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Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics

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  • Luiz G A Alves
  • Haroldo V Ribeiro
  • Ervin K Lenzi
  • Renio S Mendes

Abstract

We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.

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  • Luiz G A Alves & Haroldo V Ribeiro & Ervin K Lenzi & Renio S Mendes, 2013. "Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    • Handle: RePEc:plo:pone00:0069580
    DOI: 10.1371/journal.pone.0069580
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    3. Alves, Luiz G.A. & Andrade, José S. & Hanley, Quentin S. & Ribeiro, Haroldo V., 2019. "The hidden traits of endemic illiteracy in cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 566-574.
    4. Hyeon-Woo Kang & Hang-Bong Kang, 2017. "Prediction of crime occurrence from multi-modal data using deep learning," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-19, April.
    5. Joao Meirelles & Fabiano L. Ribeiro & Gabriel Cury & Claudia R. Binder & Vinicius M. Netto, 2021. "More from Less? Environmental Rebound Effects of City Size," Sustainability, MDPI, vol. 13(7), pages 1-20, April.
    6. Joao Meirelles & Camilo Rodrigues Neto & Fernando Fagundes Ferreira & Fabiano Lemes Ribeiro & Claudia Rebeca Binder, 2018. "Evolution of urban scaling: Evidence from Brazil," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-15, October.
    7. Gudipudi, Ramana & Rybski, Diego & Lüdeke, Matthias K.B. & Zhou, Bin & Liu, Zhu & Kropp, Jürgen P., 2019. "The efficient, the intensive, and the productive: Insights from urban Kaya scaling," Applied Energy, Elsevier, vol. 236(C), pages 155-162.
    8. Jack Sutton & Golnaz Shahtahmassebi & Haroldo V Ribeiro & Quentin S Hanley, 2022. "Population density and spreading of COVID-19 in England and Wales," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-19, March.
    9. Luiz G A Alves & Renio S Mendes & Ervin K Lenzi & Haroldo V Ribeiro, 2015. "Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-17, September.
    10. Wang, Jia & Hu, Jun & Shen, Shifei & Zhuang, Jun & Ni, Shunjiang, 2020. "Crime risk analysis through big data algorithm with urban metrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    11. Cardoso, M. & Afonso, L.H.D. & Neli, R.R. & Souza, W.E., 2024. "Simplified model relating blank and null votes to voter turnout from Brazilian state elections results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).
    12. Diego Rybski & Dominik E Reusser & Anna-Lena Winz & Christina Fichtner & Till Sterzel & Jürgen P Kropp, 2017. "Cities as nuclei of sustainability?," Environment and Planning B, , vol. 44(3), pages 425-440, May.
    13. Yves Bettignies & Joao Meirelles & Gabriela Fernandez & Franziska Meinherz & Paul Hoekman & Philippe Bouillard & Aristide Athanassiadis, 2019. "The Scale-Dependent Behaviour of Cities: A Cross-Cities Multiscale Driver Analysis of Urban Energy Use," Sustainability, MDPI, vol. 11(12), pages 1-20, June.

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