Assessing local differences between the spatio-temporal second-order structure of two point patterns occurring on the same linear network

We introduce Local Indicators of Spatio-Temporal Association (LISTA) functions on linear networks and use them to build a statistical test for local second-order structure. This allows to identify differences in the spatio-temporal clustering behaviour of two point patterns, a point pattern of interest and a background one, both occurring on the same linear network. We assess the performance of the testing procedure for local second-order structure through simulation studies under a variety of scenarios that also account for different generating point processes. We show that the proposed local test is able to correctly identify the spatio-temporal difference in the local second-order structure of two point patterns occurring on the same linear network, finding that the power of the test increases as the number of points and the clustered structure of the point pattern of interest increase. We finally use the proposed methodology for the analysis of two traffic-related problems.