Date Published: June 26, 2019
Publisher: Public Library of Science
Author(s): Nick Malleson, Wouter Steenbeek, Martin A. Andresen, Sotirios Koukoulas.
A key issue in the analysis of many spatial processes is the choice of an appropriate scale for the analysis. Smaller geographical units are generally preferable for the study of human phenomena because they are less likely to cause heterogeneous groups to be conflated. However, it can be harder to obtain data for small units and small-number problems can frustrate quantitative analysis. This research presents a new approach that can be used to estimate the most appropriate scale at which to aggregate point data to areas.
The proposed method works by creating a number of regular grids with iteratively smaller cell sizes (increasing grid resolution) and estimating the similarity between two realisations of the point pattern at each resolution. The method is applied first to simulated point patterns and then to real publicly available crime data from the city of Vancouver, Canada. The crime types tested are residential burglary, commercial burglary, theft from vehicle and theft of bike.
The results provide evidence for the size of spatial unit that is the most appropriate for the different types of crime studied. Importantly, the results are dependent on both the number of events in the data and the degree of spatial clustering, so a single ‘appropriate’ scale is not identified. The method is nevertheless useful as a means of better estimating what spatial scale might be appropriate for a particular piece of analysis.
A key issue in the analysis of many spatial processes is the choice of an appropriate scale for the analysis, when only one scale of analysis is being used. This choice may be based on, or identified through, theoretical means or the research question; and in some cases there may not be a choice because data have been provided at one spatial scale. It may, however, be based on the need to identify the scale at which no further disaggregation provides new information. For many phenomena in the latter context, smaller spatial units are generally preferable because they are more likely to be homogeneous with respect to both the events under study and the population at risk, and, therefore, represent more accurately the underlying spatial pattern—this would not be the case when a measure of heterogeneity is theoretically important, however. As urban socio-demographics can vary considerable over quite small distances, large spatial units may hide or “smooth out”  important low-level patterns. And if the relevant social processes occur at larger spatial scales, small spatial units can be aggregated easily to larger spatial units. Recognising the importance and practical benefits of (starting with) small spatial units, recent research in many social-science fields tends towards ‘micro places’. This is especially true for crime science research, which is the subject of this paper.
The aim for this work is to develop a general method that is capable of identifying the most appropriate scale for the analysis of spatial patterns, defined as that which is as large as possible without causing the underlying spatial units to become heterogeneous with respect to the phenomena under study. The method proposed here does this by creating iteratively smaller areas and, at each scale (or ‘resolution’), determining the similarity between two point patterns that should be spatially similar.
This paper has presented a new approach that can be used to identify the most appropriate scale at which to aggregate point data to areas. It does this by creating a number of regular grids with different resolutions (in a similar method to that of ) and estimating the similarity between two realisations of the point pattern at each resolution. The most ‘appropriate’ scale is the one that balances the benefits of using smaller spatial units (larger units will probably hide important heterogeneity that is apparent at higher resolutions) against the drawbacks (including difficulties in obtaining fine spatial data in the first place, as well as the risks of the underlying pattern being obscured by noise). The method is applied to the study of crime patterns in Vancouver, Canada, and the results provide evidence for the size of spatial unit that is the most appropriate for the different types of crime studied (these were residential burglary, commercial burglary, theft from vehicle and theft of bike). The method is dependent on both the size of the point patterns (the number of events) and the degree of clustering, so it is doubtful that a single ‘appropriate’ scale will ever be identified for a phenomenon. But the method is nevertheless useful as a means of better estimating what spatial scale might be appropriate for a particular piece of analysis.