Indices of residential segregation: a short overview

Today, segregation indices are well-known and increasingly used in urban studies. This is hardly surprising, since segregation indices make it possible: "1) to qualify and compare the distribution in the metropolitan area of population groups that differ in ethnic origin, birth country or region, mother tongue, visible minority status, and income, 2) to compare cities, and 3) to complete diachronic analyses" (Apparicio et al., 2008: 2).

The five dimensions of residential segregation

In a seminal paper on residential segregation indices, Massey and Denton (1988) classify them into five distinct dimensions: evenness, exposure, concentration, clustering and centralization (see Table below).

The five dimension of residential segregation
Dimension Description
  Adapted from Martori and Apparicio (2011).
  Evenness Evenness refers to the distribution of one or more population groups across the spatial units of the metropolitan area (e.g., census tracts). Evenness indices measure a group’s over- or under-representation in the spatial units of a metropolitan area: The more unevenly a population group is distributed across these spatial units, the more segregated it is.
  Exposure Exposure is the degree of potential contact between members of the same group (one group) or between members of two groups (intergroup) inside spatial units. It measures the probability that members of one group will encounter members of their own group (isolation) or another group (interaction) in their spatial unit.
  Concentration Concentration refers to the physical space occupied by a group. The less of the metropolitan area a group occupies, the more concentrated it is. According to Massey and Denton (1988), segregated minorities generally occupy a small portion of metropolitan areas.
  Clustering Other indices measure clustering. The more contiguous spatial units a group occupies—thereby forming an enclave within the city—the more clustered and therefore segregated it is, according to this dimension.
  Centralization Finally, centralization indices measure the degree to which a group is located near and in the center of the metropolitan area, which is usually defined as the central business district. The closer a group is to the city center, the more centralized and thus segregated it is according to this dimension.

For each dimension, three distinct types of indices are usually identified:

  • One-group indices that measure the distribution of a population group compared to the total population;
  • Two-group indices that compare the distribution of a population group to another;
  • Multigroup indices that analyze the distribution of several population groups simultaneously.

In addition, it is possible to map other indices, in particular:

  • The location quotient which is useful for identifying spatial units in a metropolitan area where a population group is under-represented (LQ > 1) or conversely, over-represented (LQ < 1);
  • The entropy or diversity index which is useful for identifying spatial units that are completely homogenous (inhabited by only one population group, H2 = 0) or maximally diversified (all population groups are equal in size, H2 = 1);
  • The typology proposed by Poulsen et al. (2001, 2002) which classifies the spatial units of a metropolitan area (e.g. census tracts) into six categories based on the percentages of the ethnic minorities and of the host society in the local population.

 

Indices implemented in Geo-Segregation Analyzer

One-group indices implemented in Geo-Segregation Analyzer
Dimension   Name Abbreviation Values Authors
 Adapted from Massey and Denton (1988), Apparicio (2000) and Apparicio et al. (2008).
Evenness 1. Segregation index IS [0,1] Duncan and Duncan (1955a, 1955b)
  2. Segregation index adjusted for tract contiguity IS(adj) [0,1] Morrill (1991)
  3. Segregation index adjusted for contiguous tract boundary lengths IS(w) [0,1] Wong (1993)
  4. Segregation index adjusted for contiguous tract boundary lengths and perimeter/area ratio IS(s) [0,1] Wong (1993)
  5. Entropy index H [0,1] Theil (1972), Theil and Finezza (1971)
  6. Gini index G [0,1] Duncan and Duncan (1955a)
  7. Atkinson index with b =0.1 A(0.1) [0,1] Atkinson (1970)
  8. Atkinson index with b =0.5 A(0.5) [0,1] Atkinson (1970)
  9. Atkinson index with b =0.9 A(0.9) [0,1] Atkinson (1970)
Exposure 10. Isolation index xPx [0,1] Bell (1954)
   11. Correlation ratio Eta2 [0,1] Bell (1954), White (1986)
Concentration 12. Delta index DEL [0,1] Hoover (1941), Duncan et al. (1961)
   13. Absolute concentration index ACO [0,1] Massey and Denton (1988)
 Clustering 14. Absolute clustering index ACL [0,1] Massey and Denton (1988) adapted from Geary (1954) and Dacey (1968)
15. Mean proximity between members of group X Pxx [0,∞] Massey and Denton (1988)
16. Mean proximity between members of group X (exp dij) Pxx Exp(dij) [0,∞] Massey and Denton (1988)
17. The distance-decay isolation index DPxx [0,1] Morgan (1983)
 Centralization 18. Proportion in Central City PCC [0,1] Massey and Denton (1988)
   19. Absolute centralization index ACE [-1,1] Massey and Denton (1988)

 

Two-group indices implemented in Geo-Segregation Analyzer
Dimension   Name Abbreviation Values Authors
 Adapted from Massey and Denton (1988), Apparicio (2000) and Apparicio et al. (2008).
 Evenness 20. Index of dissimilarity ID [0,1] Duncan and Duncan (1955a, 1955b)
  21. Dssimilarity index adjusted for tract contiguity Id(adj) [0,1] Wong (1993)
  22. Dssimilarity index adjusted for contiguous tract boundary lengths Id(w) [0,1] Wong (1993)
  23. Dssimilarity index adjusted for contiguous tract boundary lengths and perimeter/area ratio Id(s) [0,1] Wong (1993)
  24. Deviational ellipse index S [0,1] Wong (1999)
Exposure 25. Interaction index xPy [0,1] Bell (1954)
Concentration 26. Relative concentration index RCO [-1,1] Massey and Denton (1988)
Clustering
27. Mean proximity between members of group X and members of group Y Pxy [0,∞] White (1986)
28. Mean proximity between members of group X and members of group Y (exp dij) Pxy Exp(dij) [0,∞] White (1986)
29. Spatial proximity index SP [0,1] White (1986)
30. Relative clustering index RCL [-,∞,∞] White (1986)
  31. The distance-decay isolation index DPxy [0,1] Morgan (1983)
Centralization 32. Relative centralization index RCE [-1,1] Duncan and Duncan (1955b)

 

Multigroup indices implemented in Geo-Segregation Analyzer
Dimension   Name Abbreviation Values Authors
 Adapted from Reardon and Firebaugh (2002) and Apparicio et al. (2008).
 Evenness 33. Multigroup dissimilarity index D [0,1] Morgan (1975), Sakoda (1981)
  34. Multigroup Gini index G [0,1] Reardon (1998)
  35. Information theory index (entropy index) H [0,1] Theil (1972), Theil and Finezza (1971)
  36. Squared coefficient of variation C [0,1] Reardon and Firebaugh (2002)
  37. Deviational ellipse index S [0,1] Wong (1999)
  38. Spatial version of multigroup dissimilarity index SD [0,1] Wong (1999)
Exposure 39. Normalized exposure P [0,1] James (1986)
  40. Relative diversity R [0,1] Carlson (1992), Goodman and Kruskal (1954), Reardon (1998)

 

Local indices implemented in Geo-Segregation Analyzer
    Name Abbreviation Values Authors
 Adapted from Apparicio et al. (2008).
  41. Location Quotient QL [0,∞] Isard (1960)
  42. Entropy (diversity) measure H2 [0,1] Theil (1972), Theil and Finezza (1971)
  43. Poulsen et al. typology Poulsen [1,6] Poulsen et al. (2001, 2002)
License

Geo-Segregation Analyzer is an open source project licensed under the: