Investigating clustering and violence interruption in gang-related violent crime data using spatial-temporal point processes with covariates. (English) Zbl 1506.65014
Summary: Reported gang-related violent crimes in Los Angeles, California, from 1/1/14 to 12/31/17 are modeled using spatial-temporal marked Hawkes point processes with covariates. We propose an algorithm to estimate the spatial-temporally varying background rate nonparametrically as a function of demographic covariates. Kernel smoothing and generalized additive models are used in an attempt to model the background rate as closely as possible in an effort to differentiate inhomogeneity in the background rate from causal clustering or triggering of events. The models are fit to data from 2014 to 2016 and evaluated using data from 2017, based on log-likelihood and superthinned residuals. The impact of nonrandomized violence interruption performed by The City of Los Angeles Mayor’s Office of Gang Reduction Youth Development (GRYD) Incident Response (IR) Program is assessed by comparing the triggering associated with GRYD IR Program events to the triggering associated with sub-sampled non-GRYD events selected to have a similar spatial-temporal distribution. The results suggest that GRYD IR Program violence interruption yields a reduction of approximately 18.3% in the retaliation rate in locations more than 130 m from the original reported crimes, and a reduction of 14.2% in retaliations within 130 m.
MSC:
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
| 91D99 | Mathematical sociology (including anthropology) |
| 62F10 | Point estimation |
Software:
gamReferences:
| [1] | Anderson, E., Code of the Street: Decency Violence and the Moral Life of the Inner City (1999), New York: Norton and Company, New York |
| [2] | Balderama, E.; Schoenberg, F. P.; Murray, E.; Rundel, P. W., “Application of Branching Point Process Models to the Study of Invasive Red Banana Plants in Costa Rica, Journal of the American Statistical Association, 107, 467-476 (2012) · Zbl 1261.62103 · doi:10.1080/01621459.2011.641402 |
| [3] | Barton, M. S.; Valasik, M. A.; Brault, E.; Tita, G. E., “Gentefication” in The Barrio: Examining the Relationship Between Gentrification and Homicide in East Los Angeles, Crime & Delinquency (2019) · doi:10.1177/0011128719860835 |
| [4] | Bauwens, L.; Hautsch, N., Modelling Financial High Frequency Data Using Point Processes, 953-979) (2009), Berlin: Springer Berlin Heidelberg, Berlin · Zbl 1178.91218 |
| [5] | Bichler, G.; Norris, A.; Dmello, J. R.; Randle, J., “The Impact of Civil Gang Injunctions on Networked Violence Between the Bloods and the Crips, Crime and Delinquency, 65, 875-915 (2019) · doi:10.1177/0011128717739607 |
| [6] | Bjerregaard, B.; Lizotte, A. J., “Gun Ownership and Gang Membership, The Journal of Criminal Law and Criminology, 86, 37-58 (1995) · doi:10.2307/1143999 |
| [7] | Brantingham, P. J.; Tita, G. E.; Short, M. B.; Reid, S. E., “The Ecology of Gang Territorial Boundaries, Criminology, 50, 851-885 (2012) · doi:10.1111/j.1745-9125.2012.00281.x |
| [8] | Brantingham, P. J.; Valasik, M.; Mohler, G., “Does Predictive Policing Lead to Biased Arrests? Results From a Randomized Controlled Trial, Statistics and Public Policy, 5, 1-8 (2018) · doi:10.1080/2330443X.2018.1438940 |
| [9] | Brantingham, P. J.; Valasik, M.; Tita, G. E., “Competitive Dominance, Gang Size and the Directionality of Gang Violence, Crime Science, 8, 7 (2019) · doi:10.1186/s40163-019-0102-3 |
