Abstract
The majority of spatial studies of crime employ an inductive approach in both the modeling and interpretation of the mechanisms of influence thought to be responsible for the patterning of crime in space and time. In such studies, the spatial weights matrix is specified without regard to the theorized mechanisms of influence between the units of analysis. Recently, a more deductive approach has begun to gain traction in which the theory of influence is used to model influence in geographic space. Using data from Los Angeles, we model the spatial distribution of gang violence by considering both the relative location of the gangs in space while simultaneously capturing their position within an enmity network of gang rivalries. We find that the spatial distribution of gang violence is more strongly associated with the socio-spatial dimensions of gang rivalries than it is with adjacency-based measures of spatial autocorrelation.
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Notes
Two notable examples of this are the Project on Human Development in Chicago Neighborhoods (PHDCN) and the Los Angeles Family and Neighborhood Survey (LAFANS).
Cohen and Tita (1999) argue that processes of imitation and direct influence can be conceptualized as different types of spatial diffusion and provide examples and a discussion of the various mechanisms related to diffusion within the realm of the urban homicide patterns.
For a detailed review and critique of inductive approaches to modeling influence across space see Tita and Greenbaum (2009).
Border effects refer to the fact that the often-arbitrary boundaries of study regions may exclude information that affects outcomes within the study region (see Griffith 1983). The modifiable areal unit problem refers to the fact that the results of statistical analysis, such as correlation and regression, can be sensitive to the geographic zoning system used to group data by area (see Gehlke and Biehl 1934 or Robinson 1950 for classic examples of MAUP, or Openshaw 1996 for a more contemporary review). While well-established in geography, these issues tend to resurface in other disciplines as spatial analysis becomes more prevalent (for example, see Hipp 2007). For a review of the treatment of these issues in the spatial analysis of crime, see Weisburd et al. (2009).
City-level studies of violence, for instance, often exclude data from spatially contiguous areas located just beyond the focal city’s borders not because these areas are unimportant, but rather because the data may not be available. Because none of the rivalries extend to gangs that lie beyond the borders of the research site, there are no non-Hollenbeck rival gangs to be excluded thereby ensuring that the full extent of the social process believed to matter (gang rivalries) is being captured.
Research has demonstrated that in this area of Los Angeles, gang involved violence accounts for 75% of all lethal violence (see Tita et al. 2003). Additionally, the current analysis was performed on all violent crimes regardless of gang involvement. Not surprisingly in light of the gang dominance in the commission of violent acts, there were no differences. These analyses are available from the authors upon request.
As discussed previously, we theorize that the territoriality of gangs is at the heart of rivalry relations between gangs. However, we do not limit the W g matrix to include only units already claimed by neighboring gangs. We see areas that were unclaimed at the time of the study as something that gangs may compete over as well.
The two most common approaches to equivalence in network analysis are structural equivalence and regular equivalence. The most important difference between the two is that structural equivalence requires that equivalent actors have the same connection to the same neighbors while regular equivalent actors have the same or similar patterns to potentially different neighbors (see Doreian et al. 2005).
The choice of model should always be predicated on a particular theoretical argument. However, in exploratory work, model choice is often determined empirically based upon the results of diagnostic tests aimed at distinguishing which model (error or lag) best fits one’s data. Anselin suggests that one first consider the Lagrange multiplier test (LM). If this test is failed, then the structure of the data suggests a spatial lag process is appropriate over the alternative choice of a spatial autoregressive error model (Anselin 2002). Though the specification tests are meant for continuous variables, several transformations (logging, creating rates) of the current dependent variable (crime count) demonstrated support for the lag model over the spatial error model.
Note that by using the spatially lags of the predicted values, we used a variant of the J test as originally presented in Leenders (2002) (see Piras and Lozano-Gracia (2008) for a discussion of the J test and this alternative specification). The J test was implemented using both specifications with no substantive differences. Though there were some differences in the size of the standard errors, the coefficients did not change. Both confirm the finding that the network-based specification of W better explains the observed spatial pattern of violence involving gang members.
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Tita, G.E., Radil, S.M. Spatializing the Social Networks of Gangs to Explore Patterns of Violence. J Quant Criminol 27, 521–545 (2011). https://doi.org/10.1007/s10940-011-9136-8
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DOI: https://doi.org/10.1007/s10940-011-9136-8