space-time cluster<strong>in</strong>g: repeat victimisation. Consider<strong>in</strong>g evaluations of area-based <strong>in</strong>terventions, it ispossible to not only measure changes <strong>in</strong> burglary <strong>in</strong>cidence (the rate per 1,000 households) follow<strong>in</strong>gan <strong>in</strong>tervention but also how concentrated on <strong>in</strong>dividual properties <strong>crime</strong> is. For example, for an<strong>in</strong>tervention aimed at reduc<strong>in</strong>g repeat victimisation, simply exam<strong>in</strong><strong>in</strong>g the change <strong>in</strong> the <strong>in</strong>cidence ofburglary may be <strong>in</strong>sufficient to detect the full impact of a scheme, or the potential <strong>crime</strong> reductionmechanisms through which any change was realised. Instead, a more sensitive analysis (seeForrester et al., 1990) would be to exam<strong>in</strong>e the rate of repeat victimisation. A reduction <strong>in</strong> this type ofvictimisation would suggest an impact of the scheme, although a reduction <strong>in</strong> <strong>in</strong>cidence would berequired to demonstrate that target-switch displacement did not occur. On the other hand, a reduction<strong>in</strong> <strong>in</strong>cidence with<strong>in</strong> an area that was unaccompanied by a reduction <strong>in</strong> repeat victimisation wouldprovide less conv<strong>in</strong>c<strong>in</strong>g evidence that any reduction could reasonably be attributed to the scheme.In the same way, where strategies are employed to suppress emerg<strong>in</strong>g or endur<strong>in</strong>g hotspots of <strong>crime</strong>,as was the case <strong>in</strong> the current pilot, one desired outcome of the scheme would be to truncate thelength of space-time clusters of burglary. That is, if resources are directed to the right places at theright times <strong>in</strong> a way that anticipates where the next event <strong>in</strong> a cluster is most likely to occur, then itwould be hoped that emerg<strong>in</strong>g spatio-temporal clusters of <strong>crime</strong> would be targeted before they have achance to propagate.To exam<strong>in</strong>e this issue, software was developed to identify series of events that occurred close <strong>in</strong> bothspace and time, rang<strong>in</strong>g from two events (pairs) onwards. The approach allowed the frequency ofseries of different (k-event) lengths (e.g. pairs, triples, quads and so on) to be summarised andcompared for the periods before and dur<strong>in</strong>g the pilot.The identification and summary of series of events can be done <strong>in</strong> a variety of ways. Here, for everyburglary (the reference) event, any antecedent burglary that occurred with<strong>in</strong> a critical distance andtime of it was identified and added to the series. Us<strong>in</strong>g this approach only burglaries that occurredwith<strong>in</strong> the critical time and distance of the reference event could be identified. This precludes theidentification of other burglaries that might be l<strong>in</strong>ked to the others <strong>in</strong> a cluster. This problem isillustrated conceptually <strong>in</strong> Figure A3.3. In the top and bottom of Figure 6.8, there are four burglariesthat occurred with<strong>in</strong> a few days of each other. In the first cha<strong>in</strong>, all burglaries occur with<strong>in</strong> the criticalspatial distance of the reference event (the leftmost event) and thus one identifies a cha<strong>in</strong> of fourburglaries. For the second series, for the same reference event one would identify a cha<strong>in</strong> of onlythree burglaries as the f<strong>in</strong>al event occurred further away from the reference event than the criticaldistance. However, it occurred with<strong>in</strong> the critical distance of other events <strong>in</strong> the cha<strong>in</strong> and henceshould be <strong>in</strong>cluded <strong>in</strong> the series.Figure A3.3: An illustration of a triple (bottom) and quad cha<strong>in</strong> (top)Critical distanceAn alternative approach would be to <strong>in</strong>clude <strong>in</strong> a cluster all burglaries that are with<strong>in</strong> the criticaldistance and time of one or more events already identified as part of that series. Us<strong>in</strong>g this approach,both series shown <strong>in</strong> Figure A3.3 would be classified as be<strong>in</strong>g a four event series. In what follows thecritical distance and time used were 400m and one-week, respectively. Other def<strong>in</strong>itions could beused, and other analyses (not shown) us<strong>in</strong>g different def<strong>in</strong>itions revealed a similar pattern of results.91
To recapitulate and elaborate, the approach taken may be summarised as shown below:1. The burglary data were sorted <strong>in</strong> date order.2. For each period of time (before and dur<strong>in</strong>g the pilot), the previous week’s events were used asa historic buffer period to allow all events that occurred with<strong>in</strong> seven days of another to beidentified.3. Each burglary event was then considered <strong>in</strong> sequential order.a. For the first event considered, only the historic data were searched to see if earlierburglaries occurred with<strong>in</strong> the critical thresholds of the first event; where they did theywere added to the series for that reference event.b. For the second event considered, all of the historic data (<strong>in</strong>clud<strong>in</strong>g the first referenceevent) were searched, and events that belonged to a series identified as per step a.c. Once all <strong>crime</strong>s had been considered, for every event it was possible to calculate themaximum length of the cha<strong>in</strong> for which that event was the term<strong>in</strong>al event and howmany cha<strong>in</strong>s of every length were identified.Us<strong>in</strong>g this approach, it was possible to answer the question, ‘when a burglary occurs how many<strong>crime</strong>s previously occurred nearby <strong>in</strong> space and time?’ It is, of course, possible that any cluster soidentified could be part of a longer cluster which <strong>in</strong>cluded events that subsequently occurred.Expressed a slightly different way, clusters identified <strong>in</strong> this way may overlap with one another withone cluster <strong>in</strong>clud<strong>in</strong>g some events of another – although for any particular series length no twoclusters would <strong>in</strong>clude exactly the same events – there would be at least one different <strong>crime</strong> <strong>in</strong> thelonger cha<strong>in</strong> (the shorter be<strong>in</strong>g a subset of the other).Hav<strong>in</strong>g summarised the data <strong>in</strong> this way, it was possible to calculate what proportion of burglarieswere the term<strong>in</strong>al event for different lengths of space-time series. The results, shown as Figure A3.4,illustrate that around one-third of events occurred with<strong>in</strong> 400m and one week of at least oneantecedent both before and dur<strong>in</strong>g the pilot. Around 15 per cent of events occurred nearby and with<strong>in</strong>one-week of at least two others. For the two <strong>in</strong>tervals of time considered, the longest series identifiedconsisted of 12 burglaries that occurred close to each other <strong>in</strong> both space and time. Before discuss<strong>in</strong>gthe differences for the two periods of time, it is important to note the implication of this f<strong>in</strong>d<strong>in</strong>g, which isthat it clearly illustrates the flux of <strong>crime</strong>. If burglaries occurred <strong>in</strong> the same places all the time, eitherconsiderably longer series would have been identified, or a higher proportion of events would belongto longer series. This emphasises the need for a dynamic predictive capability for the deployment of<strong>crime</strong> reductive resources. Simply target<strong>in</strong>g the same areas over time is unlikely to direct resources tothe right places at the right times.92