV. The precise patterns differed considerably. For example, while only 8% of detected burglaries within 14 days and over 1 km apart were cleared to the same offender(s), for TFMV the percentage (27%) was much higher.

Perhaps the most persuasive support comes from the analysis of inter-crime patterns. If a systematic bias in the way that the crimes considered were detected was responsible for the patterns observed, we would expect to observe patterns in the detection data irrespective of crime type. Likewise, patterns should emerge in the detection data regardless of whether they do in the victimization data. On the other hand, if the results cannot be explained by a detection bias alone then, for offenses that do not cluster in space and time, there should be little or no regularity in the patterns observed for detected crimes of that type. For the analyses of pairs of burglary–TFMV victimizations, there was no evidence of space–time clustering in the victim data and, in line with the above logic, no pattern in the crimes detected by the police. The authors therefore suggest that the most parsimonious explanation for the results observed for burglary and TFMV is that the clustering observed was at least partly the result of offender foraging strategies.

Considering the extent to which offenders are likely to engage in strategies of the kind discussed, one possibility is that only detected offenders adopt these types of strategy. We therefore reanalyzed the victim data excluding those crimes that had been detected by the police. Although not reported here, for both types of crime, the results were identical to those presented above. The patterns of space–time clustering observed here were thus not simply generated by the activity of offenders most likely to come to police attention.

The findings have implications for the linking of undetected crimes. A reasonable inference that may be made on the basis of the current findings is that for the crimes studied, those that occur close to each other in space and time are likely to be the work of the same offender(s). In a recent study of burglary, Goodwill and Alison (2006) presented results which support this assumption, but hitherto no such analysis has been conducted for vehicle crime. Moreover, rather than simply assuming that such a heuristic will be accurate for any area or any type of crime, before undertaking the linking task it would be wise to conduct analyses of patterns in victimization data to see if the crime(s) considered cluster in space and time and, if they do, over what distance and time any effects are statistically significant. Such analysis will be useful in the calibration of any algorithm used to link crimes. For example, in the current analysis, it was evident that for TFMV the distance over which same offender involvement might be implied from the victimization data was greater than it was for burglary. This interpretation is clearly supported by the analysis of crimes detected by the police.

While the pattern in which nearby places and times suffer crime spates has so far proven universal, it need not be so. One insight gained while writing this paper is that the boost hypothesis presumes what the forager hypothesis does not. There may be circumstances where one crime diminishes the probability of its near repetition, by dint of a community’s collective efficacy or diligent policing. Such examples would be of particular interest and would not damage the foraging hypothesis, which requires only that experience informs offender decisions about what to do next.

In conclusion, the results provide support for theories of offender foraging. To help us to understand offender strategies in more detail, the authors are currently conducting ethnographic work with a focus on how offenders select targets in space and time and whether they adopt sequenced decision making strategies of the kind discussed here. A further avenue of investigation we are also engaged in is the use of computer simulation (for a general overview, see Liu and Eck 2007). The overall aim is to test the hypotheses discussed using a range of different methods so that results can be triangulated and the weaknesses of one approach offset by the strengths of another.

Footnotes
1

The inclusion of these events generated the same pattern of results as reported below.

 
2

For the spatial dimension, bandwidths of 50, 100 and 200 m were used. For the temporal parameter, bandwidths of 7 days, 14 and 28 days were used. All analyses not shown are available upon request.

 
3

As the location of events is preserved, risk heterogeneity is accounted for in the analysis.

 
4

Some TFMV events (N = 155) took place in car parks. A further analysis confirmed that the exclusion of these events did not affect the results observed.

 
5

The same patterns of results were observed for analyses for which the data for only one file was shuffled. This was the case irrespective of which dataset was shuffled.

 

Acknowledgements

This study was supported by British Academy research grant LRG 45507. The authors would like to thank Dorset police for providing the data analyzed, and in particular Derek Johnson. The authors would also like to thank (in order of geographic proximity) Kate Bowers, Wim Bernasco, Henk Elffers, George Rengert, Jerry Ratcliffe, and Mike Townsley for discussions on the topic of near repeats.

Copyright information

© Springer Science+Business Media, LLC 2008