Quantitative and Statistical Methods
A great deal of this work was conducted collaboratively with colleagues in several disciplines. The data collection was conducted in collaboration with John P. Wilson and others in the GIS Lab and Spatial Sciences Institute of USC. The statistical analyses of demographic change and segregation were conducted in collaboration with Dowell Myers and others in the USC Price School of Policy, Population Dynamics Laboratory.
Data: Collection, Scope, and Assembly
“Los Angeles” is a massive conurbation, numbering in 2006, 17.8 million residents in its widest definition as the Los Angeles-Riverside-Orange County Consolidated Metropolitan Statistical Area (CMSA). For consistency over a long historical period, we chose the County of Los Angeles as a reasonable boundary for “the metropolis.” The most populous county in the United States, Los Angeles County population numbered nearly 10 million in 2000 and contained 89 incorporated cities. The City of Los Angeles, with 3.8 million residents, is the largest of these. The second largest is Long Beach, with about half a million. The median city size in 2000 (represented by Rosemead) was about 55,000. The average size was 87,000.
We assembled two datasets. First, in order to generate the standard set of metro-wide segregation indices, we developed the Los Angeles County Union Census Tract Data Series, 1940-2000 (Ethington et al. 2006), which consists of tract-level data from the 1940-2000 U.S. Censuses, fitted to 2000 tract geography by area apportionment. Second, in order to conduct municipal-level analyses, we assembled another data set composed of block group data (Summary Tape File 1 in 1990 and Summary File 1 in 2000) from 1990 and 2000 for “municipal places.” We use the conventional four major race-ethnic groups, defined as: white, African American or black, Latino or Hispanic, and Asian and Pacific Islander. For our purposes here, we use the “Hispanic categorical dominance” method, which means that Hispanics can be of any race and the other 3 groups are non-Hispanic. The categorization of race for Census 2000 is particularly tricky because respondents could choose more than one race. The method used here is the “fractional apportionment of multiracials” which means that persons reporting more than one race are equally apportioned to each of the races they report (reporting 3 races, a respondent would be split .33 to each race-ethnic group).
We faced several challenges constructing the 1990-2000 municipal places dataset. First, the City of Los Angeles, with a 2000 population of nearly 4 million, is far and away the largest municipality in the county. It has an extremely irregular shape, resulting from decades of annexations and consolidations (absorption of preexisting municipalities, like Hollywood in 1910 and Watts in 1924). The Indexed Map of Los Angeles County Municipal Spaces shows the City of Los Angeles in bold black outline. A coordinate grid (x=A-Z y=1-40) is provided in this map to facilitate the location of municipal places discussed in this paper.
The City of Los Angeles is effectively fragmented into at least four distinctive territories: San Fernando Valley, which is separated from the rest of the city by the Santa Monica Mountains, the central city area (from Downtown through “South Central”; the “West Side,” an unofficial area that includes the coastal communities and Westwood and Brentwood (near UCLA) and the Los Angeles Harbor, connected to the rest by the “Shoestring Strip.” This municipal space is simply too attenuated and irregular to treat as comparable with the rest of the municipalities of the County, so we broke it into the fifteen Los Angeles city council districts as they stood in 2000. These council districts, averaging 250,000 in population, are each larger than any other city in the county except Long Beach (460,000, coordinates P-38). The shapes and scale of the Los Angeles City council districts, however, are very similar to those of the municipalities.
The other challenge we faced is that about one million Angelenos live in unincorporated County territories. Some of these spaces, like East Los Angeles, closely resemble municipalities. Others are just tiny fragments within and between the incorporated cities. Only some of these are listed as “census designated places” (CDP) by the Bureau of the Census, so they are missed by analyses using that designation. After refining our GIS map of incorporated places, unincorporated places, and LA City Council Districts, we then excluded all spaces with fewer than 10,000 inhabitants (except Malibu, population 5,308, because of its symbolic importance).
