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Modeling the Social and Spatial Proximity of Crime: Domestic and Sexual Violence Across Neighborhoods

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Abstract

Objectives

Our goal is to understand the social dynamics affecting domestic and sexual violence in urban areas by investigating the role of connections between area nodes, or communities. We use innovative methods adapted from spatial statistics to investigate the importance of social proximity measured based on connectedness pathways between area nodes. In doing so, we seek to extend the standard treatment in the neighborhoods and crime literature of areas like census blocks as independent analytical units or as interdependent primarily due to geographic proximity.

Methods

In this paper, we develop techniques to incorporate two types of proximity, geographic proximity and commuting proximity in spatial generalized linear mixed models (SGLMM) in order to estimate domestic and sexual violence in Detroit, Michigan and Arlington County, Virginia. Analyses are based on three types of CAR models (the Besag, York, and Mollié (BYM), Leroux, and the sparse SGLMM models) and two types of SAR models (the spatial lag and spatial error models) to examine how results vary with different model assumptions. We use data from local and federal sources such as the Police Data Initiative and American Community Survey.

Results

Analyses show that incorporating information on commuting ties, a non-spatially bounded form of social proximity, to spatial models contributes to better deviance information criteria scores (a metric which explicitly accounts for model fit and complexity) in Arlington for sexual and domestic crime as well as overall crime. In Detroit, the fit is improved only for overall crime. The distinctions in model fit are less pronounced when using cross-validated mean absolute error as a comparison criteria.

Conclusion

Overall, the results indicate variations across crime type, urban contexts, and modeling approaches. Nonetheless, in important contexts, commuting ties among neighborhoods are observed to greatly improve our understanding of urban crime. If such ties contribute to the transfer of norms, social support, resources, and behaviors between places, they may then transfer also the effects of crime prevention efforts.

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Authors and Affiliations

  1. Pennsylvania State University, 330B Thomas Building, University Park, PA, 16802, USA

    Claire Kelling

  2. Department of Statistics, Pennsylvania State University, University Park, PA, USA

    Claire Kelling & Murali Haran

  3. Department of Sociology and Criminology, Pennsylvania State University, University Park, PA, USA

    Corina Graif

  4. Biocomplexity Institute and Initiative, University of Virginia, 1100 Wilson Blvd., Arlington, VA, USA

    Gizem Korkmaz

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  1. Claire Kelling
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  2. Corina Graif
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  3. Gizem Korkmaz
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  4. Murali Haran
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Correspondence to Claire Kelling.

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Appendix

Appendix

Sensitivity Analysis

In this section, we create a sensitivity analysis for our cutoff used to define commuting proximity between two neighborhoods. In order to create a proximity matrix for commuting ties, we created a cutoff of the number of commuters which defined social ties so that if there are more than x number of commuters between two areal units, we define a social tie.

First, for both Detroit and Arlington County, we report the percentage of block groups that have more commuters than our defined cutoff, seen below in Table 14. We see that almost all of the block groups have less than 15 commuters listed for both Detroit and Arlington.

Table 14 Percent of areal units above cutoffs for commuters
Full size table

Next, we analyze the effect of these cutoffs, listed above, on the conclusions that we gain based on model performance. Specifically, we analyze if the commuting proximity combined with geographic proximity is still better than geographic proximity alone, at each level of the cutoff, and we determine if there is an optimal cutoff for the number of commuters to include. We complete this analysis for both Arlington and Detroit. We test all three CAR models included in the full analysis: the BYM and Leroux CAR Models and the sparse Spatial Generalized Linear Mixed Model (s-SGLMM).

We make ten runs of the geographic proximity model in order to assess the variability over repeated measurements (the result is similar when the commuting proximity model is repeated). Therefore, the lines for the Geographic Models in Fig. 4 are referring to the mean DIC over 10 runs of the model with geographic proximity alone, as the DIC for this model does not vary with the cutoff other than with random variability as the model does not include commuting ties, and therefore does not include the cutoff. Here, we only include the results for the sparse SGLMM and we find similar results for the BYM and Leroux models.

Fig. 4
figure 4

Sensitivity analysis

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In Fig. 4, for Arlington we see that for all levels of the cutoff, the model where we combine geographic and commuting proximity still gives us a better model fit (DIC) than the model that includes geographic proximity alone. However, we notice that there does seem to be an optimal level of commuters to include in our analysis. For Detroit, we see that when we include more commuters in the analysis, or when the cutoff for excluding commuters from the analysis is smaller, we obtain a smaller DIC value. When we include more commuters in the analysis, the DIC approaches and even exceeds the DIC of the geographic models.

For both Detroit and Arlington, we see that if we include too few commuters with a large cutoff, where we only define a tie if there are more than 15 commuters between two block groups, our model performance is worse than if we were to include more ties in the model, where the cutoff is smaller for including the social tie in the model.

For our analysis presented in the paper, we defined a social tie between the communities based on whether there are more than 3 commuters between block groups for both Detroit and Arlington, based on this sensitivity analysis. However, more investigation is needed, as LODES uses a confidentially protection algorithm that may affect the interpretation of data at small scales. Therefore, it is important to continue to investigate the implications of the data generating process in future research focused on different geographic scales and different types of ties.

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Kelling, C., Graif, C., Korkmaz, G. et al. Modeling the Social and Spatial Proximity of Crime: Domestic and Sexual Violence Across Neighborhoods. J Quant Criminol 37, 481–516 (2021). https://doi.org/10.1007/s10940-020-09454-w

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