Chainey, S

Tompson, L

Uhlig, S

English

UCL Discovery

This is a pre-print of a commentary accepted for publication by the Security Journal in 2008. It is a pre-copy-edit version of the letter that is found at http://www.palgrave-journals.com/sj/journal/v21/n4/abs/sj20087a.html  Response to Levine 2008, ‘The hottest part of a hotspot: comments on “Spencer Chainey, Lisa Tompson and Sebastian Uhlig, The utility of hotspot mapping for predicting spatial patterns of crime’.  Security Journal.  Spencer Chainey¹, Lisa Tompson², and Sebastian Uhlig³  1  Director  of  Geographical  Information  Science,  Jill  Dando  Institute  of  Crime  Science, University College London, Brook House, 2-16 Torrington Place London. WC1E 7HN 2 Research Fellow, Jill Dando Institute of Crime Science, University College London, Brook House, 2-16 Torrington Place London. WC1E 7HN 3  Project  Consultant,  Informed  Solutions,  The  Old  Bank,  Old  Market  Place,  Altrincham, Cheshire. WA14 4PA, UK  Levine  (2008)  provides  a  useful  contribution  to  the  assessment  of  hotspot techniques in their utility for predicting spatial patterns of crime – considering in particular the application of the nearest neighbour hierarchical clustering technique (Nnh) and convex hulls.  However, we think that there are some inaccuracies  in  his  statements,  and  errors  and  lack  of  rigour  in  his methodology that make his results misleading and undermine his conclusions.  Levine (2008) suggests that “the methodology they [Chainey, Tompson and Uhlig, 2008] adopted to compare several hotspot techniques was limited and, consequently, raised doubts about the conclusions they drew”.  We argue that the methodology is not limited (indeed Levine (2008) refers to it as a ‘good criterion  for  comparing  different  hotspot  techniques’).    Instead,  we  do acknowledge  that  the  range  of  hotspot  mapping  techniques  that  can  be applied  against  the  methodology  can  be  expanded.    Our  purpose,  as described  in  Chainey  et  al  (2008)  was  to  concentrate  on  exploring  the predication accuracy of the most common hotspot mapping techniques that are applied by practitioners and as evidenced by Weir and Bangs (2007) in their  survey  of  crime  analysts.    Our  assessment  was  that  the  thematic mapping  of  small  geographical  units  (e.g.  Census  Output  Areas),  spatial ellipses produced by the STAC routine, grid thematic mapping, and kernel density estimation were the most common hotspot mapping techniques used in practice.  We also illustrated this with reference to several examples of their application.   We  could  have  considered  many  others  but  felt  that  the  four mapping techniques we analysed would offer the most significant contribution to researchers and practitioners.  Indeed, we even recommended that other researchers apply the Prediction Accuracy Index (PAI) (Chainey et al, 2008) to other techniques so that other contributions could be made to this research theme.  Levine’s contribution in testing the Nnh technique and convex hulls is therefore very welcomed.  Hence, we argue that our conclusions are sound, and offer a strong foundation for other researchers to apply the PAI to other mapping  techniques,  compare  against  our  results  and  help  to  develop research into the prediction utility of hotspot mapping.  We  also  believe  that  there  are  a  number  of  inaccuracies  in  Levine’s methodology, which in turn have produced some misleading results.  These are in relation to the parameters that Levine (2008) uses in his analysis and his sample:  Parameters used by Levine (2008) for KDE, STAC ellipses and Nnh We suggested (in Chainey et al, 2008) that the parameters used for hotspot mapping  techniques  should  be  based  on  the  data  that  is  being  analysed, rather than on fixed settings that are applied to all different types of data.  In our research we used Hotspot Detective (Ratcliffe, 2002) to generate KDE surfaces.    The  parameters  that  Hotspot  Detective  determines  as  default settings  are  specific  and  are  chosen  after  an  analysis  of  the  spatial characteristics  of  the  input  data.   We  then  applied  these  settings  to  other techniques  that  used  the  same  corresponding  input  data  (i.e.  data  for  the same input data period, for the same measurement date and for the same crime type).  Cell size values were calculated by dividing the shorter side of the minimum bounding rectangle around the crime input data by 150 (Ratcliffe, 2004).  In Hotspot  Detective  the  calculation  of  the  default  bandwidth  value  used  for generating KDE surfaces is not divulged to users.  It is known, however, to be a function of the shorter side of the minimum bounding rectangle surrounding the crime data, divided by a number that provides a suitable value without requiring a significant number of iterations to generate a representative KDE surface (Ratcliffe – personal communication).  For example, the parameters determined for input data of residential burglary that covered an input data period of 3 months were a cell size value of 48m and a bandwidth value of 240m.  For theft of vehicle data that covered an input data period of 1 week the  number of  records  and  their  spatial distribution  would  be  different  and hence require different parameter settings.  For these data the cell size value was 37m and the bandwidth value was 185m (see table 1 for a full listing of parameter  values  that  illustrate  different  settings  are  required  for  different data).  Levine used a cell size of 49m and 245m on all his tests of KDE, STAC and Nnh for data from Houston, Texas.  