In the map, the fifteen LA City Council Districts are indicated as “LA1, LA 2, etc.” The other 77 incorporated municipalities included in the dataset are listed in order of their date of incorporation. Unincorporated municipal places (N=17), governed and serviced by the County of Los Angeles (counties are the highest level of municipality in California), are indicated as “Co 1, Co 2,” etc. The total of these municipal places is 109.
Segregation Indices
The long history of urban segregation research has undergone two major periods of re-adjustment: At the beginning of the Civil Rights movement, Duncan and Duncan (1955) settled a period of methodological confusion and established the Index of Dissimilarity as the standard tool. That standardization lasted until the mid-1970s, when the Index of Dissimilarity was shown by Cortese, Falk and Cohen (1976) to be seriously flawed, a finding confirmed by others. Among its many weaknesses, the Index of Dissimilarity cannot distinguish between single and multiple residential clusters for a group, and is insensitive to population size (the D for a population of 1,000,000 can be the same as that for a population of 100).
Consequently, by the early 1980s, more robust measures proliferated, but the agreement on a preferred index disappeared. Massey and Denton (1988), finding “the field of segregation studies…in a state of theoretical and methodological disarray, with different researchers advocating different definitions and measures of segregation” (282), deftly sorted such measures into five “dimensions” of segregation: evenness, exposure, concentration, clustering, and centralization. For each of these, they tested and advocated the most effective statistical index. They went on to postulate the condition of “hypersegregation,” for groups that score high on all five dimensions, and summarized their influential results in the landmark book American Apartheid (1993). Research since the early 1990s on residential segregation has proven highly productive, compatible, and comparable, with a broad acceptance of the five dimensions and the condition of “hypersegregation” as conceptual referents.
Because our approach in this study is to incorporate spatial scale by adopting the irregular institutional boundaries of municipal places, we do not use the three geometrically spatial dimensions of segregation: clustering, concentration, and centralization. Indices of those dimensions operate on the basis of measured distance, and that approach overlaps in confusing ways with our territorial, place-based framework. This is not to suggest that geometrically spatial methods are less effective than our place-based territorial approach to spatial scale. Indeed, we applaud the important uses of those approaches to spatial scale by other researchers. We simply propose another approach to the crucial importance of scale, within which the geometric approaches are not appropriate. We therefore focus on the other two major dimensions of segregation: evenness and exposure.
The recent re-examinations of segregation indices by Reardon and coauthors (2002, 2004) evaluated the utility of these measures for multi-group segregation and their effectiveness in spatial analyses. On the basis of a series of rigorous tests and comparisons, they conclude that the two most robust measures are the P* family of exposure/isolation indices, and the H, Entropy or Diversity index. Therefore, we utilize the Diversity Index (H) and the Exposure or Isolation Index (P*) as the basis for our analysis in describing the conditions of diversity for a given spatial setting and simultaneously, the isolation of a given group within that setting.
Diversity Index
Population diversity in a large multiethnic metropolis like Los Angeles could be classified by a wide range of categorical variables, such as language, religion, national origin, and race. For practical reasons and for comparability with most contemporary studies of residential segregation, residents are herein divided into four race-ethnic groups: Hispanic (also called Latino herein); White (always non-Hispanic herein); Asian and Pacific Islander (also called Asian and always non-Hispanic herein), and African American (also called black and always non-Hispanic herein).For the measurement of evenness, the most common tool for decades was the Index of Dissimilarity (D). The
weaknesses of that index have long been understood (Cortese, Falk and Cohen 1976). Just as important as its statistical limitations, the Index of Dissimilarity is also limited because it only operates on two paired groups at a time. The multiracial metropolis requires measures that operate robustly on more than two groups.
