Prospective crime mapping in operational context Final report

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e ij = n .j x n i.nWhere, e ij is the expected value for each cell, n ij is the observed, and n i and nj are the row andcolumn totals respectivelyThe results of the analysis can be interpreted by inspecting adjusted residuals, computed foreach cell using the following formula (see, Agresti, 1996, pp31-32):r ij =n ij – e ij[e ij (1-row proportion of n i+ )(1-column proportion of n +j )] 1/2Thus, the adjusted residuals are a measure of the difference between the observed andexpected values for each cell. The adjusted residuals have a mean value of zero and astandard deviation of one, hence adjusted residual scores exceeding values of two (or evenmore stringently three) are considered statistically significant. The null hypothesis is thatevents are not clustered in space and time. Negative values indicated that there are fewerevents occurring within a particular space-time interval.The majority of research concerned with crime (Johnson and Bowers, 2004; Townsley et al.,2003) has used the Knox approximation to examine space-time clustering. However, analternative approach, for which the independence of observations is not a requirement, mayalso be computed (Johnson et al., 2006). This approach uses Monte-Carlo simulation togenerate an expected distribution, rather than using the marginal totals (Besag and Diggle,1977). To do this, the data are permuted, in effect mixing up the dates and locations acrossthe events. Thus, the dates are randomly shuffled using a pseudo-random number generator,whilst the spatial locations remain fixed. The hypothesis is that if there is statisticallysignificant space-time clustering in the data then there should be more events observed tooccur close in space and time than for 95 per cent of the random permutations generated.The process of generating permutations is repeated (iterated) a number of times, typicallyaround 999, a new contingency table generated each time and compared with thecontingency table for the observed distribution. The probability that the observed value foreach cell occurred on the basis of chance may be calculated using the following formula (seeNorth, 2002):n − rank + 1p =n + 1Where n is the number of simulations, and rank is the position of the observed value in a rankordered array for that cellOne possible reservation about the p-values generated using the Monte-Carlo approach (andthe Knox residuals) is that they are not as readily interpretable as one might like.Interpretation of the results can be aided by deriving a simple measure of effect size. 2 In thiscase, a Knox ratio, which contrasts the observed value for each cell with the average‘simulated’ value for that cell (or the expected value derived using the marginal totals of thetable), was computed. Thus, a Knox ratio of 2.0 so derived would indicate that twice as manyburglaries occurred within a particular distance and time of each other than would on averagebe expected on the basis of a chance distribution. A value of one would indicate that theresult conformed to what would be expected on the basis of chance, and values of less thanone that fewer burglaries occurred within a particular distance and time of each other thanone would expect. Which measure of central tendency is best used to compute the odds ratiodepends upon the distribution of the simulated data. If the data are skewed, or there are2 The Knox residuals can be interpreted in the same way to some extent but are not as simple to understand. Insimple terms, the larger the Knox residual the larger the effect.5
extreme values, the mean can misrepresent the distribution. For this reason, the authors useboth the mean and median values for each cell. On the whole, for the data analysed the twotypically converge and hence for the results that follow, the authors will report only resultsderived using the median values.This approach is to be preferred over the Knox approximation, particularly as no assumptionsregarding the statistical distribution are required. However, limitations in computing powerhave meant that where a large number of events are to be analysed, the process can takesome time. This is particularly true where the dimensions of the contingency table or thenumber of events analysed are large. Fortunately, computing power is now sufficient forMonte-Carlo simulation of this kind to be completed for small data sets (e.g. n=1000) and a 10x 10 contingency table fairly rapidly, and for larger data sets (e.g. n=2000) over an hour or so.Larger contingency tables or data sets can still take a matter of days, but are now easilycomputed by those prepared to be as patient as the present writers!Is the risk of burglary communicable in the East Midlands?In the sections that follow, the results for each policing area that was analysed in the EastMidlands, namely Mansfield and Ashfield Sectors in Nottinghamshire, Alfreton (‘A’) Division inDerbyshire, and Corby and Wellingborough Sectors in Northamptonshire, will be presented.To allow easy direct comparisons the results will be presented here in tabular form. Anumber of analyses were conducted for each data set using both the Knox and Monte-Carlomethods described in the previous section. For instance, analyses have been conductedusing months as the temporal bandwidth whereas others have used weeks. For each areamonthly analyses will be presented for both Knox and Monte-Carlo approaches. As willbecome apparent these varied little. Thus, analyses for the Knox approximation only will bepresented looking at the communication