Adjusting for Social Groups in Spatial Point Process Models for Waiting Pedestrian Configurations

Abstract

The spatial distribution of waiting pedestrians has two primary drivers: environmental preference and interaction with other pedestrians. Spatial point processes naturally capture both spatial heterogeneity and repulsive interaction. In previous work (Sickert Karam et al., arXiv:2606.14532, 2026), we proposed a Gibbs model with inhomogeneous intensity and a modified Diggle-Gates-Stibbard interaction function, which reproduces many phenomena in replicated patterns of pedestrians waiting at a train station. Its single interaction function acts as an effective interaction, averaging over behavioral regimes such as interactions within social groups and among strangers. In this article, we show how groups affect distance-based summary statistics and take first steps towards accounting for them. We detect groups from pairwise distances and contact durations, replace each group by a ``macro-pedestrian'' at its average position, and refit the model. This yields a larger interaction range and better agreement in nearest-neighbor statistics than the original model, although the two fits concern different datasets and centroid-based distances likely overstate repulsion. This first attempt thus resolves some discrepancies but falls short of a fully adequate solution, opening avenues for further research.