Abstract
Objectives
To join the literature on spatial analysis with research testing the racial invariance hypothesis by examining the extent to which claims of racial invariance are sensitive to the spatial dynamics of community structure and crime.
Methods
Using 1999–2001 county-level arrest data, we employ seemingly unrelated regression models, spatial lag models, and geographically weighted regression analyses to (1) compare the extent of racial similarity/difference across these different modeling procedures, (2) evaluate the impact of spatial dependence on violent crime across racial groups, and (3) explore spatial heterogeneity in associations between macro-structural characteristics and violent crime.
Results
Results indicate that spatial processes matter, that they are more strongly associated with white than black violent crime, and that accounting for space does not significantly attenuate race-group differences in the relationship between structural characteristics (e.g., structural disadvantage) and violent crime. Additionally, we find evidence of significant variation across space in the relationships between county characteristics and white and black violent crime, suggesting that conclusions of racial invariance/variation are sensitive to where one is looking. These results are robust to different specifications of the dependent variable as well as different units of analysis.
Conclusions
Our study suggests the racial invariance debate is not yet settled. More importantly, our study has revealed an additional level of complexity—race specific patterns of spatially heterogeneous effects—that future research on social structure and racial differences in violence should incorporate both empirically and theoretically.
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Notes
For example, of the 3,141 counties in the United States, only 1,906 have at least 200 blacks living in them.
We utilize the maximum number of counties while taking into account (1) the under-reporting (or the absence of reporting) of race-specific crimes in the UCR’s county-level database, (2) the reliability of UCR crime counts that were provided, (3) the necessity of including counties with a reasonably reliable number of both whites and blacks, and (4) our spatial requirement of having relatively contiguous counties. As such, we arrived at our sample of 1,315 counties after imposing what we see as reasonable selection criteria. It should be noted, however, that we estimated all of our models on a smaller sample of counties which used a more stringent constraint on our spatial requirements and limited our sample to only 1,114 counties, which largely excluded the West and South-West counties. Our substantive results were identical using this sample.
We thank an anonymous reviewer for this helpful suggestion.
At the county-level, these three measures are highly correlated and load well on one factor using principle component analysis (all factor loadings above .88). In supplemental analysis we ran our SUR models using each measure independently and found substantively similar results.
Our entropy measure is calculated for each county (Reardon and Firebaugh 2002). The entropy index (E) is a measure of the diversity of a geographic area, calculated as:
\( \mathop E\limits_{m = 1}^{M} = \sum {\pi_{m} \ln (1/\pi_{m} )} \, \)
where, π m is the proportion of people in race m (e.g., proportion black) and M is the total number of racial groups (here, white and black). E has a minimum value of 0 when a census place has no diversity and is composed entirely of one racial group and a maximum value of 1 when groups are equally represented. Racial heterogeneity scores were divided by their maximum values (1.099) to impose a range of 0 to 1 for E.
We recognize that police per capita is an imperfect measure of police activity and may capture the effect of police force size (i.e., larger police forces) rather than the likelihood of arrest. To verify the robustness of our findings we estimated all of our models using an alternative measure, clearance ratios (arrests made divided by offenses known). Our substantive results were identical to those reported in the tables (available from authors). We thank an anonymous reviewer for this suggestion.
Given its importance in research on the spatial analysis of crime (Baller et al. 2001), we (a) ran supplemental baseline SUR models with a “South” dummy variable and (b) conducted Lagrange Multiplier tests to determine if the spatial relationship (spatial error vs. spatial lag) differed in Southern counties than in non-Southern counties for our exploratory spatial analyses. Results suggest that there is little meaningful difference between South and non-South counties—a “South” dummy variable has trivial or non-significant effects in our baseline SUR models and the functional form of the spatial relationship (i.e., lag vs. error) is the same in Southern counties as in non-Southern counties. Therefore, we omit the South/non-South distinction in our final models.
Using a spatial weights matrix, Moran’s I statistic assesses the extent to which the pattern of values are spatially random. Rejection of this null hypothesis indicates significant spatial clustering.