These were based on  parameter settings that we determined for three of the eighty different input datasets in our research using crime data for Camden and Islington in London.  Levine should have determined the specific parameter settings (such as the KDE cell size and bandwidth) from a similar analysis of his input data.  Instead he uses the parameters we determined which are not comparable to his dataset: for example,  4243  theft  of  vehicle  offences  in  Camden  and  Islington  in comparison to 21352 offences of burglary of vehicle offences for the much larger  geographic  area  of  Houston.    We  suggest  that  this  error  in  his methodology  undermines  his  conclusions  and  renders  his  results  as misleading.  PAI values for different input and measurement date periods Levine (2008) performed analysis that compared 12 months of input data from 2005 to 12 months of measurement from 2006.  We performed our analysis for a combination of 100 different input data and measurement data periods for four different crime types, for two different measurement dates (i.e. 800 experiments) in order to provide a representative sample of PAI results.  We suggest  that  for  Levine  to  determine  that  certain  methods  are  better  than others requires a similar rigour to that which we applied.  A sample that is based on analysis of only one input data period and one measurement period for  one  measurement  date  may  produce  results  that  are  not  fully representative of the performance of hotspot mapping techniques.  We suggest that Levine repeats his analysis following the methodology we have described in Chainey et al (2008) if he wishes to confirm the conclusions he arrives at.  We do consider his explanation of the Nnh technique as being particularly worthwhile and that the application of convex hulls for determining crime hotspots as offering a potentially useful technique for predicting spatial patterns of crime.  Similarly, Chainey and Tompson are currently researching the application of the Nnh technique, convex hulls and the Gi* statistic (Getis and Ord, 1996) for predicting spatial patterns of crime using the dataset for Camden and Islington.  We plan to publish the results at some future point.  Hotspot Detective default values for all crime types and input data time periods (cell size / bandwidth) for 01/01/03 Input  data time period Residential Burglary Street Crime Theft  from vehicle Theft  of vehicle    C.S.  B.  C.S.  B.  C.S.  B.  C.S.  B. 12 months  49  245  49  245  49  245  48  240 6 months  49  245  49  245  49  245  46  230 3 months  48  240  48  240  49  245  46  230 2 months  48  240  48  240  48  250  46  230 1 month  46  230  46  230  46  230  46  230 2 weeks  44  220  45  225  45  225  45  225 1 week  44  220  44  220  45  225  37  185 3 days  38  190  44  220  44  220  34  170 2 days  38  190  31  155  40  200  34  170 1 day  38  190  2  10  40  200  27  135 (a) Hotspot Detective default values for all crime types and input data time periods (cell size / bandwidth) for 13/03/03 Input  data time period Residential Burglary Street Crime Theft  from vehicle Theft  of vehicle    C.S.  B.  C.S.  B.  C.S.  B.  C.S.  B. 12 months  46  230  46  230  46  230  45  225 6 months  45  225  46  230  46  230  45  225 3 months  45  225  44  220  45  225  45  225 2 months  45  225  43  215  45  225  45  225 1 month  43  215  43  215  44  220  44  220 2 weeks  41  205  43  215  42  210  42  210 1 week  39  195  42  210  41  205  42  210 3 days  39  195  39  195  40  200  36  180 2 days  30  150  39  195  40  200  31  155 1 day  25  125  38  190  32  160  27  135 (b) Table 1.  Hotspot Detective KDE default values (C.S. – cell size and B. – bandwidth)  for  each  crime  type  and  each  period  of  input  data,  for  (a)  a measurement date of the 1st January 2003 and (b) a measurement date of the 13th  March  2003.    Bandwidth  measures  were  used  to  determine  alternate search radii for spatial ellipses, and alternate grid thematic mapping cell sizes.  For example, a grid thematic map was generated from one month of street crime data, for the 01/01/2003 measurement date, using a grid cell size of 230m.  Reproduced from Chainey et al (2008).  References Chainey,S.P., Tompson,L., Uhlig,S. (2008). The utility of hotspot mapping for predicting spatial patterns of crime. Security Journal.  Getis,  A.  and  Ord,  J.K.  (1996).    Local  spatial  statistics  :  an  overview.    In Longley,  P.  and  Batty,  M.  (Eds),  Spatial  Analysis:  Modelling  in  a  GIS Environment.  GeoInformation International: Cambridge, England, 261-277.  Levine,  N.  (2008)  ‘The  hottest  part  of  a  hotspot:  comments  on  “Spencer Chainey, Lisa Tompson and Sebastian Uhlig, The utility of hotspot mapping for predicting spatial patterns of crime’.  Security Journal.  Ratcliffe,  J.,  (2002)  HotSpot  Detective  2.0  for  MapInfo  Professional  7.0. Available online at http://jratcliffe.net/hsd/   Ratcliffe, J. (2004) HotSpot Detective for MapInfo Helpfile Version 2.0 

HotSpot Detective 2.0 for MapInfo Professional 7.0. Available online at http://jratcliffe.net/hsd/

Local spatial statistics : an overview. In

The hottest part of a hotspot: comments on “Spencer Chainey, Lisa Tompson and Sebastian Uhlig, The utility of hotspot mapping for predicting spatial patterns of crime’.

The utility of hotspot mapping for predicting spatial patterns of crime.

The "Hottest" Part of a Hotspot: Comments on "The Utility of Hotspot Mapping for Predicting Spatial Patterns of Crime" Response

The "Hottest" Part of a Hotspot: Comments on "The Utility of Hotspot Mapping for Predicting Spatial Patterns of Crime" Response

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