1. Multi-Scale Analyses Using Spatial Measures of Segregation Flávia Feitosa New Frontiers in the Field of Segregation Measurement and Analysis Monte Verita, July 1-6 2007

2. Residential Segregation Measures: Why?

3. Brazilian Patterns of Segregation  Up to the 1980 ’ s  “ Center-Periphery pattern ”  Macrosegregation Wealthy Center Poor Periphery  Nowadays  Not so simple  Macrosegregation  Sectorial: wealthy axis expanding into a single direction  At smaller scales  Slums (favelas)  Gated communities

4. So many demands…  Spatial measures  Able to overcome the checkerboard problem

5. So many demands…  Spatial measures  Able to capture different scales of segregation  Depict different patters of residential segregation

6. So many demands…  Spatial measures  Able to capture different scales of segregation  Global and local measures  Global: show the segregation degree of the whole city  Local: depict segregation in different areas of the city, can be visualized as maps

7. So many demands…  Spatial measures  Able to capture different scales of segregation  Global and local measures  Different dimensions of segregation  Massey and Denton (1998): evenness, exposure, clustering, centralization, and concentration  Reardon and O ’ Sullivan (2004): all dimensions are spatial Evenness/Clustering: Balance of the population groups distribution Exposure/Isolation: Chance of having members from different groups living side-by-side

8. So many demands…  Spatial measures  Able to capture different scales of segregation  Global and local measures  Different dimensions of segregation  Interpretation of measures / Validation  How to interpret the result of the measures?  Do they indicate a segregated city or not?  Grid problem

9. Spatial Segregation Measures  An urban area has different localities, places where people live and exchange experiences with the neighbors Key issue for segregation studies Measure the intensity of exchanges/contact amongst different population groups Vary according to the distance (given a suitable concept of distance)

10. Spatial Segregation Measures Population characteristics of a locality   Local population intensity of a locality j  Kernel estimator placed on the centroid of the areal unit j  Computes a geographically-weighted population average that takes into account the distance between groups  Weights are given by the choice of the function and bandwidth of kernel estimator LOCAL POPULATION INTENSITY

11. Global Segregation Measures Global Segregation Measures 1) Generalized Dissimilarity Index   Measures the average difference between the population composition of the localities and the population composition of whole city  Varies between 0 and 1 (max. segregation)  Evenness/clustering dimension (Sakoda, 1981)

12. Global Segregation Measures Global Segregation Measures 2) Neighbourhood Sorting Index   Total variance of a variable X = between-area variance + intra-area variance  High between-areas variance  High segregation  Spatial version: proportion of variance between different localities that contributes to the total variance of X in the city.  Evenness/clustering dimension  Good for socioeconomic studies (continuous data) (Jargowsky, 1996)

13. 3) Exposure Index of group m to n   Average proportion of group n in the localities of each member of group m  Ranges from 0 to 1 (max. exposure)  Results depend of the overall composition of the city  Exposure/isolation dimension Global Segregation Measures Global Segregation Measures (Bell, 1954)

14. 4) Isolation Index of group m   Particular case of exposure index  Expresses the exposure of group m to itself.  Ranges from 0 to 1 (max. isolation)  Exposure/isolation dimension Global Segregation Measures Global Segregation Measures (Bell, 1954)

15. Local Measures of Segregation Local Measures of Segregation  Decomposition of spatial measures  Local Measures: able to show how much each unit contributes to the global segregation measure  Display as maps  Observe segregation degree in different points of the city  Detect segregation patterns  Understand the results of global indices

16. Validation of Segregation Indices Validation of Segregation Indices  Hard to interpret the magnitude of values obtained from segregation measurement Do they indicate a segregated population distribution?  Values are sensitive to the scale of data (grid problem)  Not possible to have a fixed threshold that asserts whether the results indicate a segregated situation  For an insight in this direction:  random permutation test (Anselin 1995)

17. Validation of Segregation Indices Validation of Segregation Indices  Random permutation test  Randomly permute the population data to produce spatially random layouts  Compute the spatial segregation index for each random layout  Build an empirical distribution and compare with the index computed for the original dataset

18. Validation of Segregation Indices Validation of Segregation Indices  Empirical example?  Interesting for exposure indices  Real examples where the degree of exposure between groups is lower, equal, or higher than random arrangements.  In practice, pseudo-significance level (p-value)  Low p-value = significant index Number of simulated statistics that are > or = than the original Total number of random permutations

19. Nonspatial X Spatial Measures Nonspatial X Spatial Measures Generalized Dissimilarity Index Nonspatial 1 1 0 Spatial 0.86 0.05 0 Neighbourhood Sorting Index Nonspatial 1 1 0 Spatial 0.82 0.07 0 (p-value = 0.01) (p-value = 1)

20. Nonspatial X Spatial Measures Nonspatial X Spatial Measures Dissimilarity Index Nonspatial Dissimilarity Index Spatial

