Space and Gang Crime: Modeling Social Processes in the Spatial Autocorrelation Matrix

1. Space and Gang Crime: Modeling Social Processes in the Spatial Autocorrelation Matrix George Tita Criminology, Law and Society University of California, Irvine

2. Crime, especially violence, exhibits strong patterns of positive spatial autocorrelation • With few exceptions, spatial regression models fail to explicitly model specific social processes (diffusion) • Exceptions: Mears/Bhati 2006; Tita 2006; Tita and Greenbaum 2009 • Task 1: Compare a contiguity based spatial regression analysis of gang violence with an analysis that considers the spatial features of gang rivalries • Alternative approach - Conduct positional social network analysis of each gang by considering both the network space and geographic space • Task 2: Create set of “structurally equivalent” geographies • Task 3: Determine if geographies identified as structurally similar experience similar levels of violence?

3. Gangs of Hollenbeck Spatial Regression – Specifications of “W” Structural Equivalence Equivalent Geographies Discussion

4. The Implications of Connectivity: Space Matters “The urban village model of cities is further compromised by the assumption that network of personal ties map neatly on to the geographically defined boundaries of neighborhoods, such that neighborhoods can be analyzed as independent social entities. In fact, social network in the modern city frequently traverse traditional ecological boundary, many of which are permeable and vaguely defined. Living in close proximity to high-crime neighborhoods may increase the risk of crime no matter what the density of social networks in an adjacent neighborhood. It follows that neighborhoods them- selves need to be conceptualized as nodes a larger network of spatial relations.” (Sampson, 2004)

5. Modeling Diffusion • Growing spatial analysis of violence literature suggestive of “Diffusion” • Suggestive because: • Crime is not random (spatial autocorrelation) • Spatial lag models over spatial error models • Need space and time models

6. The Spatial Analysis of Violence • Extant literature shows significant clustering beyond structural covariates • County (Anselin, Hawkins, Messner & Baller; Land & Deane) • City (Morenoff & Sampson; Cohen &Tita; Rosenfeld,Bray &Egley) • For city-level, gangs markets emerge as primary explanation • Assumes that rival gang neighborhoods are adjacent • Retaliation • Space (contiguity) as a proxy for a social phenomenon

7. General Autocorrelation Models • General Spatial Models • Spatial error: • Spatial Lag: • Theory Should Drive Model Selection • Correlated error model suggests “unobserved” process, similarity among neighboring geographic units • Lag model captures specific social process

8. Specification of the Spatial Autocorrelation Matrix (W) • Question: Can we make social processes explicit? • Gangs are geographically oriented (space) • Gangs are linked to other gangs (networks) • Gang violence is retaliatory (structure) •  Social Influence Models (Marsden & Friedkin, 1994) • Attempts to combine space/networks • Gould (1991) - Paris Commune resistance • Land, Deane & Blau (1991) – church adherence • Doreian (1981) - voting

9. Mapping the Social and Geographical Space of Gangs • “Criminally active street gangs” (n=29) • excludes taggers, skate crews • Mapping gangs • “set space”/turf - the activity space and hang outs of gangs • relied on experts from police and probation • Collecting network data • police, probation, service providers • gang members

10. Using Space and Networks • Start with spatial distribution of gangs • Overlay social network of gang rivalries • What explains the crime distribution: • Spatial ties among geographic units • Social ties among geographic units

11. Building Weight Matrices • Geographic is straight forward (contiguity) using GeoDa • Social requires several steps using Spacestat/Ucinet: • Create gang location network (120 x 29) • Create gang rivalry network (29 x 29) • Matrix Algebra Geographic rivalry network • Gang_loc * rivalry * Transpose(Gang_loc)

12. Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings Hollenbeck Composed of several neighborhoods (Boyle Heights, Lincoln Heights, El Sereno) each with a long history of gangs 84% Latino 39% born outside US 30% below poverty line 35% no HS degree (U.S. Census 2000)

13. Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings 1,223 gang-related violent crimes from 2002-2003 (Tita et al. 2003) Does an under-standing of the gang rivalries aid in interpreting this geography of violence?

14. Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings Rivalries - network of negative relations (Tita et al. 2003) Coded as dichotomous (0 or 1) and symmetric

15. Network of Ties Among Hollenbeck Block Groups

16. Gangs by Block Groups

17. Geographic Rivalry Network

19. Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings Turf locations and boundaries of all 29 gangs were mapped at the census block group level (Tita et al. 2003) Placing the rivalry network into the turf geography suggests a complex social landscape

20. Testing for Spatial Autocorrelation: Moran’s I • Moran’s I (global indicator) • HO: events are randomly distributed • HA: events exhibit a pattern • Wij (similarity in space) • Aij (similarity in value) • how do Wij and Aij co-vary • positive spatial autocorrelation (1.0) • high/high or low/low • negative spatial autocorrelation (-1.0) • high/low or low/high • Can only suggest diffusion or spatial processes

21. Spatial/Social Autocorrelation of Violent Crime • Geography (spatial lag) • Moran’s I = 0.105 (p=0.053) • Social (social lag) • Moran’s I = 0.124 (p=0.015)

22. Estimation Strategy • Determine if there is spatial dependence • OLS inappropriate, but…. • Statistical Tests support spatial lag, not spatial error • “Anselin Alternative Method” (Kubrin/Weitzer) • Two-state approach (Land/Deane) • Negative binomial to get predicted values of Y • Create lagged variable of predicted values

23. Model • Dependent Variable = # of violent crimes (2002 – 2003; n=1,223, excludes rape, domestic) • Independent (120 block groups): • Population density • Poverty (extreme, high), income (per capita) • Residential turnover (% new residents) • Percent rent • Crime prone ages (12 – 24 year olds) • Education (percent 25+ yrs old w/o HS degree) • Lags: • Predicted number of crimes

24. Results • Non-spatial model: • Extreme poverty (-), %rent (+), mobility (-) • Spatial model: • Extreme poverty (-), %rent (+), mobility (-), but NOT spatial lag • Social influence model: • Extreme poverty, Social Lag

25. Structural Equivalence: Gang rivalries can be analyzed as a struggle over territorial control that occurs both within a larger network of social relationships and a geographic context Spatializing social networks allows for the simultaneous analysis of an actor’s position in both network and geographic space