Identifying a spatial scale for the analysis of residential burglary: An empirical framework based on point pattern analysis

Abstract

A key issue in the spatial and temporal analysis of residential burglary is the choice of scale: spatial patterns might differ appreciably for different time periods and vary across geographic units of analysis. Based on point pattern analysis of burglary incidents in Columbus, Ohio during a 9-year period, this study develops an empirical framework to identify a useful spatial scale and its dependence on temporal aggregation. Our analysis reveals that residential burglary in Columbus clusters at a characteristic scale of 2.2 km. An ANOVA test shows no significant impact of temporal aggregation on spatial scale of clustering. This study demonstrates the value of point pattern analysis in identifying a scale for the analysis of crime patterns. Furthermore, the characteristic scale of clustering determined using our method has great potential applications: (1) it can reflect the spatial environment of criminogenic processes and thus be used to define the spatial boundary for place-based policing; (2) it can serve as a candidate for the bandwidth (search radius) for hot spot policing; (3) its independence of temporal aggregation implies that police officials need not be concerned about the shifting sizes of risk-areas depending on the time of the year.

Fig 1. Residential burglary (represented with black +) overlaid with kernel density map indicating hotspots around downtown Columbus during 1994–2002.

In each subplot, the year and the number of offenses are separated by “:”; For example, in the first subplot on the top left, “1994: 8863” indicates that there were 8863 residential burglary offences in year 1994. The unit of the density map is one residential burglary per km².

Fig 2. Spatial covariates for modeling the spatial trend.

a–residential area, b–parcel density (unit: One parcel per km²).

Fig 3. An example inhomogeneous L function, assuming inhomogeneous Poisson process (IPP).

The black line (including the thick segment in the middle) is the estimated L function from the data; the red dashed line is the theoretical L function (null model) for IPP; the shaded area indicates the simulation envelope constructed with 39 Monte Carlo simulations of the fitted IPP model. The blue dashed line indicates the minimum scale of interaction (h₀); the blue solid line indicates the range of interaction (h_r).

Fig 4. Estimated relative intensity.

Fig 5. Fitted intensity map for mapped point pattern (all residential burglary during 1994–2002).

Unit: One residential burglary incident per km².

Fig 6. The distribution of the characteristic scale of clustering (h_c) across the 234-point patterns.

The red vertical line highlights the grand mean of h_c (2243 m).

Fig 7

The boundaries and radius distribution for four area units: zip codes (a and e), communities (b and f), neighborhoods (c and g), and census tracts (d and h). For the boundaries of communities and zip codes, we included only the units that most of their areas fall within the study area and excluded those that most boundaries extend beyond the study area.

Fig 8. The configuration of communities and neighborhoods in the study area.