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Modeling the Influence of Places on Crime Risk Through a Non-Linear Effects Model: a Comparison with Risk Terrain Modeling

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Abstract

Analyzing how the proximity to certain features or particular places in a city increases or decreases crime risk across space is a fundamental issue in quantitative criminology from both explanatory and predictive perspectives. Regarding the latter, the detection of high-risk cells is of special interest for practical reasons. There are several statistical modeling approaches that can be implemented in order to fulfil these two main objectives. The purpose of this study is to compare risk terrain modeling (RTM), a method widely used among quantitative criminologists, with a non-linear effects model that considers a non-linear function of distances to the selected places. To this end, a dataset containing crime events recorded in Valencia (Spain) along four years was used to perform the comparison. Several socio-demographic covariates and a selection of places in the city were considered for modeling crime counts with both the RTM and the non-linear approaches. The two modeling techniques were moderately coherent with regard to detecting certain types of places as responsible of higher (or lower) crime rates, but several differences arose. Furthermore, the non-linear model was more accurate than RTM to predict future crime occurrences for each of the three crime types that were considered for the analysis. In conclusion, the possibility of modeling the effect of a place on crime risk through non-linear functions appears as one competitive alternative or at least complement to RTM that may deserve further consideration.

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References

  • Alves, L.G., Lenzi, E., Mendes, R., & Ribeiro, H. (2015). Spatial correlations, clustering and percolation-like transitions in homicide crimes. EPL (Europhysics Letters), 111(1), 18002.

    Article  Google Scholar 

  • Andresen, M.A., & Hodgkinson, T (2018). Predicting property crime risk: An application of risk terrain modeling in Vancouver, Canada. European Journal on Criminal Policy and Research, 24(4), 373–392.

    Article  Google Scholar 

  • Ayyad, C., Mateu, J., & Tamayo-Uria, I. (2018). Non-linear spatial modeling of rat sightings in relation to urban multi-source foci. Journal of Infection and Public Health, 11(5), 667–676.

    Article  Google Scholar 

  • Baddeley, A., Rubak, E., & Turner, R. (2015). Spatial point patterns: methodology and applications with R. Boca Raton: CRC Press.

    Book  Google Scholar 

  • Besag, J., York, J., & Mollié, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43(1), 1–20.

    Article  Google Scholar 

  • Bivand, R., & Piras, G (2015). Comparing implementations of estimation methods for spatial econometrics. Journal of Statistical Software, 63(18), 1–36.

    Article  Google Scholar 

  • Block, R., & Block, C. (2005). Spatial and temporal analysis of crime (STAC). In N. Levine (Ed.) CrimeStat III: a spatial statistics program for the analysis of crime incident locations (version 3.0). Houston: Ned Levine & Associates. Washington, DC: The National Institute of Justice (pp. 7.1–7.18).

  • Brantingham, P., & Brantingham, P. (1995). Criminality of place. European Journal on Criminal Policy and Research, 3(3), 5–26.

    Article  Google Scholar 

  • Briz-Redón, Á., Martínez-ruiz, F., & Montes, F. (2019). Estimating the occurrence of traffic accidents near school locations: a case study from Valencia (Spain) including several approaches. Accident Analysis & Prevention, 132, 105237.

    Article  Google Scholar 

  • Buonanno, P., & Montolio, D. (2008). Identifying the socio-economic and demographic determinants of crime across Spanish provinces. International Review of Law and Economics, 28(2), 89–97.

    Article  Google Scholar 

  • Bürkner, P.-C. (2017). Brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1–28.

    Article  Google Scholar 

  • Caplan, J.M., & Kennedy, L.W. (2013). Risk terrain modeling diagnostics utility (version 1.0) Newark, NJ: Rutgers Center on Public Security.

  • Caplan, J.M., Kennedy, L.W., & Miller, J. (2011). Risk terrain modeling: Brokering criminological theory and GIS methods for crime forecasting. Justice Quarterly, 28(2), 360–381.

    Article  Google Scholar 

  • Caplan, J.M., Kennedy, L.W., Piza, E.L., & Barnum, J.D. (2020). Using vulnerability and exposure to improve robbery prediction and target area selection. Applied Spatial Analysis and Policy, 13, 113–136.

    Article  Google Scholar 

  • Chainey, S., Tompson, L., & Uhlig, S. (2008). The utility of hotspot mapping for predicting spatial patterns of crime. Security Journal, 21(1-2), 4–28.

    Article  Google Scholar 

  • Connealy, N.T., & Piza, E.L. (2019). Risk factor and high-risk place variations across different robbery targets in Denver, Colorado. Journal of Criminal Justice, 60, 47–56.

    Article  Google Scholar 

  • Daley, D., Bachmann, M., Bachmann, B.A., Pedigo, C., Bui, M.-T., & Coffman, J. (2016). Risk terrain modeling predicts child maltreatment. Child Abuse & Neglect, 62, 29–38.

