Directional analysis for point patterns on linear networks

Abstract

Statistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on R-2, some tests based on the K-function and nearest neighbour orientation function have been proposed to check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes on linear networks, as the implicit geometry of the network forces particular directions that the points of the pattern have to necessarily meet. In this paper, we adapt such tests to the case of linear networks and discuss how to use them to detect particular directional preferences, even at some angles that are different from the main angles imposed by the network. Through a simulation study, we check the performance of our proposals under different settings, over a linear network and a dendrite tree, showing that they are able to precisely detect the directional preferences of the points in the pattern, regardless the type of spatial interaction and the geometry of the network. We use our tests to highlight the directional preferences in the spatial distribution of traffic accidents in Barcelona (Spain), during 2019, and in Medellin (Colombia), during 2016.