by Dan O’Brien
Urban researchers and policymakers often talk about “disparities” and “inequities” across the city, but the geographic scale of these issues is often unclear. Many speak of disadvantaged neighborhoods, but are Dorchester, South Boston, and Allston-Brighton homogeneous regions, with every pocket looking and feeling the same? How do things like crime, disorder, educational attainment, and pollution vary by census tract? By street? By address? This is a deceptively difficult question to answer as these three levels of geography are literally nested within each other. BARI has developed a new methodology that solves this issue, made possible by our Geographical Infrastructure for the City of Boston. Here I illustrate this new methodology by addressing the concentration of physical disorder (i.e., “broken windows”) across the census tracts, streets, and addresses of Boston, which is also presented in a recent article in Journal of Research in Crime and Delinquency.
The new methodology is called the “nested Gini.” Before describing what it does, consider the following problem. We want to know which geographic scale is responsible for the distribution of crime events, which can help us to design efforts around prevention or response that target the appropriate level, be it at-risk neighborhoods, hotspot streets, or “problem properties.” This is a more difficult question than it might appear to be on the surface. For example, take a city where crime events are unevenly distributed across neighborhoods. Suppose then that the crimes within each neighborhood are distributed perfectly evenly across all the streets therein. In this case, it would be inaccurate to attribute any of the distribution of crime to streets. Nonetheless, if streets are analyzed directly, they will appear to exhibit just as much variation as neighborhoods. Put another way, if the same number of events are distributed across a far greater number of units, concentrations will inevitably look greater.
The nested Gini disentangles concentrations at multiple geographic scales by combining the quantitative power of the Gini coefficient with the logic of—you guessed it—nesting. The Gini coefficient calculates the overall level of inequality in a set of items. It is most commonly used for income, but it can be applied to any quantity, in this case crime events. The methodology is “nested” in how it compares quantities across units. Instead of calculating the concentration of crime, for example, across all streets in a city, it calculates them for the streets within a census tract. It then does so for all census tracts, generating an estimate of the typical level of concentration of crime events across streets accounting for the distribution of crime across neighborhoods. It can also be applied to addresses, nested within street segments.
To illustrate, we will leverage BARI’s Geographical Infrastructure for the City of Boston, which can accommodate any data set with addresses and then nests them within the appropriate street segment and census geographies. In order to demonstrate down to the address level, we will opt, however, to use incidents of physical disorder (drawn from 311 reports), or “broken windows,” rather than crime events, which can be more sensitive.
Figure 1 shows how the nested Gini works. The census tracts of Boston are reasonably diverse in the number of physical disorder events occurring within them, amounting to a moderate Gini of .46. Let us then zoom in on a single high-crime census tract in Mattapan. The incidents of physical disorder occurring within that neighborhood are largely concentrated on a handful of street segments, generating a more marked Gini of .80. If we zoom in further on one of these hotspots, we see that the 20 or so incidents occurred at only four addresses, with one generating more than half. This Gini is similarly high at .83.
This single example suggests that hotspot streets and problem properties are the primary concern when considering the distribution of physical disorder—provided the patterns are consistent. It turns out that they are. The average tract had a Gini of .70 for the distribution of physical disorder across its streets, and the average street had a Gini of .73 for the distribution of physical disorder across its addresses.
To summarize, the nested Gini is a new methodology developed by BARI to disentangle concentrations at multiple levels. In this case, it revealed the importance of attending particularly to street segments and addresses as loci for physical disorder, but it might be applied to any quantity distributed unevenly across the urban landscape. Further, it is one of many methodologies that are possible thanks to BARI’s Geographical Infrastructure, which facilitates the linkage of data describing the same geographic units; the seamless aggregation of data across nested geographic scales; and the straightforward visualization of the results.
To learn more about the nested Gini, please see the recent paper “The Action is Everywhere, but Greater at More Localized Spatial Scales” published in Journal of Research in Crime and Delinquency.