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

Matrix

George TitaCriminology, Law and Society

University of California, Irvine

• 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?

Gangs of Hollenbeck

Spatial Regression – Specifications of “W”

Structural Equivalence

Equivalent Geographies

Discussion

“The urban village model of cities is further compromisedby the assumption that network of personal ties map neatly on to the geographically defined boundaries of neighborhoods,such that neighborhoods can be analyzed as independentsocial entities. In fact, social network in the modern city frequently traverse traditional ecological boundary, many of which are permeable and vaguely defined. Living in closeproximity to high-crime neighborhoods may increase the riskof crime no matter what the density of social networks in anadjacent neighborhood. It follows that neighborhoods them-selves need to be conceptualized as nodes a largernetwork of spatial relations.” (Sampson, 2004)

The Implications of Connectivity:Space Matters

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

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

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

, Xy W XWyy

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

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

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

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)

HollenbeckComposed of several neighborhoods (Boyle Heights, Lincoln Heights, El Sereno) each with a long history of gangs

84% Latino39% born outside US30% below poverty line35% no HS degree(U.S. Census 2000)

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?

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

Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings

Network of Ties Among Hollenbeck Block Groups

Gangs by Block Groups

Geographic Rivalry Network

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

Introduction Gangs of Hollenbeck Structural Equivalence Equivalent Geographies Findings

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

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)

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

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

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

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