A spatio-temporal K-function for point processes near spatial linear networks
Conference
66th ISI World Statistics Congress
Format: WSC 2027: IPS Abstract
Keywords: criminology, k-functions, spatial statistics
Abstract
The analysis of spatial point patterns near linear networks has important applications in criminology, where road networks may influence the distribution of criminal events occurring in their vicinity. While recent methodological developments have introduced approaches for quantifying the spatial relationship between point processes and nearby linear networks, the temporal dimension of these relationships remains largely unexplored. This study extends the projection-based spatial K-function, K_snap (r), to a spatio-temporal framework, introducing K_snap (u,v), to investigate clustering across spatial distances and temporal lags. The methodology is evaluated through simulation studies considering different degrees of spatial attraction to the network and temporal clustering, both independently and jointly. An application to crime data from Khayelitsha, South Africa, illustrates the potential of the proposed approach to provide new insights into the spatial and temporal dynamics of crime in relation to road networks.