«Urban Problems and sPatial methods VolUme 17, nUmber 1 • 2015 U.S. Department of Housing and Urban Development | Office of Policy Development and ...»
Exhibit 4 (for St. Louis) and exhibit 5 (for Chicago) show that results of correlation analysis in exhibits 3a and 3b, respectively, are manifested spatially in the two cities. By comparing the geographical distributions of Di with SDi (4a versus 4b and 5a versus 5b), as well as Hi with SHi (4c versus 4d and 5c versus 5d), it is clear that local aspatial segregation measures and their spatial counterparts do not exactly resemble similar spatial patterns; noticeably, SDi (4b and 5b) and SHi (4d and 5d) show much “smoother” spatial patterns and lower segregation levels than Di (4a and 5a) and Hi (4c and 5c), respectively. In addition, neither the geographical distributions of Di (4a and 5a) nor SDi (4b and 5b) are the opposite of Hi (4c and 5c) and SHi (4d and 5d). Put differently, areas with the highest (or lowest) values of Di and SDi do not always correspond to the lowest (or highest) values of Hi and SHi in the two cities.
As emphasized earlier, percentages of racial and ethnic groups should not be used as a measure of segregation, because the geographical distributions of percent White, Black, Hispanic, and Asian cannot quantify how different population groups are distributed across areal units. For example, in St. Louis, areas with higher percentages of White (exhibit 6a), Black (exhibit 6b), Hispanic (exhibit 6c), and Asian (exhibit 6d) residents coincide in the central, northwestern, and lower eastern parts of
Cityscape 107Oka and Wong
St. Louis. Similarly in Chicago, areas with higher percentages of White (exhibit 7a), Black (exhibit 7b), Hispanic (exhibit 7c), and Asian (exhibit 7d) residents coincide along the shore of Lake Michigan and in the northern, central, and southern parts of Chicago. Taken together, a higher percentage of a racial/ethnic group could refer to both a racially/ethnically dominated and diverse (or integrated) neighborhood in the two cities. More importantly, simple percentages can capture the within-unit relationships, but they cannot capture the between-unit relationships as modeled in spatial segregation measures. Despite their simplicity, both exhibits 6 and 7 demonstrate that the percentage of racial/ethnic groups is not an appropriate measure of segregation (Johnston, Poulsen, and Forrest, 2007; Massey and Denton, 1988; Massey, White, and Phua, 1996; Reardon and O’Sullivan, 2004).
Discussion A series of correlation and visual analysis of St. Louis and Chicago (exhibits 3 through 7) leads to two main conclusions: (1) local spatial segregation measures (SDi and SHi) produce a “smoother” spatial pattern and lower segregation levels than their aspatial counterparts (Di and Hi, respectively), and (2) the two-group-based dissimilarity measures (Di and SDi) do not capture the local variation of segregation as the multiple-group-based diversity measures (Hi and SHi) do (aspatial and spatial alike). These results, in turn, highlight two important remarks about the measurement of segregation.
For the first remark, the difference between aspatial and spatial approaches to measure segregation reflects the recent methodological achievements. Most segregation indexes introduced in the early era of developing segregation measures are aspatial in nature (for example, Morrill, 1991; White, 1983; Wong, 1993). A typical example used to demonstrate the aspatial nature is a checkerboard pattern in which each cell is dominated by only one group and cells are arranged in a spatially alternate manner. Calculating D for such a pattern produces a value of 1, indicating perfect segregation. Clustering together all cells that belong to one group, creating a perceivably more segregated pattern, will also produce a D value of 1. The bottom line is that D does not consider the spatial relationship of population distribution and, thus, exaggerates segregation levels. A similar demonstration can be conducted for H. To overcome this limitation, existing measures were modified to incorporate spatial information into the formulations so that these spatial versions of the indexes consider the spatial distributions of different population groups.
A common approach is to include populations in the neighboring units when evaluating the population characteristics of a unit (Feitosa et al., 2007; Reardon and O’Sullivan, 2004; Wong, 2008, 2002). Doing so implicitly allows for the mixing of neighboring populations, removing the artificial boundaries between units in separating the populations. Both Reardon and O’Sullivan (2004) and Feitosa et al. (2007) adopted the fancy concept of a spatial kernel to derive the weights to count populations in the neighboring units toward the reference unit. The kernel implements the distance decay concept so that population at and near the reference unit will be counted more and populations in farther away units will be counted less. Nevertheless, the basic principle of using the simplistic composite population count (Wong, 2008, 2002) or the elegant spatial kernels is the same. Because local spatial segregation measures (compared with their aspatial counterparts) provide a more realistic portrayal of the spatial (and thus social) interaction among neighbors, future studies should consider using local spatial segregation indexes.