21. Case Study: São José dos Campos Case Study: São José dos Campos  Segregation in São José dos Campos, SP, Brazil (1991 – 2000)  Urban population: 425.132 (1991) and 532.717 (2000)  Socio-economic variables: income and education

22. Case Study: São José dos Campos Case Study: São José dos Campos  Segregation indices computed with Gaussian kernel estimators and 8 different bandwidths (from 200m to 4400m) Gaussian function, bandwidth = 400 m Gaussian function, bandwidth = 2000 m

23. São José dos Campos Dimension evenness/clustering Generalized Dissimilarity Index & Neighborhood Sorting Index  All results were significant (p-value = 0,01) INCOME (1991-2000)  Both indices indicate the same trend  Increase in segregation – all scales

24. São José dos Campos Dimension evenness/clustering Generalized Dissimilarity Index & Neighborhood Sorting Index  All results were significant (p-value = 0,01) EDUCATION (1991-2000)  Larger scales: increase in segregation  Smaller scales: decrease in segregation

25. São José dos Campos Dimension evenness/clustering Local dissimilarity index - Income (Gaussian function – bandwidth = 400 m)

26. São José dos Campos Dimension exposure/isolation Spatial Isolation Index –  Remarkable isolation of head of households with income greater than 20 minimum wages  Increased during period 1991-2000  Example bw = 400 m  4X superior than the proportion of the group in the city

27. São José dos Campos Dimension exposure/isolation Isolation of householders with more than 20 m.w. (Gaussian function, bandwidth = 400 m) INCREASE

28. São José dos Campos Dimension exposure/isolation Isolation of “better of” families (Gaussian function, bandwidth = 400 m)

29. São José dos Campos Dimension exposure/isolation Isolation of “better of” families (Gaussian function, bandwidth = 400 m)

30. Case Study II: São Paulo Case Study II: São Paulo  City with more than 11 million people  Metropolitan area: more than 19 million (fifth most populous metropolitan area in the world)

31. São Paulo X Violence  Homicides in Sao Paulo  Homicides in 2000 : 6,091  Decrease more than 3 years of life expectancy (1999-2004)

32. Homicides X Segregation  Most of homicides occur in poor areas What about the combination of poverty and segregation?  How is segregation (poverty concentration) associated to homicides?  Which scales of segregation are the most related to homicides?

33. Homicides X Segregation  Compute local exposure/isolation indices using 12 different bandwidths (100 to 10000 meters)  Variable: head of household income/education (2000)

34. Homicides X Segregation Local isolation index (Gaussian function – bandwidth = 6000 m) Income higher than 20 mw Income inferior to 2 mw

35. Homicides X Segregation Homicides in 2000 (Density surfaces) By place of residence By place of occurrence

36. Homicides X Isolation  Isolation of head of households (HoH) with HIGH-INCOME/EDUCATION  Very similar results for income and education  Negative correlation: Increase in isolation of HoH with high- income/education is related to lower homicides rates  Vulnerability to homicides is smaller at large scales BY PLACE OF OCCURENCE BY PLACE OF RESIDENCE

37. Homicides X Isolation  Isolation of HoH with LOW-INCOME/EDUCATION  Positive correlation: an increase in the isolation of HoH with low-income/education is related to higher homicides rates  Results are more constant: correlation increases till bw = 2000 m  Vulnerability to homicides is smaller at small scales BY PLACE OF OCCURENCE BY PLACE OF RESIDENCE

38. Homicides X Exposure  Exposure of HoH with LOW-INCOME/EDUCATION to HoH with HIGH-INCOME/EDUCATION  Measures the average proportion of high-income/education families in the localities of each family with low-income/education  Small bandwidths: negative correlation  Larger bandwidths: positive correlation BY PLACE OF OCCURENCE BY PLACE OF RESIDENCE

39. Homicides X Exposure  Exposure of HoH with HIGH-INCOME/EDUCATION to HoH with LOW-INCOME/EDUCATION  Correlation is always negative  More constant through different scales BY PLACE OF OCCURENCE BY PLACE OF RESIDENCE

40. Final Remarks Final Remarks  Potentiality of multi-scale analysis using segregation indices  São José dos Campos  Detecting/understand patterns of the phenomenon  Trends of segregation along the time  São Paulo  Understand how different scales of segregation are related to other intra-urban indicators  E.g., poor families are less vulnerable to homicides when not segregated at larger scales/ exposed to high-status families at smaller scale.

41. Thank you for the attention!!!

42. Multi-Scale Analyses Using Spatial Measures of Segregation Flávia Feitosa New Frontiers in the Field of Segregation Measurement and Analysis Monte Verita, July 1-6 2007

43. Residential Segregation Measures: Why?  Monitor the phenomenon through time  Identify trends  Understand segregation better  Identify different patterns of segregation and see their relationship with other urban indicators (unemployment, violence, etc.)  Guide/evaluate dynamic models  Evaluate scenarios resulting from different urban policies