    Article  Google Scholar 

  • Diggle, P., Morris, S., Elliott, P., & Shaddick, G. (1997). Regression modelling of disease risk in relation to point sources. Journal of the Royal Statistical Society: Series A (Statistics in Society), 160(3), 491–505.

    Article  Google Scholar 

  • D’Orsogna, M.R., & Perc, M (2015). Statistical physics of crime: A review. Physics of Life Reviews, 12, 1–21.

    Article  Google Scholar 

  • Drawve, G. (2016). A metric comparison of predictive hot spot techniques and RTM. Justice Quarterly, 33(3), 369–397.

    Article  Google Scholar 

  • Drawve, G., Moak, S.C., & Berthelot, E.R. (2016). Predictability of gun crimes: a comparison of hot spot and risk terrain modelling techniques. Policing and Society, 26(3), 312–331.

    Article  Google Scholar 

  • Dugato, M., Favarin, S., & Bosisio, A. (2018). Isolating target and neighbourhood vulnerabilities in crime forecasting. European Journal on Criminal Policy and Research, 24(4), 393–415.

    Article  Google Scholar 

  • Entorf, H., & Spengler, H. (2000). Socioeconomic and demographic factors of crime in Germany: Evidence from panel data of the German states. International Review of Law and Economics, 20(1), 75–106.

    Article  Google Scholar 

  • Favarin, S. (2018). This must be the place (to commit a crime). Testing the law of crime concentration in Milan, Italy. European Journal of Criminology, 15(6), 702–729.

    Article  Google Scholar 

  • Garnier, S., Caplan, J.M., & Kennedy, L.W. (2018). Predicting dynamical crime distribution from environmental and social influences. Frontiers in Applied Mathematics and Statistics, 4, 13.

    Article  Google Scholar 

  • Gaviria, A., & Pagés, C. (2002). Patterns of crime victimization in Latin American cities. Journal of Development Economics, 67(1), 181–203.

    Article  Google Scholar 

  • Giménez-Santana, A., Medina-Sarmiento, J.E., & Miró-Llinares, F. (2018). Risk terrain modeling for road safety: Identifying crash-related environmental factors in the province of cádiz, Spain. European Journal on Criminal Policy and Research, 24(4), 451–467.

    Article  Google Scholar 

  • Goeman, J.J. (2010). L1 penalized estimation in the Cox proportional hazards model. Biometrical Journal, 52(1), 70–84.

    Google Scholar 

  • He, Z., Xie, Z., Wu, L., & Tao, L. (2020). Discovering significant situational profiles of crime occurrence by modeling complex spatial interactions. Spatial Statistics, 100463.

  • Heffner, J. (2013). Statistics of the RTMDx utility. Risk Terrain Modeling Diagnostics Utility User Manual, 35–39.

  • Hijmans, R.J. (2019). Raster: Geographic Data Analysis and Modeling. R package version 3.0-7.

  • Hunt, J.M. (2016). Do crime hot spots move? Exploring the effects of the modifiable areal unit problem and modifiable temporal unit problem on crime hot spot stability. PhD thesis, American University.

  • Johnson, S.D., Bowers, K.J., Birks, D.J., & Pease, K. (2009). Predictive mapping of crime by ProMap: accuracy, units of analysis, and the environmental backcloth. In Putting crime in its place (pp. 171–198). Springer.

  • Kennedy, L.W., & Dugato, M. (2018). Forecasting crime and understanding its causes. Applying risk terrain modeling worldwide. European Journal on Criminal Policy and Research, 24(4), 345–350.

    Article  Google Scholar 

  • Kennedy, L.W., Caplan, J.M., Piza, E.L., & Buccine-Schraeder, H. (2016). Vulnerability and exposure to crime: Applying risk terrain modeling to the study of assault in Chicago. Applied Spatial Analysis and Policy, 9(4), 529–548.

    Article  Google Scholar 

  • Kinney, J.B., Brantingham, P.L., Wuschke, K., Kirk, M.G., & Brantingham, P.J. (2008). Crime attractors, generators and detractors: Land use and urban crime opportunities. Built Environment, 34(1), 62–74.

    Article  Google Scholar 

  • Levine, N. (2008). The “Hottest” part of a hotspot: comments on “The utility of hotspot mapping for predicting spatial patterns of crime”. Security Journal, 21(4), 295–302.

    Article  Google Scholar 

  • Lindgren, F., Rue, H., & et al. (2015). Bayesian spatial modelling with r-INLA. Journal of Statistical Software, 63(19), 1–25.

    Article  Google Scholar 

  • Mohler, G.O., Short, M.B., Brantingham, P.J., Schoenberg, F.P., & Tita, G.E. (2011). Self-exciting point process modeling of crime. Journal of the American Statistical Association, 106(493), 100–108.

    Article  Google Scholar 

  • Moran, P.A. (1950a). Notes on continuous stochastic phenomena. Biometrika, 37(1/2), 17–23.

