Segregation is in many ways the core of urban inequality research; any discussion of urban analytics is incomplete without decent coverage of segregation measurement. One of the most obvious and long-studied avenues for creating inequality between groups is to partition access to different resources. This is also one of the most important legacies of institutionalized racism in the United States, where the unequal distribution of public resources has repeatedly been shown to be illegal. In other words, there is an important legacy of urban inequality research closely related to legal challenges against federal policy; if policies governing public resources (like education, housing, transportation infrastructure, clean air and water, etc.) result in segregation (for some protected class), then they are inherently unequal (and ultimately unconstitutional, thanks to the equal protection clause).
Segregation of white and colored children in public schools has a detrimental effect upon the colored children. The impact is greater when it has the sanction of the law, for the policy of separating the races is usually interpreted as denoting the inferiority of the Negro group… Any language in contrary to this finding is rejected. We conclude that in the field of public education the doctrine of ‘separate but equal’ has no place. Separate educational facilities are inherently unequal.
In concept, segregation is about separation; when we measure residential segregation, we are asking whether people belonging to different groups share the same space, often conceived as the same ‘neighborhood’. This is a more ambiguous task than measuring, for example, educational segregation, where the shared resource such as schools are very well-defined. Residential space can be measured at the scale of the room, housing unit, building, collection of buildings, neighborhood, city, region, and all the way on (we explore this variable concept of scale in the next section).
Thus in the case of residential segregation we are forced to rely on the fuzzy notion of neighborhoods. In practice, this means that researchers simply adopt the tract or blockgroup as a placeholder for the neighborhood, then examine segregation as defined by these units. Here, we’ll use PySAL’s segregation module to analyze residential segregation by race and ethnicity in Southern California, and we begin by collecting data for the entire region, then partitioning it into the coastal and inland sections.
/Users/knaaptime/miniforge3/envs/urban_analysis/lib/python3.12/site-packages/geosnap/io/constructors.py:218: UserWarning: Currency columns unavailable at this resolution; not adjusting for inflation
warn(
Coastal and Inland Southern California
16.1 Residential Segregation Measures
The segregation package calculates dozens of segregation indices, each of which captures something different about the ways that population groups interact or remain separated in space. Most of the commonly-used statistics are global or aggregate measures, meaning they summarize the total level of segregation across all units in a study region. For an overview of segregation measure nomenclature, formulae, and canonical citations, see the tables at the end of Grannis (2002).
16.1.1 Single-Group Indices
Single-group indices measure the partitioning of one population group relative to everyone else. Early segregation work in the U.S. tends to focus on Black-white segregation, but it is also common to see work focused on a particular minority population versus the rest of the population (e.g. Black vs all other groups). To generate a single-group measure using the segregation package, you pass a dataframe holding population counts for each geographic unit, and the names of the columns for the focal population and the reference population (i.e. the minority the total population).
Here, we fit three segregation measures: Dissimilarity (\(D\)), Gini (\(G\)), and Entropy (also called the Information Theory index, sometimes denoted [Thiel’s] \(H\)) for the Black population and the Hispanic/Latino populations in the southern California region. Each class has a statistic attribute that holds the computed value for each segregation measure.
Code
dissim_hisp.statistic
np.float64(0.4995777695234679)
Code
dissim_black.statistic
np.float64(0.547197680270968)
Code
gini_hisp.statistic
0.6602166788700566
Code
gini_black.statistic
0.7234615852802052
Code
entropy_hisp.statistic
np.float64(0.2714618709533524)
Code
entropy_black.statistic
np.float64(0.2616509031724341)
According to the Dissimilarity and Gini indices, the black population in southern California is more segregated than the Latinx/Hispanic population, but the reverse is true according to the Entropy index.
16.1.1.1 Batch Computation
To examine several indices at once, segregation provides a set of “batch_compute” functions. Instead of a fitted Class, the batch_compute_singlegroup function returns a table of segregation indices and is a convenient way of collecting many statistics simultaneously.
Multi-group measures capture the partitioning of several population groups simultaneously. Most multi-group measures are extensions of single-group measures and have a more recent history in the literature (Reardon & Firebaugh, 2002).
Regardless which index is used, multigroup segregation is higher in the coastal region than the inland one
16.1.2.1 Batch Computation
Again, the measures can be “batch computed”
Code
socal_all_multigroup
Statistic
Name
GlobalDistortion
335.5186
MultiDissim
0.5131
MultiDivergence
0.3498
MultiDiversity
1.1664
MultiGini
0.6766
MultiInfoTheory
0.2999
MultiNormExposure
0.3048
MultiRelativeDiversity
0.2955
MultiSquaredCoefVar
0.2508
SimpsonsConcentration
0.3517
SimpsonsInteraction
0.6483
16.1.3 Local Segregation Measures
Unlike global measures, local segregation statistics measure segregation in each geographic unit rather than summarizing segregation across the region. For example the recently proposed Distortion index is designed to visualize how segregation changes over a region (Bézenac et al., 2022; Olteanu et al., 2019).
The use of trajectory convergence analysis provides a flexible way for capturing change across all scales from small spatial units and how the rate of convergence to the citywide average modifies over space. Thus, the method provides an analysis of how far, in spatial terms, any individual or neighborhood is from the citywide multigroup distribution.
