Sampling the City: Revisiting the Neighborhood Effect Averaging Problem through the Interplay between Mobility and Socio-spatial Contexts

The neighborhood effect averaging problem (NEAP) describes mobility-based measurements (MBMs) of environmental exposure converging toward a regional average versus residence-based measurements (RBMs). Although widely documented, the underlying statistical mechanisms remain unclear. We propose a novel framework conceptualizing MBMs as repeated microenvironmental samples through Markov process with means that converge per the mean ergodic theorem (MET) and distributions that approach normality per the Lindeberg–Feller central limit theorem (LCLT), with real-world spatiotemporal autocorrelation and heterogeneity modulating this convergence. Analyzing trajectories of 732 Hong Kong residents across nine urban services using multilevel mixed-effects models, we examined MBM central tendency (coefficient of variation) and normality (Shapiro–Wilk W) as functions of mobility patterns, service distribution, and initial RBM distributions. The results confirm that greater exposure diversity, driven by higher mobility entropy and dispersed time-available services, intensifies NEAP, supporting our MET–LCLT mechanism. Crucially, a three-way interaction emerged: Clustered services constrain mobility’s averaging effect, perpetuating residential disparities, whereas well-distributed, time-available services enable mobility to overcome segregation barriers. These findings demonstrate that the NEAP arises from the interplay of individual movement, social (segregation) context, and spatial (environmental factor distribution) contexts, highlighting exposure diversity as the core mechanism and providing crucial insights for both mobility-based research and equity-oriented urban planning.