The spatial weights matrix used in all spatial analyses is the queen’s 1st order, where each county is weighted by the values of all of its direct contiguous neighbors. Alternative weights matrices, including the rook’s 1st order and 10 nearest neighbors showed similar results with the latter displaying slightly less spatial autocorrelation. For example, the Moran’s I statistic for the white violence index rate was .34, .34, and .30 using the queen’s 1st order, the rook 1st order, and the 10 nearest neighbors weights matrices, respectively. The corresponding statistics for the black violence index were .23, .23, and .18, respectively. We utilize the queen’s 1st order matrix for two reasons. First, there are several areas where counties have few contiguous neighboring counties that have complete data (specifically in western Texas and Northern Kentucky). As a result, the nearest neighbor criterion weights the effects of counties that, while closest to that county, are in fact a significant distance away and are not theoretically likely to exert a strong influence on that “neighbor.” Moreover, specifying the number of neighbors is an arbitrary choice driven by neither contiguity concerns nor theory. Second, previous research has shown that contiguous counties are likely to have larger influences than non-contiguous counties (Baller et al. 2001).
While spatial dependence can be treated as a “nuisance” by constructing spatial error models, we chose to construct spatial lag models because (1) supplemental analysis reveals similar substantive results and model fit statistics with spatial error models and (2) choosing the appropriate modeling procedure should be based on theoretical considerations (Ward and Gleditsch 2008), and we conceptualize spatial dependence as substantively meaningful. Because lag models are more theoretically interpretable and appropriate for the hypothesized relationships between crime in one county affecting crime in another, we utilize a spatial lag approach.
We note that our sample of counties is less urban than the United States as a whole (50.3% compared to 68.4%), which may affect our results. However, our series of robustness tests using different dependent variables and different units of analysis lend confidence that our substantive conclusions regarding disadvantage, spatial proximity, and crime are meaningful.
Spatial econometrics utilizes two general models, spatial error and spatial lag models. Briefly, the spatial error model evaluates the extent to which the clustering of violence rates not explained by measured independent variables can be accounted for with reference to the clustering of error terms. Thus, it captures the spatial influence of unmeasured independent variables (Baller et al. 2001) and treats spatial dependence as a “nuisance.” In contrast, the spatial lag model incorporates the spatial influence of unmeasured independent variables as well as the effect of neighboring units’ dependent variable (i.e., the lagged dependent variable). The spatial lag model is appropriate when crime in one county is directly influenced by crime in that county’s “neighbors” above and beyond other covariates specific to that county. This model is most compatible with notions of “spillover” processes, implying the influence of neighbors’ violence rates independent of measured or unmeasured independent variables (see in Baller et al. 2001 for visual representation of these different models).
Since our baseline SUR model produces only a single AIC (Akaike Information Criterion) value and our spatial lag models produce two, we computed AIC values for baseline OLS models for model-fit comparisons. Findings suggest that spatial lag models (white AIC = 2,873.7, black AIC = 3,045.7) are a better fit than baseline models (white AIC = 3,007.5, black AIC = 3,116.4).
While these models can assess whether the effects of county level characteristics are spatially invariant for white and black models, they cannot test whether this spatial variability is significantly different between models. In other words, while parameter estimates may vary across geographic space in each model, we have no formal way of testing whether these “local parameters” are significantly different between whites and blacks.
We used vital statistics data on homicide deaths for ages 17 and up because the vital statistics data does not provide an age category with a threshold at age 18 which would allow us to separate out adults (i.e., 18 and up). Additionally, we averaged the number of homicide deaths across the years 1999–2005 in order to leverage a greater number of rare homicides and to avoid suppression of the data for small counties which the CDC employs to protect the anonymity of victims which cannot be assured even without personal identifiers.
The dependent variable for this analysis is the race-specific rate of homicide victimization in each tract for the years 1985–1995. These years were used because the dataset only covers homicides from 1965 to 1995 and to limit the number of tracts that had no homicides in any 1 year. All independent variables were taken from the 1990 census. While we tried to utilize the same measures as our main analysis, certain information was unavailable. For example, the census did not collect race-specific mobility information at the tract level in 1990. Because of this, our measure of residential instability in the Chicago supplement is a total (i.e. not race-specific) measure of instability. Also, because all of Chicago is urban, we used a measure of population density as opposed to our population structure variable. Finally, clearance ratios and police per capita information were not available at the tract level. All other measures are identical to those used in our main analysis. The sample is limited to tracts that had had at least 100 whites for the white models (N = 568) and 100 blacks for the black models (N = 540).
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Acknowledgments
We would like to thank Darrell Steffensmeier, Stephen Matthews, Jeffrey Ulmer, Michael Massoglia, Luke Bonkiewicz and three anonymous reviewers for their helpful comments.
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Light, M.T., Harris, C.T. Race, Space, and Violence: Exploring Spatial Dependence in Structural Covariates of White and Black Violent Crime in US Counties. J Quant Criminol 28, 559–586 (2012). https://doi.org/10.1007/s10940-011-9162-6
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DOI: https://doi.org/10.1007/s10940-011-9162-6