Are the absent always wrong? Dealing with zero values in urban scaling

Abstract

Both theoretical and empirical studies have shown the ability of scaling laws to reveal processes of emergence in urban systems. Nevertheless, a controversy about the robustness of results obtained with these models on empirical cases remains, regarding for instance the definition of the ‘city’ considered or the way the estimations are performed. Another source of bias is highlighted in this contribution, with respect to the non-ubiquitous character of some urban attributes (i.e. their partial absence from several cities of the system). The problem with the zero count for cities where these attributes are absent is that the technical necessities of usual estimation procedures make the analysis ignore them altogether even when they represent some valid information. This could seriously impact the results. A precise exploration of the effects of this arbitrary filtering is conducted here, and several solutions are proposed to overcome this limitation. In a case study about foreign investment towards French cities, we show that some erroneous conclusions about a hierarchical diffusion could be drawn when adopting the classical ordinary least squares approach. The framework we suggest specifies how it is possible to avoid misinterpretations deriving from the exclusion of zero values by using methods of analysis which deal with zero values specifically. The conclusion of a diffusion of foreign investment in the French urban system is then rejected.

Rural–urban scaling of age, mortality, crime and property reveals a loss of expected self-similar behaviour

“…A number of issues have been noted when fitting power laws to urban scaling data sets 22 and particularly when data sets have null values or zeros 23 . In the data considered here, this issue is occasionally severe.…”

“…Different age ranges clustered with different indicator classes. Young people(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34) clustered with crime. Older people (55 and above) clustered with mortality except for bone cancer.…”

An Urban Scaling Estimation Method in a Heterogeneity Variance Perspective

“…The universality of urban scaling has been questioned in recent studies [ 21 ]. It has been observed that the scaling exponent is sensitive to the definition of the city [ 13 ], the utilized database [ 22 ], and the regression method [ 23 ]. For example, the scaling of transportation-related CO2 emissions changes with the population results in different conclusions at different aggregation levels [ 7 ].…”

“…For example, the scaling of transportation-related CO2 emissions changes with the population results in different conclusions at different aggregation levels [ 7 ]. Opposite conclusions about the foreign investment in the French urban system can be reached using the traditional ordinary least squares (OLS) approach and the computing framework avoiding zero values proposed by Finance [ 23 ]. These situations call for more solid statistical support for the study of urban scaling laws.…”

Macro-level estimation of present and future seismic loss by modelling spatio-temporal dynamics of exposure

“…Urban growth dynamics are nonlinear, and their prediction is a highly challenging and complex task. Due to this complexity, several researchers (Bettencourt, 2007;Fragkias et al, 2017;Sarkar et al, 2018;Finance and Cottineau, 2019) For example, linear/logistic regressions can fail to capture non-linearity in spatial growth, as they are not capable of offering high modelling capabilities (Hu and Lo, 2007). Artificial neural networks have a black box nature, and sometimes create overcomplex structures which result in over-fitting (Almeida et al, 2008).…”