Abstract

The study of point patterns on linear networks has seen significant theoretical development, with common applications including traffic accidents, wildlife collisions, street crimes, and the distribution of roadside trees. In these cases, the points of interest are confined to the linear network itself. However, there are scenarios where the focus is on understanding the spatial relationship between point patterns located near, but not on, the linear network. For instance, crimes occurring away from roads or human-caused fires – where the point pattern may be influenced by its proximity to the road network. In crime analysis, a potential relationship could exist where the road network facilitates criminal activity in the surrounding area. Despite the relevance, research on spatial points in the Euclidean space surrounding a linear network, particularly in quantifying the relationship between a linear network and nearby point processes, is limited. This work explores and quantifies the relationship between point processes in the vicinity of a linear network. The methodology is validated through simulations and applied to crime data from Khayelitsha, South Africa, demonstrating that, for certain types of crimes, the road network indeed acts as a facilitator, with crimes clustering around it.