Comparison of planar and network K -functions in traffic accident analysis Ikuho Yamada, Jean-Claude Thill * Department of Geography, University at Buffalo, The State University of New York, 105 Wilkeson Quadrangle, Buffalo, NY 14261, USA Abstract The network and planar K-function methods are applied to traffic accident data to illustrate the risk of false positive detection associated with the use of a statistic designed for a planar space to analyze a network-constrained phenomenon. We also dem- onstrate the benefits of using a method specifically designed for a network space. The results clearly indicate that the planar K- function analysis is problematic since it entails a significant chance of over-detecting clustered patterns. Analyses are implemented based on Monte Carlo simulation and applied to 1997 traffic accident data in the Buffalo, NY area. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: K-function analysis; Networks; Traffic accidents; Point pattern analysis; Monte Carlo simulation 1. Introduction Traffic accidents are commonly anticipated to form clusters in the geographic space and over time for the reason that their occurrence is tied to traffic volumes, which themselves exhibit distinct spatial and temporal patterns, as well as because of their link to natural environmental factors such as snow and fog, configu- ration of highway networks such as locations of access and egress points, and deficient design and maintenance of highways (Black, 1991). Therefore, a good under- standing of the spatial and temporal distribution of accidents makes a considerable contribution to devel- oping appropriate accident reduction programs and to evaluating their effectiveness. This paper demonstrates how the network version of a common method of spatial pattern analysis called K -function can be implemented in accident analysis and compares it to its conventional planar counterpart. Levine et al. (1995a) divide research on spatial dependence of traffic accidents into four main catego- ries. The first category of studies compares different types of spatial environments, such as urban and rural settings on the basis of accident prevalence, and usually involves highly aggregated data and large geographical units. The second looks for causal relationships between traffic accidents and attributes of the roadway system, for example, traffic volumes and roadway types. This category would include the identification and analysis of locations producing more accidents than other locations in a given network, also known as ‘‘hot spots’’ or ‘‘blackspots’’ (McGuigan, 1981). Studies of the third type examine accidents in particular areas or corridors while emphasizing socially and ecologically integrated analysis units. At the other end of the spectrum, the last line of research focuses on system-wide variations in traffic accidents, in other words, how local patterns of accidents compose a global-scale pattern. The work re- ported here belongs to the latter tradition. Another important aspect that sets studies of traffic accident distributions apart is the spatial resolution of the data analyzed. For instance, when data is available only in aggregate form such as counts per road segment or administrative zone, or when the relationship be- tween accident risk and road/zone attributes is of interest, one may conduct a road-based or zone-based analysis. On the other hand, when information is available for individual accident events and their loca- tions are recorded as points in the geographic space or as mileposts on the road network, one may adopt a method for point pattern analysis. The research reported here is of the latter type. * Corresponding author. Tel.: +1-716-645-2722; fax: +1-716-645- 2329. E-mail addresses: iyamada@buffalo.edu (I. Yamada), jcthill@buf- falo.edu (J.-C. Thill). 0966-6923/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtrangeo.2003.10.006 Journal of Transport Geography 12 (2004) 149–158 www.elsevier.com/locate/jtrangeo