Spatial interactions in urban scaling laws

Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling explicitly the effect of interactions between individuals at different locations. Parameters that describe the scaling law and the spatial interactions are inferred from data simultaneously, allowing for rigorous (Bayesian) model comparison and overcoming the problem of defining the boundaries of urban regions. Results in five different datasets show that including spatial interactions typically leads to better models and a change in the exponent of the scaling law.