Investigating Clustering and Violence Interruption in Gang-Related Violent Crime Data using Spatial-temporal Point Processes with Covariates

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 non-parametrically 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 2014-2016 and evaluated using data from 2017, based on log-likelihood and superthinned residuals. The impact of non-randomized 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 meters from the original reported crimes, and a reduction of 14.2% in retaliations within 130 meters.

本研究针对2014年1月1日至2017年12月31日期间美国加利福尼亚州洛杉矶市上报的涉帮派暴力犯罪数据，采用带协变量的时空标记霍克斯点过程（spatial-temporal marked Hawkes point processes）开展建模。本研究提出一种算法，以人口统计协变量为函数，对随时空动态变化的背景发生率进行非参数估计。为尽可能精准地拟合背景发生率，本研究采用核平滑（kernel smoothing）与广义可加模型（generalized additive models），旨在将背景发生率的非均匀性与事件的因果聚集或触发效应加以区分。模型以2014-2016年的数据集进行拟合，并基于对数似然（log-likelihood）与超稀疏残差（superthinned residuals）指标，采用2017年的数据集对模型性能进行评估。本研究通过对比洛杉矶市市长办公室帮派减少与青年发展（Gang Reduction Youth Development，简称GRYD）事件响应（Incident Response，简称IR）项目相关事件的触发效应，与按相似时空分布抽样选取的非GRYD事件的触发效应，评估了该项目所实施的非随机暴力干预措施的效果。研究结果表明，GRYD IR项目的暴力干预措施可使距原上报犯罪地点130米以外区域的报复率降低约18.3%，并使130米范围内的报复行为减少14.2%。