Instead, we have selected the H index of diversity to represent evenness of group representation within each municipal place. While there are many variants of diversity measures, the most basic and widely-used of these is the H or Shannon index. The methodological lineage of this index grew from Claude Shannon’s theories of information (Shannon 1948; Shannon and Weaver 1949), to studies of biodiversity, linguistic diversity, and studies of segregation (Lieberson 1964). Accordingly, there are many important variations and levels of sophistication available in the family of diversity indices (Thiel and Finizza 1971; Lieberson 1969). But most are built atop Shannon’s original index, which satisfies the following conditions, among others: “1) diversity should be maximized when all groups are present in equal proportions. 2) in two populations in which all groups are equally represented, the population with the greatest number of groups will be more diverse” (White 1986: 200). To avoid confusion and recognize its most common purpose, we shall refer to the Entropy (H) index as defined by White (1986) as the Diversity Index (H):
Diversity Index
There is considerable confusion about the proper name for this index. White (1986) refers to this formula as the Entropy Index, but most, including Massey and Denton (1988: 285), reserve the name “Entropy” for a modification of that formula proposed by Thiel (1972; Theil and Finizza 1971), which norms the index, gives it an upper bound of 1.0, and makes it comparable across different geographic cases. We use the simpler, unweighted version, as in the displayed formula, and use the name Diversity rather than “Entropy."
Where:
N=total population size
Nk =number of persons in Kth group
Pk = Nk/N
Isolation Index
The next main consideration is to determine, within a known context of high or low diversity, how “segregated” those groups are within each municipal place. For this purpose, we use the P* family of indices, one the biggest winners in the marathon contest between segregation indices. The P* family of indices is known both as the “exposure” (xP*y) or “isolation” (xP*x) index. The P* family of indices measures the probability that members of one group will have members of any other group (or the member’s own group) as neighbors. It is sensitive to relative population sizes, and is asymmetric (Lieberson 1981). If groups are of unequal population size (as they nearly always are), then the probability that members of group x will have group y neighbors is not the mere inverse of the probability that members of group y will have group x neighbors. As Lieberson and Carter (1982) observe, the asymmetrical and size-sensitive qualities of the P* family of indices help us to explain “why racial and ethnic groups have different perceptions about the magnitude of and trends in segregation” (1982: 296). Sensitivity to population size and direction of exposure is also of great utility for studying the changing dynamics of multiethnic metropolises. The Exposure and Isolation Index (P*) are given by Massey and Denton (1988: 288) as:Where:
xi = number of X members in the areal subunit i
yi =number of Y members in the areal subunit i
ti = Total population of number of the areal subunit i
X =Number of X members county-wide
The Isolation-Diversity Plot (IDP)
We also developed a new approach for studying metropolitan residential segregation, which accomplishes the goals we have so far identified: of capturing the spatial scale, the levels of diversity, the degree of segregation, and also categorical “types” of segregation. Additionally, this approach also allows the identification of municipal places that exhibit different types and degrees (from good to bad) of segregation. We developed the Isolation-Diversity Plot (IDP) method to measure both the degree of segregation for groups and to begin sorting the type of their segregation. The IDP rests on three basic premises: 1) That the geographic scale of “municipal place” is a crucial scale of interest, yet needing to be contextualized within its metropolis and region; 2) That the diversity of municipal places and metros is fundamental to understanding the “context” of segregation; and 3) That by pairing the diversity (H) index with the isolation (xP*x) index, the resulting analysis of municipal places can simultaneously sort the condition of a given group into clearer categories (the type of segregation experienced) and indicate the degree of segregation. It also displays the metropolitan context in a single graphic format.The Isolation-Diversity Plot charts the Diversity Index (H) for each municipal place against the isolation index (xP*x) for each group within that place, with diversity plotted along the x axis and isolation along the y axis. The schematic form of the resulting matrix is illustrated in Figure 1. The IDP displays the contextualized segregation condition of each of the race-ethnic component groups separately, stratified by the municipal places of the overall metro. Thus, if a metropolis is being analyzed by four race-ethnic groups, African-American, Asian, Hispanic, and White, stratified by 109 municipal places (as in our analyses of Los Angeles), then an IDP analysis of the entire metro by municipal places would generate four IDP charts: one chart for each race-ethnic group, and each chart composed of 109 plotted points.
Figure 1 displays four logical combinations of isolation and diversity, each representing a distinct way that a given race-ethnic group can be segregated. People live in places that are either more diverse or less diverse, and their group is either more or less isolated within those municipal places.