| [10] | Bray, A.; Schoenberg, F. P., “Assessment of Point Process Models for Earthquake Forecasting, Statistical Science, 28, 4, 510-520 (2013) · Zbl 1331.86016 · doi:10.1214/13-STS440 |
| [11] | Broyden, C. G., “The Convergence of a Class of Double-rank Minimization Algorithms, Journal of the Institute of Mathematics and Its Applications, 6, 76-90 (1970) · Zbl 0223.65023 · doi:10.1093/imamat/6.1.76 |
| [12] | Cespedes, G.; Herz, D., The City of Los Angeles Mayor’s Office of Gang Reduction and Youth Development (GRYD) Comprehensive Strategy (2011), Los Angeles, CA: Mayor’s Office of Gang Reduction and Youth Development, Los Angeles, CA |
| [13] | Clements, R. A.; Schoenberg, F. P.; Veen, A., Evaluation of Space-time Point Process Models Using Super-thinning, Environmetrics, 23, 606-616 · doi:10.1002/env.2168 |
| [14] | Curry, G. D.; Spergel, I. A., “Gang Homicide, Delinquency, and Community, Criminology, 26, 381-406 (1988) · doi:10.1111/j.1745-9125.1988.tb00847.x |
| [15] | Daley, D.; Vere-Jones, D., An Introduction to the Theory of Point Processes (2003), New York: Springer, New York · Zbl 1026.60061 |
| [16] | Daly, M.; Wilson, M. (1988), Homicide. New York: Aldine de Gruyter, Homicide. New York |
| [17] | Decker, S. H., “Collective and Normative Features of Gang Violence, Justice Quaterly, 13, 243-264 (1996) · doi:10.1080/07418829600092931 |
| [18] | Diggle, P. J., Statistical Analysis of Spatial and Spatio-temporal Point Patterns (2014), Boca Raton, FL: CRC Press, Boca Raton, FL · Zbl 1435.62004 |
| [19] | Esbensen, F.-A.; Huizinga, D.; Weiher, A. W., “Gang and Non-Gang Youth: Differences in Explanatory Factors, Journal of Contemporary Criminal Justice, 9, 2, 94-116 (1993) · doi:10.1177/104398629300900203 |
| [20] | Fox, E. W.; Coronges, K.; Schoenberg, F. P.; Short, M. B.; Bertozzi, A. L., “Modeling e-mail Networks and Inferring Leadership Using Self-exciting Point Processes, Journal of the American Statistical Association, 111, 1-21 (2016) · doi:10.1080/01621459.2015.1135802 |
| [21] | Gravel, J.; Bouchard, M.; Descormiers, K.; Wong, J. S.; Morselli, C., “Keeping Promises: A Systematic Review and a New Classification of Gang Control Strategies, Journal of Criminal Justice, 41, 228-242 (2013) · doi:10.1016/j.jcrimjus.2013.05.005 |
| [22] | Green, B.; Horel, T.; Papachristos, A. V., “Modeling Contagion Through Social Networks to Explain and Predict Gunshot Violence in Chicago, 2006 to 2014, JAMA Internal Medicine, 177, 326-333 (2017) · doi:10.1001/jamainternmed.2016.8245 |
| [23] | Harte, D. S., “Bias in Fitting the ETAS Model: A Case Study Based on New Zealand Seismicity, Geophysical Journal International, 192, 390-412 (2013) · doi:10.1093/gji/ggs026 |
| [24] | Hastie, T. (2018), gam: Generalized Additive Models, R package version 1.16. |
| [25] | Heckman, J. J., “Identifying the Hand of Past: Distinguishing State Dependence From Heterogeneity, American Economic Review, 81, 75-79 (1991) |
| [26] | Howell, J. C., Gangs in America’s Communities (2011), Thousand Oaks, CA: Sage Publications, Thousand Oaks, CA |
| [27] | Huebner, B. M.; Martin, K.; Moule, R. K. Jr; Pyrooz, D.; Decker, S. H., “Dangerous Places: Gang Members and Neighborhood Levels of Gun Assault, Justice Quarterly, 33, 836-862 (2016) · doi:10.1080/07418825.2014.984751 |
