6533b7dafe1ef96bd126dc76

RESEARCH PRODUCT

Local indicators of spatio-temporal association on linear networks

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In this work, we extend the Local Indicators of Spatio-Temporal Association (LISTA) functions (Siino et al. 2018) to the non-Euclidean space of linear networks. We introduce the local version of some inhomogeneous second-order statistics for spatio-temporal point processes on linear networks (Morandi and Mateu, 2019), namely the K-function and the pair correlation function. Following the work of Adelfio et al. (2019) for the Euclidean case, we employ the proposed LISTA functions to assess the goodness-of-fit of different spatio-temporal models fitted to point patterns occurring on linear networks. Indeed, the peculiar lack of homogeneity in a network discourages the usage of traditional spatial and spatio-temporal methods based on stationary processes. Therefore, the weighted second-order statistics are appropriate diagnostic tools since they directly apply to data without assuming homogeneity. We provide simulation studies, by generating both inhomogeneous and self-exiting spatio-temporal point processes on networks, and by carrying out diagnostics on different fitted intensities. By comparing the values of the LISTA functions and their theoretical values, we show that the LISTA can correctly identify the true intensity when this is constrained on a network.