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Shooting on the Street: Measuring the Spatial Influence of Physical Features on Gun Violence in a Bounded Street Network

Abstract

Objectives

Accurately estimate the strength and extent (distance) of the spatial influence of physical features on gun violence using a street network measurement strategy.

Methods

Treating disaggregated point locations as the unit-of-analysis, the spatial influence of various physical features of place on all 2012 incidents of gun violence in Newark, NJ is estimated along a street network plane rather than a planar plane, and using a continuous operationalization of street network distances as opposed to Euclidean or Grid distances. Network-based computation methods clarify the path distances over which physical features of place, or shooting attractors, exert a significant spatial influence on gun violence. Segmented regression models estimate feature-specific distance decay patterns by demarcating the exact network distances at which the strength of attraction weakens or dissipates entirely.

Results

Findings show that liquor stores, grocery stores, bus stops, and residential foreclosures are shooting attractors in Newark, NJ. The magnitude of spatial influence is strongest in the immediate vicinity of each physical feature, and declines precipitously thereafter; yet the nature and strength of the decay varies by feature. A comparison of results analyzed on a street network plane to those based on an unbounded plane illustrates the potential biases in traditional approaches.

Conclusions

Determining whether and how strongly physical features operate as crime attractors requires constraining the analyses to the street network plane and accurately measuring continuous distances along the street network. The methodology articulated in this study can be used to more precisely estimate the spatial influence and distance decay of various physical features of place on crime density.

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Notes

  1. 1.

    The geocoding hit rates for all data were in excess of 85 %, satisfying the threshold of a reliable matching process (Ratcliffe 2004).

  2. 2.

    The authors thank Dr. Leslie Kennedy for generously providing access to the 2012 Newark crime data and for helpful comments on earlier versions of this paper.

  3. 3.

    The Network Cross K Function is calculated with the SANET software package developed by Okabe et al. (1995).

  4. 4.

    For ease of illustration, we compute the Network Cross K Function up to 3000 ft from the physical feature in Newark because the average size of one street block is approximately 280 ft. This means that anything occurring outside 10 blocks is not considered when measuring degree of attraction. While the specific outside distance buffers can vary by researcher preferences and city characteristics, research has generally shown that the effects of physical features are strongest in the immediate vicinity of the feature and fall rather dramatically thereafter (Fagan and Davies 2000; Groff 2014; McNulty and Holloway 2000; Ratcliffe 2012).

  5. 5.

    Unlike other approaches, the Monte Carlo simulation is restricted within the street networks of Newark, rather than across the whole plane of Newark. For each simulated Network Cross K Function analysis, a fifty times of Monte Carlo simulation is conducted within each distance band to obtain the expected distributions. In a random distribution, each point event has an equal probability of occurrence at any location in space; the presence of one point event at a location does not impact the possibility that other point events will occur. Monte Carlo simulation relies on repeated trials to produce sufficient output for generalization.

  6. 6.

    The XY coordinates of all the shooting incidents, physical features’ locations, and the boundaries of the study area were first calculated in ArcGIS using the North American Datum 1983 State Plane New Jersey 2900 ft projected coordinate system and then exported to R.

  7. 7.

    To the extent that city street widths vary, some minor error may be introduced in our decision to treat street length rather than total area of streets as the denominator. Nonetheless, city streets tend to be reasonably similar in width, and thus the total area of streets within a specified distance buffer should be largely proportional to the cumulative length of the streets within the same buffer.

  8. 8.

    Each shooting point is counted only once within a scale of distance, even if it is within the range of multiple liquor stores. Consequently, a shooting that occurs within 300 ft of multiple liquor stores is counted as occurring within 300 ft of only the most proximate liquor store to the shooting.

  9. 9.

    The segmented regression model is estimated for the observations (x1, y1), … (x n , y n ), where x1 < … < x n represent the network distance variable. Y i , where i = 1, 2, …, n is the response variable or, in this case, shooting density. The regression equation can be written as:

    $$E[y|x] = \beta_{0} + \beta_{1} x + \gamma_{1} (x - \tau_{1} )^{ + } + \cdots + \gamma_{n} (x - \tau_{k} )^{ + }$$
    (2)

    where β0, β1, γ1, …, γn are regression coefficients and the τ k , k = 1, 2, …, n, n < N, is the kth unknown change point in which (x i  − τ k )+ = (x i  − τ k ) if (x i  − τ k ) > 0. To determine change points, we use the grid search method, rather than Hudson’s method, because it is computationally more efficient. In these analyses, the minimum number of observations between two change points was set at four. To find the optimal model (i.e. the optimal number of change points and the optimal locations of those change points), the Bayesian Information Criterion (BIC) is used. The model with the minimum BIC is the best fitting model.

  10. 10.

    The shooting densities reported in Table 1 are multiplied by 100 to magnify the slope values for ease of interpretation; this is necessary when the values of slopes are very small.

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Xu, J., Griffiths, E. Shooting on the Street: Measuring the Spatial Influence of Physical Features on Gun Violence in a Bounded Street Network. J Quant Criminol 33, 237–253 (2017). https://doi.org/10.1007/s10940-016-9292-y

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Keywords

  • Spatial influence
  • Physical features of place
  • Street network
  • Network Cross K Function
  • Gun violence