«Urban Problems and sPatial methods VolUme 17, nUmber 1 • 2015 U.S. Department of Housing and Urban Development | Office of Policy Development and ...»
Introduction Residential segregation and the persistence thereof have long been topics of interest to a wide variety of academic disciplines (for example, sociology, demography, geography, political science, and public health) and to professionals or practitioners in multiple fields (for example, law enforcement, urban planning, and health service providers). Particularly in the United States, such phenomena have been viewed as a key factor of significant separation between White and Black residents.
Cityscape 97 Cityscape: A Journal of Policy Development and Research • Volume 17, Number 1 • 2015 U.S. Department of Housing and Urban Development • Office of Policy Development and Research Oka and Wong Therefore, formulating potential solutions to reduce the levels of residential segregation have been considered as a major societal concern (for example, Anderson et al., 2003; Charles, 2003; Clark, 1986; Massey and Fischer, 2000; Taeuber, 1968; Williams, 1999; Williams and Collins, 2001).
Note that all racial groups in this article refer to the non-Hispanic populations.
With a view to inform public policies and decisionmaking, however, the use of effective and meaningful segregation measures is fundamental and crucial to develop a reliable depiction and understanding of the social environment that different population groups experience in their place of residence (Johnston, Poulsen, and Forrest, 2014).1 Since the publication of the review papers (for example, Massey and Denton, 1988; Massey, White, and Phua, 1996) that assessed several dozens of segregation measures, many more segregation measures have been introduced. Many of these newer measures are extensions or modifications of existing measures (for example, Feitosa et al., 2007; Reardon and O’Sullivan, 2004; Wong, 2008, 2002), but some are actually not measures of segregation (for example, Brown and Chung, 2006; Reibel and Regelson, 2007). The mushrooming in the number of segregation measures reflects that the concept of segregation is fluid, difficult to pin down, and multifaceted so that one or a few simple definitions are not capable of capturing its essence entirely. As a result, rather ineffective and insufficient ways of measuring segregation are evident in research and practice.
One major “malpractice” quite prevalent among studies focusing on neighborhood comparisons is using the percentage of racial and ethnic groups (for example, percent Black) as a measure of segregation to examine, for instance, the possible effects of residential segregation on academic performance (for example, Bennett, 2011; Card and Rothstein, 2007), home equity (for example, Deng, Ross, and Wachter, 2003; Kim, 2000), and health (for example, Inagami et al., 2006;
Vinikoor et al., 2008). Census statistical units (tracts or block groups) have been used to denote the “neighborhoods” in most U.S. studies (including the six studies listed previously). Percentages, however, are not a measure of segregation (Johnston, Poulsen, and Forrest, 2007; Massey and Denton, 1988; Massey, White, and Phua, 1996; Reardon and O’Sullivan, 2004). A segregation measure needs to quantify how two or more population groups are distributed across space and to account for the potential of spatial interaction among population groups across areal units (Feitosa et al., 2007; Reardon and O’Sullivan, 2004; White, 1983; Wong, 2008, 2004, 2002, 1998, 1993).
Because the conceptual and methodological foundations of segregation studies have not been adequately translated into research and practice, the objectives of this article are threefold: (1) to explain a spatial approach for measuring the level of segregation at the neighborhood (or local) level, (2) to demonstrate the deficiencies of using a percentage of racial and ethnic group as a measure of segregation, and (3) to clarify the appropriateness of two commonly used indexes of dissimilarity and diversity. Data from two cities in the U.S. Midwest, St. Louis, Missouri, and Chicago, Illinois, are used to discuss such conceptual and methodological concerns.
We do realize that measuring segregation should not be constrained to residential space only, but segregation in the residential space, nevertheless, has received the most attention.
Methods In this section, we first provide an overview about how measures that depict segregation levels at the local or neighborhood level are formulated. Both aspatial and spatial versions of these measures will be discussed. Then, we apply these measures to study the two cities.
Segregation Measures The dissimilarity index (D) and the entropy-based diversity index (H) are two common segregation indexes used to measure the unequal or differential distributions of population groups (that is, the evenness dimension of segregation). D was introduced by Duncan and Duncan (1955), and its use was advocated by Massey and his colleagues (Massey and Denton, 1988; Massey, White, and Phua, 1996). On the other hand, H was introduced by Shannon (1948a, b) or Theil (1972), depending on the fields of study (also referred to as the Shannon index or Theil index, respectively), and its use in segregation studies was advocated by White (1986) and Reardon and Firebaugh (2002).
Both D and H share a limitation and a shortcoming, however. First, they are global measures that summarize the condition of the entire region (for example, a city or a metropolitan area); thus, they fail to recognize the variations at the neighborhood (or local) scale (Feitosa et al., 2007; Reardon and O’Sullivan, 2004; Wong, 2004, 1996). Second, they are aspatial measures that do not account for the spatial relationships between areal units; thus, swapping the entire populations between areal units will not change the index values (Morrill, 1991; White, 1983; Wong, 2004, 1998, 1993).
To address these two issues, Wong (1998) implemented the concept of composite population count to capture spatial relationships for modifying the global aspatial segregation indexes into local spatial segregation indexes (2008, 2002).
Borrowing the concept of modeling spatial autocorrelation, modifications of segregation indexes were achieved by adapting the function cij(.) (Wong, 2008, 2002). Here, cij(.) is the element of a (0, 1) matrix where cij = 1 indicates areal units i and j are neighbors, and cij = 0 otherwise; however, i can equal j and thus cii = 1. Therefore, the composite population count of group G in areal unit i (cgi ) is modeled as
cgi = ∑ cij g j, j
where g j is the population count of group G in areal unit j. In other words, a composite population count refers to the population count in areal unit i plus the population counts in its neighboring units j. This implicitly accounts for the spatial interaction of population groups across areal unit boundaries. Exhibit 1 illustrates how the function cij(.) can be used to calculate the composite population count.