| [28] | Hughes, L. A.; Short, J. F., “Disputes Involving Youth Street Gang Members: Micro-social Contexts, Criminology, 43, 43-75 (2005) · doi:10.1111/j.0011-1348.2005.00002.x |
| [29] | Jacobs, B. A.; Wright, R. T., Street Justice: Retaliation in the Criminal Underworld (2006), Cambridge, UK: Cambridge University Press, Cambridge, UK |
| [30] | Johnson, D. H., “Point Process Models of Single-neuron Discharges, Journal of Computational Neuroscience, 3, 275-299 (1996) · doi:10.1007/BF00161089 |
| [31] | Klein, M. W.; Maxson, C. L., Street Gang Patterns and Policies (2006), New York: Oxford University Press, New York |
| [32] | Kubrin, C. E.; Weitzer, R., Retaliatory Homicide: Concentrated Disadvantage and Neighborhood Culture, Social Problems, 50, 157-180 · doi:10.1525/sp.2003.50.2.157 |
| [33] | Kyriacou, D. N.; Hutson, H. R.; Anglin, D.; Peek-Asa, C.; Kraus, J. F., “The Relationship Between Socioeconomic Factors and Gang Violence in the City of Los Angeles,”, The Journal of Trauma: Injury, Infection, and Critical Care, 46, 334-339 (1999) |
| [34] | Lewis, P. A. W.; Shedler, G. S., “Simulation of Nonhomogeneous Poisson Processes by Thinning, Naval Research Logistics Quarterly, 26, 403-413 (1979) · Zbl 0497.60003 · doi:10.1002/nav.3800260304 |
| [35] | Martinez, C., The Neighborhood Has Its Own Rules: Latinos and African Americans in South Los Angeles (2016), NYU Press |
| [36] | Meyer, S.; Elias, J.; Höhle, M., “A Space-time Conditional Intensity Model for Invasive Meningococcal Disease Occurrence, Biometrics, 68, 607-616 (2012) · Zbl 1274.92034 · doi:10.1111/j.1541-0420.2011.01684.x |
| [37] | Mohler, G. O., “Marked Point Process Hotspots Maps for Homicide and Gun Crime Prediction in Chicago, International Journal of Forecasting, 30, 491-497 (2014) · doi:10.1016/j.ijforecast.2014.01.004 |
| [38] | Mohler, G. O.; Brantingham, P. J.; Carter, J.; Short, M. B., “Reducing Bias in Estimates for the Law of Crime Concentration, Journal of Quantitative Criminology (2019) · doi:10.1007/s10940-019-09404-1 |
| [39] | Mohler, G. O.; Short, M. B.; Brantingham, P. J.; Schoenberg, F. P.; Tita, G. E., “Self-exciting Point Process Modeling of Crime, Journal of the American Statistical Association, 106, 100-108 (2011) · Zbl 1396.62224 · doi:10.1198/jasa.2011.ap09546 |
| [40] | Mohler, G. O.; Short, M. B.; Malinowski, S.; Johnson, M.; Tita, G. E.; Bertozzi, A. L.; Brantingham, P. J., “Randomized controlled field trials of predictive policing, Journal of the American Statistical Association, 110, 512, 1399-1411 (2015) · doi:10.1080/01621459.2015.1077710 |
| [41] | Office of Juvenile Justice and Delinquency Prevention, OJJDP Comprehensive Gang Model: Planning for implementation.ce (2009), Washington, DC: Institute for Intergovernmental Research, U.S. Department of Justice, Washington, DC |
| [42] | Ogata, Y., “The Asymptotic Behavior of Maximum Likelihood Estimators for Stationary Point Processes, Annals of the Institute of Statistical Mathematics, 30, 243-261 (1978) · Zbl 0451.62067 · doi:10.1007/BF02480216 |
| [43] | Ogata, Y., “Space-time Point-process Models for Earthquake Occurrences, Annals of the Institute of Statistical Mathematics, 50, 379-402 (1998) · Zbl 0947.62061 |
| [44] | Papachristos, A. V., “Murder by Structure: Dominance Relations and the Social Structure of Gang Homicide, American Journal of Sociology, 115, 74-128 (2009) · doi:10.1086/597791 |