    Article  Google Scholar 

  • Moran, P.A. (1950b). A test for the serial independence of residuals. Biometrika, 37(1/2), 178–181.

    Article  Google Scholar 

  • Neath, A.A., & Cavanaugh, J.E. (2012). The Bayesian information criterion: background, derivation, and applications. Wiley Interdisciplinary Reviews: Computational Statistics, 4(2), 199–203.

    Article  Google Scholar 

  • Nobles, M.R., Ward, J.T., & Tillyer, R. (2016). The impact of neighborhood context on spatiotemporal patterns of burglary. Journal of Research in Crime and Delinquency, 53(5), 711–740.

    Article  Google Scholar 

  • Ohyama, T., & Amemiya, M. (2018). Applying crime prediction techniques to Japan: a comparison between risk terrain modeling and other methods. European Journal on Criminal Policy and Research, 24(4), 469–487.

    Article  Google Scholar 

  • Onat, I. (2019). An analysis of spatial correlates of terrorism using risk terrain modeling. Terrorism and Political Violence, 31(2), 277–298.

    Article  Google Scholar 

  • OpenStreetMap contributors. (2019). Planet dump retrieved from https://planet.osm.org. https://www.openstreetmap.org.

  • R Core Team. (2019). R language definition Vienna. Austria, R foundation for statistical computing.

  • Ramis, R., Diggle, P., Cambra, K., & López-Abente, G. (2011). Prostate cancer and industrial pollution: Risk around putative focus in a multi-source scenario. Environment International, 37(3), 577–585.

    Article  Google Scholar 

  • Reinhart, A., & Greenhouse, J. (2018). Self-exciting point processes with spatial covariates: modelling the dynamics of crime. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67(5), 1305–1329.

    Google Scholar 

  • Rigby, R.A., & Stasinopoulos, D.M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3), 507–554.

    Google Scholar 

  • Rodrigues, A., Diggle, P., & Assuncao, R. (2010). Semiparametric approach to point source modelling in epidemiology and criminology. Journal of the Royal Statistical Society: Series C (Applied Statistics), 59(3), 533–542.

    Google Scholar 

  • Rosser, G., & Cheng, T. (2019). Improving the robustness and accuracy of crime prediction with the self-exciting point process through isotropic triggering. Applied Spatial Analysis and Policy, 12(1), 5–25.

    Article  Google Scholar 

  • Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2), 319–392.

    Article  Google Scholar 

  • Rummens, A., & Hardyns, W. (2020). Comparison of near-repeat, machine learning and risk terrain modeling for making spatiotemporal predictions of crime. Applied Spatial Analysis and Policy, 1–19.

  • Sampson, R.J., Raudenbush, S.W., & Earls, F. (1997). Neighborhoods and violent crime: a multilevel study of collective efficacy. Science, 277 (5328), 918–924.

    Article  Google Scholar 

  • Short, M.B., Brantingham, P.J., Bertozzi, A.L., & Tita, G.E. (2010). Dissipation and displacement of hotspots in reaction-diffusion models of crime. Proceedings of the National Academy of Sciences, 107(9), 3961–3965.

    Article  Google Scholar 

  • Summers, L., & Caballero, M. (2017). Spatial conjunctive analysis of (crime) case configurations: Using Monte Carlo methods for significance testing. Applied Geography, 84, 55–63.

    Article  Google Scholar 

  • Sypion-Dutkowska, N., & Leitner, M. (2017). Land use influencing the spatial distribution of urban crime: A case study of Szczecin, Poland. ISPRS International Journal of Geo-Information, 6(3), 74.

    Article  Google Scholar 

  • Valente, R. (2019). Spatial and temporal patterns of violent crime in a Brazilian state capital: A quantitative analysis focusing on micro places and small units of time. Applied Geography, 103, 90–97.

    Article  Google Scholar 

  • Weisburd, D. (2015). The law of crime concentration and the criminology of place. Criminology, 53(2), 133–157.

    Article  Google Scholar 

  • Wheeler, A.P., & Steenbeek, W. (2020). Mapping the risk terrain for crime using machine learning. Journal of Quantitative Criminology, 1–36.

  • Wickham, H. (2016). Ggplot2: Elegant graphics for data analysis. New York: Springer.

    Book  Google Scholar 

  • Yoo, Y., & Wheeler, A.P. (2019). Using risk terrain modeling to predict homeless related crime in Los Angeles, California. Applied Geography, 109, 102039.

    Article  Google Scholar 

  • Zhuang, J., & Mateu, J. (2019). A semiparametric spatiotemporal Hawkes-type point process model with periodic background for crime data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 182(3), 919–942.

    Article  Google Scholar 

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Briz-Redón, Á., Mateu, J. & Montes, F. Modeling the Influence of Places on Crime Risk Through a Non-Linear Effects Model: a Comparison with Risk Terrain Modeling. Appl. Spatial Analysis 15, 507–527 (2022). https://doi.org/10.1007/s12061-021-09410-6

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