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.