1. Near repeat burglary chains: describing the physical and network properties of a network of close burglary pairs. Dr Michael Townsley, UCL Jill Dando Institute m.townsley@ucl.ac.uk

2. Outline Near repeat victimisation literature Poly–order near repeats (chains) Physical properties of near repeat chains Network properties of near repeat chains Modelling of near repeat chains

3. Near repeat victimisation literature Research shows prior victimisation gives an elevated risk of future victimisation, but this declines over time. New research indicates the same finding for targets near prior victims, with identical time signature. We call this near repeat victimisation

4. Near repeat pairs – pairs of events that occur close in space and time For N events generate the complete set of pairs (So N*(N-1)/2 pairs) For each pair: –Calculate the spatial distance –Calculate the temporal distance Tabulate the number of pairs occuring at different space-time thresholds.

6. Poly–order near repeats (chains) So far, most treatments are a-spatial and a-temporal Want to look at the spatial distribution of these near repeats in order to ascertain further patterns. For example, like to know whether near repeats tend to be ‘linked’ to form chains with each other more often than ‘ordinary’ pairs, or even if near repeat chains continue to propagate over long time periods or are short lived and ephemeral.

7. A near repeat chain is defined to be any group of events (crimes) where each member is close in space and time to at least one other member of the chain

8. Using graph theory to specify near repeats The events (crimes) are called nodes When two nodes are near repeats they are connected by an edge. By considering the temporal order of the events the graph can be specified as being directed. Near repeat chains are therefore directed walks/paths/chains (sequences of alternating nodes and edges)

9. Descriptive statistics Physical properties –Chain lifetime – duration of chain –Chain area – size of min. spanning ellipse and eccentricity

10. Network properties of near repeat chains Node degree – in-degree and out-degree Degree distributions Node motif – classification of nodes Chain order – nodes/chain Chains/network Triangles Node motif distribution/network

17. Data Two years burglary data (N=951 events, ~450K pairs) Space threshold 600 metres Time threshold 14 days Generated 2007 close pairs

18. Methods Generated expected distribution via resampling (999 iterations + obs = 1000 sample size) Constructed adjacency matrix (951-by-951) where entry ij = 1 if close in space and time, but 0 if not Descriptive statistics are either summary measures or many values

19. Results for the observed data - general 951 events formed 264 distinct chains. Predominantly small in size (about 100 chains were comprised of single events – i.e. order 1). Relatively short-lived; the vast bulk expired within three weeks.

20. Results (red = observed, black = expected)

22. Node motif summaries

28. Summary Some consistency of result with null hypothesis Differences observed for node motifs Limitations in scope (one site, one pair of selected thresholds)

29. Future directions – statistical modelling of pair and chain dynamics Some work on near repeat pair consistency by method of entry, point of entry and time of day p* models allow node attributes to be used as covariates for predicting the likelihood of connections between nodes Hierarchical p* models allow parameter estimates to be computed at the chain level.