3,551 3,005 2,515 21,695
The concept and method of local spatial segregation measures did not emerge until recently (Wong, 2008, 2002). To explain the difference between aspatial and spatial segregation measures, specifications of the local aspatial dissimilarity index (Di ) and its spatial version (SDi ) along with the local aspatial diversity index (Hi ) and its spatial version (SHi ) are given in the following discussion.
The local aspatial dissimilarity index (Di ) is defined as
where wi and bi are the White and Black population counts in areal unit i, respectively, and W and B are the White and Black population counts for the entire study area, respectively. This index is the local aspatial version of the popular D. To derive the spatial version of this index, the local spatial dissimilarity index (SDi), all population counts are replaced by their respective composite population counts—
where cwi and cbi are the composite White and Black population counts in areal unit i, respectively, and CW and CB are the composite White and Black population counts for the entire study area, respectively. This index is the local spatial version of the popular D.
where pik is the population count of mutually exclusive group k in areal unit i (for example, White, Black, Hispanic, … n), and ti is the population count of total population in areal unit i. This index is the local aspatial version of the popular H. To derive the spatial version of this index, the local spatial diversity index (SHi ), all population counts are replaced by their respective composite population counts—
where cpik is the composite population count of mutually exclusive group k in areal unit i (for example, White, Black, Hispanic, … n), and cti is the composite population count of total population in areal unit i. This index is the local spatial version of the popular H.
To demonstrate the use of these four local segregation indexes, they were computed in R (R Core Team, 2014) based on the 2005–2009 American Community Survey (ACS) data. Population counts by race and ethnicity at the census tract level were obtained for St. Louis (that is, St. Charles County, St. Louis County, and St. Louis City) and Chicago (that is, Cook County). Census tract data were used because they (unlike other areal units) are designed to be relatively homogeneous with respect to population characteristics, economic status, and living conditions (U.S. Census Bureau, 2014). Note that the 5-year ACS estimates are based on a larger sample size and, therefore, are more reliable than the 1- and 3-year estimates. Because census tract boundaries extend into rivers and include large ponds and lakes, such water bodies were removed when the total land area (in square kilometers) was recalculated in ArcGIS 10. The population and selected geographic characteristics of these two Midwestern U.S. cities are summarized in exhibit 2.
km = kilometers.
Derived from the Geographic Information System calculation by authors.
a Derived from the 2005–2009 American Community Survey.
b Analysis To examine the relationships of local aspatial and spatial segregation measures derived from the previous section (that is, Di, Hi, SDi, and SHi ), two separate correlation statistics (Friendly, 2002) were computed in R (Wright, 2012) for St. Louis (exhibit 3a) and Chicago (exhibit 3b). Correlations and scatterplot matrixes were used to display the relationships. The upper off-diagonal panels show the correlation coefficients with associated 95-percent confidence intervals (in parentheses), and the lower off-diagonal panels show the scatter plots.
Correlations of Local Aspatial and Spatial Segregation Measures in Two Midwestern U.S. Cities: (a) St. Louis and (b) Chicago Note: Data represent 340 census tracts in St. Louis and 1,327 census tracts in Chicago.
As a way to understand the spatial patterns of racial and ethnic groups, the geographic distributions of local aspatial and spatial segregation measures are shown in maps for St. Louis (exhibit 4) and Chicago (exhibit 5). For demonstration purposes, the geographical distributions of percent White, Black, Hispanic, and Asian are also shown in maps for St. Louis (exhibit 6) and Chicago (exhibit 7). In these four maps, a quantile classification scheme was used to display the levels of segregation.
Exhibit 4 Geographic Distributions of Local Aspatial and Spatial Segregation Measures in St. Louis
Results As illustrated in exhibit 1, the basic principle of the composite population count uses the function cij (.) to remove the enumeration boundaries as the absolute barriers for intergroup interaction by aggregating population counts across adjacent (or contiguous) neighborhoods. Such operation provides a more realistic portrayal of the spatial (and thus social) interaction among neighbors in their place of residence than that of such interaction to occur only within the confined unit boundary (that is, colored cells on the right versus left).
The two Midwestern U.S. cities were examined because they are in the same geographic region with similar total areas, but they have different population characteristics (exhibit 2). In St. Louis, about 70.0 percent of the population was White and 23.3 percent was Black. In Chicago, however, the population was composed of fewer White residents relatively (45.2 percent), about the same proportion of Black residents (25.3 percent), and a larger proportion of Hispanic residents (22.5 percent). The proportion of the Asian population was slightly larger in Chicago (5.6 percent) than it was in St. Louis (2.6 percent).
Exhibit 3 displays the relationships between the local aspatial and spatial segregation measures in St. Louis (exhibit 3a) and Chicago (exhibit 3b). Overall, similar trends can be seen in the two cities. Comparing local aspatial segregation measures with their spatial counterparts, Di and Hi are moderately and positively correlated with SDi (r = 0.76 in St. Louis and r = 0.73 in Chicago) and SHi (r = 0.78 in St. Louis and r = 0.79 in Chicago), respectively; scatterplot matrixes also suggest modest linear associations but relatively high degrees of variation between the two types of measures in the two cities. As explained previously, such differences are attributable to the incorporation of the function cij (.) or the lack thereof (exhibit 1). Moreover, in comparison with dissimilarity and diversity measures, both Di and SDi are weakly, but negatively correlated (or not correlated) with Hi and SHi (-0.27 ≤ r ≤ -0.38 in St. Louis and -0.33 ≤ r ≤ -0.39 in Chicago); the only exception here is that SDi is moderately, but negatively, correlated with SHi (r = -0.54) in Chicago.