An Urban Scaling Estimation Method in a Heterogeneity Variance Perspective.

Wenjia Wu,Peichao Gao,Hongrui Zhao,Qifan Tan

doi:10.3390/e21040337

Wenjia Wu, Peichao Gao + Show 2 more

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https://doi.org/10.3390/e21040337

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Abstract

Urban scaling laws describe powerful universalities of the scaling relationships between urban attributes and the city size across different countries and times. There are still challenges in precise statistical estimation of the scaling exponent; the properties of variance require further study. In this paper, a statistical regression method based on the maximum likelihood estimation considering the lower bound constraints and the heterogeneous variance of error structure, termed as CHVR, is proposed for urban scaling estimation. In the CHVR method, the heterogeneous properties of variance are explored and modeled in the form of a power-of-the-mean variance model. The maximum likelihood fitting method is supplemented to satisfy the lower bound constraints in empirical data. The CHVR method has been applied to estimating the scaling exponents of six urban attributes covering three scaling regimes in China and compared with two traditional methods. Method evaluations based on three different criteria validate that compared with both classical methods, the CHVR method is more effective and robust. Moreover, a statistical test and long-term variations of the parameter in the variance function demonstrate that the proposed heterogeneous variance function can not only describe the heterogeneity in empirical data adequately but also provide more meaningful urban information. Therefore, the CHVR method shows great potential to provide a valuable tool for effective urban scaling studies across the world and be applied to scaling law estimation in other complex systems in the future.

Highlights

Urban scaling law, as one of the most significant regulations in urban science [1], has drawn much attention for providing powerful universalities of the variations of urban attributes with city size [2,3,4,5,6]
Three comparing methods are applied to estimating the urban scaling exponents β of six urban attributes in China, including Gross Domestic Product (GDP), total income, household water consumption, household electricity consumption, road surface area, and built-up area
The summary of the urban scaling exponents, the corresponding standard errors, and method evaluations for these six urban attributes, using the demographic data with high accuracy provided by the census, are demonstrated in Table 1, which were derived from the CHVR method and the traditional methods in China in 2010

Summary

Introduction

As one of the most significant regulations in urban science [1], has drawn much attention for providing powerful universalities of the variations of urban attributes with city size [2,3,4,5,6]. The urban scaling law state that the relationship between urban attributes and population is well-described by the power-law scaling of the form y = ax b [2], which was inspired by the allometric scaling in biology [7,8]. This law provides a systematic and quantitative framework for urban sustainable development [2,9]. Urban scaling laws have been widely applied to analyzing urban hierarchy [17], infrastructure strategies [18], urban designs [19], and environmental strategies [20]

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