UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE ! ! Does bus-related crime “float in space”? ! ! ! Henry Partridge PhD candidate, UCL Department of Security and Crime Science 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Planar space Most crime hotspot analysis techniques use straight-line (Euclidean) distance and assume that space is continuous, homogeneous and uniform in all directions. In other words, these techniques assume that crime can happen anywhere. But many crime events are constrained by a one-dimensional subset of this space, network space: • Street robbery • Bus-related crime • IED attacks • Perhaps any crime geocoded to a property address 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Network space Network space constrains the location of crime events and the routine movements of victims and offenders. 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Applying planar methods to network constrained events ….. • Ignores the layout of urban space • Underestimates actual travel distance • Can produce spurious evidence of clustering when applied to network constrained data like road collisions (Yamada and Thill 2004) and vehicle thefts (Lu & Chen 2007) 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Planar K function Random points on a network analysed on a plane Network K function 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Random points on a bus route analysed on a plane Planar K function Network K function 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Research questions 1) Are recent incidents of disorder clustered on a bus route? 2) If clustering is present is it a function of the network? 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Data and method 84 Driver Incident Reports of Disturbance during 2013 on a single bus route run. OS MasterMap Integrated Transport Layer. ! ! Planar K-function using spatstat package in R. 1m distance interval. No edge correction. 99 simulations. Network K-function in GeoDa Net. 1m distance interval. Edge correction unavailable. 99 simulations. 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Incidents of disorder on a bus route Network K function Planar K function 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Conclusions Clustering is present in both outputs of the K function. Therefore, clustering is not a function of incidents being constrained by a bus route. ! So what is responsible?…… 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Policy implications Spatial analysis techniques that use shortest path distance are recommended for network constrained crime events to reduce the detection of potentially spurious clustering patterns. ! Where data is highly constrained (e.g. bus-related crime) it is necessary to adopt network spatial methods. ! 

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE References Lu, Y. & Chen, X. (2007). On the false alarm of planar K-function when analyzing urban crime distributed along streets. Social Science Research, 36 (2) 611-632. Okabe, A. & Yamada, I. (2001). The K-function method on a network and its computational implementation. Geographical Analysis, 33, 271–290. Okabe, A. & Sugihara, K. (2012). Spatial Analysis Along Networks. Chichester, West Sussex: John Wiley & Sons. Tompson, L, Partridge, H, & Shepherd, N. (2009). Hot Routes: Developing a New Technique for the Spatial Analysis of Crime. Crime Mapping: A Journal of Research and Practice, 1 (1) 77-96. Yamada, I. & Thill, J-C. (2004). Comparison of planar and network K-functions in traffic accident analysis. Journal of Transport Geography, 12, 149-158. !