Spatial patterns and processes in a longitudinal framework

This article explores the conceptual equivalence between hazard models applied to both temporal data and distance data by focusing on the "at-risk" concept, which is central to longitudinal models but has not received sufficient attention in the application of hazard models in spatial settings. A proper conceptualization in a spatial (distance) setting is based on distant-dependent Markovian transition probabilities describing the risk of switching between states. Such a conceptualization is possible for continuous spatial processes, as well as for point-generating processes leading to spatial point patterns. Hazard models for a series of scenarios simulating various point generation trajectories are compared. This process-oriented perspective is further augmented by explicitly accounting for temporal dimensions (speed) of point-generating processes.