Removing spatial autocorrelation in urban scaling analysis

Abstract

Analyzing urban scaling relations can help predict the future development of cities and derive scale adjusted metropolitan indicators (SAMIs) to characterize the city's performance. However, existing studies treat cities as individual systems but ignore the spatial autocorrelation between them. Here, we propose a framework that incorporates the influence of spatial autocorrelation into urban scaling analysis. We use an eigenvector spatial filtering (ESF) model to capture the spatial effect when modeling the scaling relations of cities. Based on the residuals of the ESF model, we propose a new set of urban indicators—spatial and scale adjusted metropolitan indicators (SSAMIs)—to address the effect of spatial autocorrelation on SAMIs. The results of our experiments in China and the United States show that compared with non-spatial models, the ESF model could generate better-fitted results when estimating the scaling relations. The results also reveal that using SSAMIs could avoid overestimations of cities in developed regions and underestimations of cities in less developed regions. This study proposes a novel attempt to deal with the spatial autocorrelation effect in urban scaling analysis. It provides insights for understanding the urban scaling law and enhanced indicators for the evaluation of cities.