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PLOS ONE  2013 

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

DOI: 10.1371/journal.pone.0069580

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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.


[1]  Amaral LAN, Ottino JM (2004) Augmenting the framework for the study of complex systems. The European Physical Journal B 38: 147–162.
[2]  Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Reviews of Modern Physics 81: 591–646.
[3]  Conte R, Gilbert N, Bonelli G, Cioff-Revilla C, Deffuant G, et al. (2012) Manifesto of computa-tional social science. The European Physical Journal Special Topics 214: 325–346.
[4]  Mantovani MC, Ribeiro HV, Moro MV, Picoli Jr S, Mendes RS (2011) Scaling laws and univer-sality in the choice of election candidates. Europhysics Letters 96: 48001.
[5]  Chatterjee A, Mitrovi? M, Fortunato S (2013) Universality in voting behavior: an empirical analysis. Scientific Reports 3: 1049.
[6]  Rozenfeld HD, Rybski D, Andrade Jr JS, Batty M, Stanley HE, et al. (2008) Laws of population growth. Proceedings of the National Academy of Sciences U. S. A. 105: 1870218707.
[7]  Rybski D, Buldyrev SV, Havlin S, Liljeros F, Makse HA (2009) Scaling laws of human interaction activity. Proceedings of the National Academy of Sciences U. S. A. 106: 1264012645.
[8]  Stanley MHR, Amaral LAN, Buldyrev SV, Havlin S, Leschhorn H, et al. (1996) Scaling behaviour in the growth of companies. Nature 379: 804–806.
[9]  Mantegna RN, Stanley HE (2007) Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge: Cambridge University Press.
[10]  Peron TKD, Costa LF, Rodrigues FA (2012) The structure and resilience of financial market networks. Chaos 22: 013117.
[11]  Wichmann S (2008) The emerging field of language dynamics. Language and Linguistics Compass 2: 442–455.
[12]  Petersen AM, Tenenbaum J, Havlin S, Stanley HE (2012) Statistical laws governing fluctuations in word use from word birth to word death, Scientific Reports. 2: 313.
[13]  Amancio DR, Oliveira Jr ON, Costa LF (2012) Unveiling the relationship between complex net-works metrics and word senses. Europhysics Letters 98: 18002.
[14]  Kates RW, Parris TM (2003) Long-term trends and a sustainability transition. Proceedings of the National Academy of Sciences U. S. A. 100: 8062–8067.
[15]  Gordon MB, Iglesias JR, Semeshenko V, Nadal JP (2009) Crime and punishment: the economic burden of impunity. The European Physical Journal B 68: 133–144.
[16]  Iglesias JR, Semeshenko V, Scheneider EM, Gordon MB (2012) Crime and punishment: does it pay to punish? Physica A 391: 3942–3950.
[17]  Crane P, Kinzig A (2005) Nature in the metropolis. Science 308: 1225.
[18]  World Resources Institute website. Available: Accessed 2013 Feb 1.
[19]  Becker GS (1968) Crime and punishment: an economic approach. Journal of Political Economy 76: 169–217.
[20]  Ehrlich I (1975) The deterrent effect of capital punishment: a question of life and death. The American Economic Review 65: 397–417.
[21]  Ehrlich I (1996) Crime, punishment, and the market for offenses. Journal of Economic Perspectives 10: 43–67.
[22]  Glaeser EL, Sacerdote B, Scheinkman JA (1996) Crime and social interactions. Quarterly Journal of Economics 111: 507–548.
[23]  Glaeser EL, Sacerdote B (1999) Why is there more crime in cities? Journal of Political Economy 107: S225–S258.
[24]  Blau JR, Blau PM (1982) The cost of inequality: metropolitan structure and violent crime. American Sociological Review 47: 114–129.
[25]  Bailey W (1984) Poverty, inequality and homicide rates. Criminology 22: 531–550.
[26]  Levitt SD (1997) Using electoral cycles in police hiring to estimate the effect of police on crime. The American Economic Review 87: 270–290.
[27]  Kennedy BP, Kawachi I, Prothrow-Stith D, Lochner K, Gupta V (1998) Social capital, income inequality, and firearm violent crime. Social Science & Medicine. 47: 7–17.
[28]  Kelly M (2000) Inequality and crime. The Review of Economics and Statistics 82: 530–539.
[29]  Levitt SD (2001) Alternative strategies for identifying the link between unemployment and crime. Journal of Quantitative Criminology 17: 377–390.
[30]  Hojman DE (2002) Explaining crime in Buenos Aires: the roles of inequality, unemployment, and structural change. Bulletin of Latin American Research 21: 121–128.
[31]  Hojman DE (2004) Inequality, unemployment and crime in Latin American cities. Crime, Law & Social Change 41: 33–51.
[32]  Sachsida A, Mendon?a MJC, Loureiro PRA, Gutierrez MBS (2010) Inequality and criminality revisited: further evidence from Brazil. Empirical Economics 39: 93–109.
[33]  Poveda AC (2012) Violence and economic development in Colombian cities: a dynamic panel data analysis. Journal of International Development 24: 809–827.
[34]  Gordon MB (2010) A random walk in the literature on criminality: a partial and critical view on some statistical analysis and modelling approaches. European Journal of Applied Mathematics 21: 283–306.
[35]  Bettencourt LMA, Lobo J, Helbing D, Kuhnert C, West GB (2007) Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences U. S. A. 104: 7301–7306.
[36]  Bettencourt LMA, Lobo J, West GB (2008) Why are large cities faster? Universal scaling and self-similarity in urban organizations and dynamics. The European Physical Journal B 63: 285–293.
[37]  Bettencourt LMA, West GB (2010) A unified theory of urban living. Nature 467: 912–913.
[38]  Bettencourt LMA, Lobo J, Strumsky D, West GB (2010) Urban scaling and its deviations: re-vealing the structure of wealth, innovation and crime across cities. PLoS ONE 5: e13541.
[39]  Gomez-Lievano A, Youn H, Bettencourt LMA (2012) The statistics of urban scaling and their connections to Zipf's law. PLoS ONE 7: e40393.
[40]  Alves LGA, Ribeiro HV, Mendes RS (2013) Scaling laws in the dynamics of crime growth rate. Physica A: 10.1016/j.physa.2013.02.002.
[41]  Podobnik B, Horvatic D, Kenett DY, Stanley HE (2012) The competitiveness versus the wealth of a country. Scientific Reports 2: 678.
[42]  Brazil's Public healthcare System (SUS), Department of Data Processing (DATASUS). Available: Accessed 2013 Feb 1.
[43]  Angel S, Sheppard CS, Civco DL, Buckley P, Chabaeva A, et al.. (2005) The Dynamics of Global Urban Expansion. Washington DC: World Bank.
[44]  Efron B, Tibshirani R (1993) An Introduction to the Bootstrap. New York: Chapman & Hall.
[45]  Corder GW, Foreman DI (2009), Nonparametric Statistics for non-Statisticians: a Step-by-Step Approach. New Jersey: Wiley.
[46]  Davidson R, MacKinnon JG (1993) Estimation and Inference in Econometrics. New York: Oxford University Press.
[47]  Preacher KJ, Hayes AF (2008) Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods 40: 879–891.


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