Regarding the second remark, the difference between dissimilarity and diversity measures (aspatial and their spatial versions alike) warns that a careful consideration is needed before choosing the segregation index in future studies. Both D and H measure the evenness dimension of segregation.
From a conceptual standpoint, these two measures are the inverse of each other (Massey and Denton, 1988; Massey, White, and Phua, 1996). Such an expectation does not generally hold, however (exhibits 3 through 5). D has become one of the most popular measures of segregation.2 The popularity of D is, in part, induced by its easy calculation and interpretation. Also, the use of D was popularized by the strong endorsements from Massey and his colleagues (Massey and Denton, 1988; Massey, White, and Phua, 1996).3 Despite many desirable properties, the use of D in segregation studies has long been criticized for its inconsistencies with the notions of segregation (for example, Reiner, 1972; Winship, 1978;
Zelder, 1972). In fact, Cortese, Falk, and Cohen (1976) demonstrated some of the systematic biases in D nearly four decades ago. More recently, a major concern of D raised by White (1983) is that the measure is insensitive to the spatial arrangement of population distribution. Simply put, by swapping the populations in any two subareas (for example, neighborhoods) within a larger region (for example, a city or a metropolitan area), the value of D will not change; D is influenced only by the population mix within each areal unit and does not consider who are “next” to each other. On the other hand, H has been determined to be a superior measure. It conceptually and mathematically satisfies the desirable decomposition properties for handling multiple population groups in segregation studies (Reardon and Firebaugh, 2002; White, 1986). Because H is global and aspatial in nature, future studies should consider using its local spatial version (that is, SHi).
In summary, local spatial segregation measures produce “smoother” spatial patterns at lower segregation levels than their aspatial counterparts, and the dissimilarity measures cannot handle multiple-group comparisons as effectively as the diversity measures. For these reasons, the use of SHi (instead of SDi) is recommended to measure the unequal or differential distributions of racial and ethnic groups (that is, the evenness dimension of segregation) in future studies.
Limitations Two challenges should be considered when using SHi in future studies. First, SHi captures only the evenness dimension of segregation that Massey and Denton (1988) claimed to be the most important dimension of segregation. It fails to evaluate another important and distinct dimension of segregation, however—isolation (that is, the potential interaction of population groups; Johnston, Poulsen, and Forrest, 2007; Reardon and O’Sullivan, 2004). The isolation index (P*) (Lieberson,
1981) has been regarded as the standard index to measure isolation. Wong (2008, 2002) introduced the local spatial version of P*, denoted as the local spatial isolation index (Si). Although the detailed explanation of Si is beyond the scope of this article, SHi and Si should be used to reflect the evenness and isolation dimensions of segregation, respectively.
A search on http://www.scholar.google.com (on September 16, 2014) showed that the paper by Duncan and Duncan (1955) has been cited 1,898 times.
A search on http://www.scholar.google.com (on September 16, 2014) showed that these seminal review papers together have been cited 1,911 times (1,731 and 180 times, respectively).
Second, SHi (as well as all spatial segregation indexes) is influenced by the boundary or edge effect.
Such effect introduces bias into the identification of spatial distribution and the parameter estimates of spatial processes (Griffith, 1983). Several solutions have been proposed, but none can fully solve the problem (Griffith, 1987, 1980). One rather simple practical solution, which was not implemented in this study, is to include a buffer zone around the study area. Because the function cij (.) adopted to implement the concept of composite population involves only the immediate neighboring units (Wong, 1998), a buffer zone including the first order adjacent units along the study area will be sufficient for using SHi to measure the level of segregation.4 Conclusion The use of effective and meaningful segregation measures holds the key to examining the possible (that is, adverse, protective, or null) effects of residential segregation on its residents (Johnston, Poulsen, and Forrest, 2014). Otherwise, only limited (if not biased) knowledge can be gained to formulate potential solutions to reduce the levels of segregation, and then to inform public policies and decisionmaking. A gap between the conceptual and methodological achievements in segregation studies and their implementations in different fields is quite prevalent, however, especially among those focusing on neighborhood comparisons.
From a critical point of view, the continued uses (or misuses) of ineffective and insufficient segregation measures will substantially undermine the purposes of research and their potential contributions to inform public policies and decisionmaking. Hence, future research needs to build on the conceptual and methodological foundations of segregation studies established by demographers, geographers, and sociologists.
Authors Masayoshi Oka is a postdoctoral researcher with the Social and Cardiovascular Epidemiology Research Group in the School of Medicine at the University of Alcalá.
David W.S. Wong is a professor in the Department of Geography at the University of Hong Kong and in the Department of Geography and GeoInformation Science at George Mason University.
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Because the cij (.) function can be implemented differently (for instance, including higher order neighbors), the buffer size should be adjusted accordingly to contain the edge effect.
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