| [45] | Papachristos, A. V.; Kirk, D. S., Neighborhood Effects on Street Gang Behavior, 63-84 (2006), New York: AltaMira, New York |
| [46] | Patillo-McCoy, M., Black Picket Fences: Privilege and Peril among the Black Middle Class (1999), Chicago, IL: University of Chicago Press, Chicago, IL |
| [47] | Reinhart, A.; Greenhouse, J., “Self-exciting Point Processes With Spatial Covariates: Modeling the Dynamics of Crime, Journal of the Royal Statistical Society, Series C, 67, 1305-1329 (2018) · doi:10.1111/rssc.12277 |
| [48] | Rosenfeld, R.; Bray, T. M.; Egley, A., “Facilitating Violence: A Comparison of Gang-motivated, Gang-affiliated, and Nongang Youth Homicides, Journal Of Quantitative Criminology, 15, 495-516 (1999) |
| [49] | Sampson, R. J.; Raudenbush, S. W.; Earls, F., “Neighborhoods and Violent Crime: A Multilevel Study of Collective Efficacy, Science, 277, 918-924 (1997) · doi:10.1126/science.277.5328.918 |
| [50] | Schoenberg, F. P., Facilitated Estimation of ETAS, Bulletin of the Seismological Society of America, 103, 601-605 (2013) · doi:10.1785/0120120146 |
| [51] | Sheather, S. J.; Jones, M. C., “A Reliable Data-based Bandwidth Selection Method for Kernel Density Estimation, Journal of the Royal Statistical Society, Series B, 53, 683-690 (1991) · Zbl 0800.62219 · doi:10.1111/j.2517-6161.1991.tb01857.x |
| [52] | Skogan, W. G.; Hartnett, S. M.; Bump, N.; Dubois, J., Evaluation of CeaseFire-Chicago (2009), Washington, DC: U.S. Department of Justice, Office of Justice Programs, National Institute of Justice, Washington, DC |
| [53] | Spergel, I. A., The Youth Gang Problem: A Community Approach (1995), Oxford University Press |
| [54] | Tita, G.; Griffiths, E., “Traveling to Violence: The Case for a Mobility-based Spatial Typology of Homicide, Journal of Research in Crime and Delinquency, 42, 275-308 (2005) · doi:10.1177/0022427804270051 |
| [55] | Tita, G.; Ridgeway, G., “The Impact of Gang Formation on Local Patterns of Crime, Journal of Research in Crime and Delinquency, 44, 208-237 (2007) · doi:10.1177/0022427806298356 |
| [56] | Tremblay, A.; Herz, D. C.; Kraus, M., The Los Angeles Mayor’s Office of Gang Reduction and Youth Development Comprehensive Strategy (2020), Los Angeles, CA: The Los Angeles Mayor’s Office of Gang Reduction and Youth Development, Los Angeles, CA |
| [57] | Valasik, M.; Barton, M. S.; Reid, S. E.; Tita, G. E., “Barriocide: Investigating the Temporal and Spatial Influence of Neighborhood Structural Characteristics on Gang and Non-gang Homicides in East Los Angeles, Homicide Studies, 21, 287-311 (2017) · doi:10.1177/1088767917726807 |
| [58] | Valasik, M.; Tita, G., The Oxford Handbook of Environmental Criminology, “Gangs and Space,”, 843-871 (2018), Oxford: Oxford University Press, Oxford |
| [59] | Yuan, B.; Hao, L.; Bertozzi, A. L.; Brantingham, P. J.; Porter, P., “Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction, ” SIAM J. Mathematics of Data Science, 1, 356-382 (2019) · Zbl 1499.60154 · doi:10.1137/18M1226993 |
| [60] | Zhuang, J.; Mateu, J., “A Semi-parametric Spatiotemporal Hawkes-type Point Process Model With Periodic Background for Crime Data,”, JRSS A, 182, 919-942 (2019) |
| [61] | Zhuang, J.; Ogata, Y.; Vere-Jones, D., “Stochastic Declustering of Space-time Earthquake Occurrences, Journal of the American Statistical Association, 97, 369-380 (2002) · Zbl 1073.62558 · doi:10.1198/016214502760046925 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
