George E. Tita

Self-Exciting Point Process Modeling of Crime

Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime-specific patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, near the location of an initial event. Space–time clustering is modeled in seismology by self-exciting point processes and the focus of this article is to show that these methods are well suited for criminological applications. We first review self-exciting point processes in the context of seismology. Next, using residential burglary data provided by the Los Angeles Police Department, we illustrate the implementation of self-exciting point process models in the context of urban crime. For this purpose we use a fully nonparametric estimation methodology to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.

A STATISTICAL MODEL OF CRIMINAL BEHAVIOR

Motivated by empirical observations of spatio-temporal clusters of crime across a wide variety of urban settings, we present a model to study the emergence, dynamics, and steady-state properties of crime hotspots. We focus on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker. The dynamics of criminals and of the attractiveness field are coupled to each other via specific biasing and feedback mechanisms. Depending on parameter choices, we observe and describe several regimes of aggregation, including hotspots of high criminal activity. On the basis of the discrete system, we also derive a continuum model; the two are in good quantitative agreement for large system sizes. By means of a linear stability analysis we are able to determine the parameter values that will lead to the creation of stable hotspots. We discuss our model and results in the context of established crim...

Diffusion in Homicide: Exploring a General Method for Detecting Spatial Diffusion Processes

This article proposes a new method for examining dynamic changes in thespatial distribution of a phenomenon. Recently introduced exploratoryspatial data analysis (ESDA) techniques provide social scientists with anew set of tools for distinguishing between random and nonrandom spatialpatterns of events (Anselin, 1998). Existing ESDA measures, however, arestatic and do not permit comparisons of distributions of events in the samespace but across different time periods. One ESDA method—the Moranscatterplot—has special heuristic value because it visually displayslocal spatial relationships between each spatial unit and its neighbors. Weextend this static cross-sectional view of the spatial distribution ofevents to consider dynamic features of changes over time in spatialdependencies. The method distinguishes between contagious diffusion betweenadjoining units and hierarchical diffusion that spreads broadly throughcommonly shared influences. We apply the method to homicide data, lookingfor evidence of spatial diffusion of youth-gang homicides acrossneighborhoods in a city. Contagious diffusion between neighboring censustracts is evident only during the year of peak growth in total homicides,when high local rates of youth-gang homicides are followed by significantincreases in neighboring youth- nongang rates. This pattern is consistentwith a spread of homicides from gang youth to nongang youth. Otherwise, theincreases in both youth-gang and youth- nongang homicides generally occursimultaneously in nonneighboring tracts.

Dissipation and displacement of hotspots in reaction-diffusion models of crime

The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.

Reducing Gun Violence: Results from an Intervention in East Los Angeles

To assess whether an initiative to reduce gun violence that had been successful in Boston could be adapted for use elsewhere, researchers selected an East Los Angeles area for a similar intervention that was to include both law enforcement and social service components. Although the latter component was not widely available when the intervention began, researchers found that the intervention helped reduce violent and gang crime in the targeted districts and that crime also decreased in surrounding communities.

The Impact of Gang Formation on Local Patterns of Crime

Research has demonstrated that even after controlling for individual level attributes, individuals who join gangs commit more crimes than do nongang members. Furthermore, the offending level of gang members is higher when they report being active members of the gang. Therefore, gang membership clearly facilitates offending above and beyond individual level characteristics. But what impact does the onset of gangs have on aggregate crime patterns? By exploring levels and patterns of crime in an “emergent gang city” (Pittsburgh, Pennsylvania), the authors test whether the individual level finding linking gang membership to increased offending equates to more crime at the aggregate, citywide level. They also explore the impact that gang formation has on local patterns of crime. Gangs tend to be territorial, but although many qualitative accounts describe the crime-gang relationship within the community, few empirical studies have explored how gangs shape the spatial distribution of crime in and around their territory.

Traveling to Violence: The Case for a Mobility-Based Spatial Typology of Homicide

According to routine activities theory, crime is the result of an intersection between victims and offenders in both time and space. We introduce a spatial typology that identifies five combinations of victim and offender mobility to homicide incident locations: internal, predatory, intrusion, offense mobility, and total mobility types. The authors’ argue that the joint mobility pattern of the victim and offender is the mechanism underlying routine activities theory, and made explicit by the spatial typology. Using information on the 420 homicides in Pittsburgh, Pennsylvania, between 1987 and 1995, we demonstrate that the majority of homicides involve at least some mobility on the part of victims and/or offenders. Our results also indicate that mobility to homicide incident locations is most associated with event characteristics such as motive, rather than with characteristics of the participants. With most offenders committing the homicide outside of their own neighborhood, levels of lethal violence in a community are influenced more by the interaction among nonlocal participants than by the violent actions of local residents.

The Impact of Violence Surges on Neighbourhood Business Activity

Theoretical and empirical arguments suggest that fear of violence will cause consumers, employees and entrepreneurs to alter their routine activities in areas that experience a surge in violent activity. This paper argues that understanding how businesses respond to violence has important implications for understanding community crime cycles and offers further evidence of how crime impacts the choices individuals make with regard to where they live, shop and work. Using newly available longitudinal business data and homicide data disaggregated to the ZIP code level, an examination is made of the impact of violence surges on the creation, destruction and growth of business establishments in five large US cities between 1987 and 1994. Controlling for pre-existing levels of violence, it is found that increased violence has the greatest consequences for service-related establishments in low-crime neighbourhoods. This finding is consistent with the notion that the fear of victimisation imposes additional indirect costs to society through its negative impact on local business establishments.

Crime, Neighborhoods, and Units of Analysis: Putting Space in Its Place

Research has long established that crime is not randomly distributed, and spatial regression models of crime have clearly demonstrated that crime patterns cannot be explained merely by the socio-economic characteristics of a particular place. These findings are a reminder that “space matters” and that neighborhoods are not analytically independent units. Modeling the clustering of crime through spatial regression requires two important decisions. First, one must choose a unit of analysis that is consistent with the social processes believed to be driving the observed patterns. Second, one must consider the relationships among these units such that the model captures the influence the activities in other areas have on outcomes in the neighborhood. Within criminology, this second feature has been given insufficient consideration. Instead, the connectedness of spatial units has been taken as given and modeled solely through adjacency or a distance decay function. This chapter critiques such inductive approaches used to model and explain the spatial distribution of crime. Drawing upon the modeling of network autocorrelation within the social influence literature, we describe a deductive approach wherein specific social processes are posited, measured and modeled a priori. An empirical example using gang violence demonstrates this deductive approach and we find that the spatial distribution of violence is influenced by neighbors defined by the socio-spatial dimensions of gang rivalries rather than simply by geographically contiguous neighbors. We emphasize that a complete discussion of the appropriate unit of analysis must also consider the spatial dimensions of the social phenomena thought to be responsible for the spatial patterning.

Predicting Recidivism in Homicide Offenders Using Classification Tree Analysis

Given the severity of the crime and the lengthy sentences often accompanying convictions, homicide tends to be seen as the culminating event in a criminal career. In an attempt to better understand the types of individuals who commit homicide, many studies have examined the offense history of those convicted of murder and manslaughter. Only recently have researchers begun to realize that in some cases homicide is not an end point in the trajectory of one’s criminal career but rather a potential predictor in a continuing criminal career. Building on existing research, the present study uses a sample of 320 homicide offenders convicted, sentenced, imprisoned, and released in New Jersey from 1990 to 2000 to assess which factors predict future recidivism. We find that classification tree analysis in random forests outperform logistic regressions in classification and prediction of recidivism.