of risk over weekly intervals. In all analyses, for thesake of simplicity, repeat victimisation is excluded. Thus, the results consider the distanceover which the risk of a household’s burglary is communicated to different households and forhow long this endures. Because of the exclusion of repeats against the same household, thebenefits of patrolling and resourcing patterns based upon propinquity in time and space to aburgled home will be considerably understated in what follows.To anticipate the results, it would appear that as a general rule the risk of burglary iscommunicable up to a distance of around 400m for at least one month. There was no area forwhich this was not the case, hence universal application of the 400m one-month rule is in nocase inappropriate, it merely excludes a proportion of other high-risk homes. The sensitivityanalyses conducted to examine the duration of the elevation in risk suggested that thisextended beyond one month in most cases, up to around eight weeks. This will subsequentlybe referred to as the classic profile. Those not wishing to understand the detail of areadifferences should skip to the next section, in which the value of prospective mapping inoperational context is explored.Mansfield Police SectorFor Mansfield, the data analysed cover the period January-December 2004 and comprised1,156 burglary events. The results of the monthly Knox and Monte-Carlo analyses are shownas Tables 2.2 and 3.2 respectively. The results are consistent in showing that the risk ofburglary communicates up to a distance of 200m and endures for one month. Additionally,the Monte-Carlo results suggest that for houses within 100m of burgled homes the riskendures for up to two months. The same (two-month) result is apparent for the Knox residualanalysis, although it marginally fails to be statistically reliable.6
Page 2 and 3: 1. UCL JILL DANDO INSTITUTE OF CRIM
Page 4 and 5: ContentsAcknowledgementsExecutive s
Page 6 and 7: 2.5 Illustration of a simple neares
Page 8 and 9: Project outcomesPatterns of burglar
Page 10 and 11: those that involved collaboration w
Page 12 and 13: 1. IntroductionThis report represen
Page 14 and 15: optimally calibrated system, the go
Page 18 and 19: Table 2.2: Knox ratios for Mansfiel
Page 20 and 21: Table 2.6: Monte-Carlo results for
Page 22 and 23: Table 2.10: Weekly Knox ratios for
Page 24 and 25: Table 2.14: Monte-Carlo results for
Page 26 and 27: Figure 2.1: The five policing areas
Page 28 and 29: The results for area 5 again demons
Page 30 and 31: The bandwidth used to generate the
Page 32: a densely populated urban area this
Page 35 and 36: Table 2.24: Average number of crime
Page 37 and 38: Patrolling efficiencyAs discussed e
Page 39 and 40: 3. Tactical options and selecting a
Page 41 and 42: Selecting a pilot siteThe decision
Page 43 and 44: Table 3.2: Tactical options matrixT
Page 45 and 46: Type ofinterventionStudyUse ofintel
Page 47 and 48: Other potential tactical optionsAt
Page 49 and 50: 4. System development and evolution
Page 51 and 52: the same time of day as each other
Page 53 and 54: unfortunately, implementation or us
Page 55 and 56: any tactical options were employed
Page 57 and 58: the end of the pilot. In addition t
Page 59 and 60: Figure 5.1: Promap dissemination pr
Page 61 and 62: the busy schedule of the new Divisi
Page 63 and 64: Tactical deliveryCommand Team daily
Page 65 and 66: Table 5.3: Number of respondents wh
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permitted, up to four plain clothed
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observation made by those who used
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A simple time-series analysis (see
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Two approaches were used to compute
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Figure 6.3: Changes in the proporti
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Figure 6.5: Changes in the proporti
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With respect to implementation real
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ReferencesAggresti, A. (1996) An In
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Johnson, S.D., Summers, L., and Pea
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Appendix 1. The information technol
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Figure A1.2: Stand-alone applicatio
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Recommendations that may be realise
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Section 1: knowledge and understand
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Extra Comments (please outline any
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In relation to the evaluation of in
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Time-series analysisFor the purpose
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Figure A3.1: Changes in the spatial
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Figure A3.2: Lorenz curves showing
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To recapitulate and elaborate, the
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Concluding comments on methodThe te
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Figure A5.2: An enlargement of the
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Figure A5.6: Prospective map magnif
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Produced by the Research Developmen
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Prospective crime mapping in operational context Final report

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