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Multi-Scale Analyses Using Spatial Measures of Segregation Flávia Feitosa New Frontiers in the...
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Multi-Scale Analyses Using Multi-Scale Analyses Using Spatial Measures of Spatial Measures of SegregationSegregation
Flávia Feitosa
New Frontiers in the Field of Segregation Measurement and AnalysisMonte Verita, July 1-6 2007
Residential Segregation Measures: Residential Segregation Measures: Why?Why?
Brazilian Patterns of Brazilian Patterns of SegregationSegregation
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
So many demands…So many demands…
Spatial measures Able to overcome the checkerboard problem
So many demands…So many demands…
Spatial measures
Able to capture different scales of segregation Depict different patters of residential segregation
So many demands…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
So many demands…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
So many demands…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
Spatial Segregation MeasuresSpatial Segregation Measures
An urban area has different localities, places where people live and exchange experiences with the neighbors
Key issue for segregation studiesMeasure the intensity of exchanges/contact
amongst different population groups
Vary according to the distance (given a suitable concept of distance)
Spatial Segregation MeasuresSpatial 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
Global Segregation MeasuresGlobal 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)
Global Segregation MeasuresGlobal 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)
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 MeasuresGlobal Segregation Measures
(Bell, 1954)
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 MeasuresGlobal Segregation Measures
(Bell, 1954)
Local Measures of SegregationLocal Measures of Segregation
Decomposition of spatial measures
Local Measures: able to show how much each unit contributes to the global segregation measure
Display as mapsObserve segregation degree in different
points of the cityDetect segregation patternsUnderstand the results of global indices
Validation of Segregation IndicesValidation 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)
Validation of Segregation IndicesValidation 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
Validation of Segregation IndicesValidation 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
Nonspatial X Spatial MeasuresNonspatial X Spatial Measures
Generalized Dissimilarity IndexNonspatial 1 1 0Spatial 0.86 0.05 0
Neighbourhood Sorting IndexNonspatial 1 1 0Spatial 0.82 0.07 0
(p-value = 0.01)
(p-value = 0.01) (p-value = 1)
(p-value = 1)
Nonspatial X Spatial MeasuresNonspatial X Spatial Measures
Dissimilarity Index
Nonspatial
Dissimilarity Index
Spatial
Case Study: São José dos Case Study: São José dos CamposCampos
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
Case Study: São José dos Case Study: São José dos CamposCampos
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
São José dos CamposSão José dos Campos
Dimension evenness/clusteringDimension 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
São José dos CamposSão José dos Campos
Dimension evenness/clusteringDimension 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
São José dos CamposSão José dos Campos
Dimension evenness/clusteringDimension evenness/clustering
Local dissimilarity index - Income(Gaussian function – bandwidth = 400 m)
São José dos CamposSão José dos Campos
Dimension exposure/isolationDimension 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
São José dos CamposSão José dos Campos
Dimension exposure/isolationDimension exposure/isolation
Isolation of householders with more than 20 m.w.
(Gaussian function, bandwidth = 400 m)
INCREASE
São José dos CamposSão José dos Campos
Dimension exposure/isolationDimension exposure/isolation
Isolation of “better of” families(Gaussian function, bandwidth = 400 m)
São José dos CamposSão José dos Campos
Dimension exposure/isolationDimension exposure/isolation
Isolation of “better of” families(Gaussian function, bandwidth = 400 m)
Case Study II: São PauloCase 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)
São Paulo X ViolenceSão Paulo X Violence
Homicides in Sao Paulo Homicides in 2000 : 6,091 Decrease more than 3 years of life expectancy
(1999-2004)
Homicides X SegregationHomicides 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?
Homicides X SegregationHomicides X Segregation
Compute local exposure/isolation indices using 12 different bandwidths (100 to 10000 meters)
Variable: head of household income/education (2000)
Homicides X SegregationHomicides X Segregation
Local isolation index (Gaussian function – bandwidth = 6000 m)
Income higher than 20 mw Income inferior to 2 mw
Homicides X SegregationHomicides X Segregation
Homicides in 2000 (Density surfaces)
By place of residence By place of occurrence
Homicides X IsolationHomicides 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
Homicides X IsolationHomicides 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
Homicides X ExposureHomicides 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
Homicides X ExposureHomicides 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 OCCURENCEBY PLACE OF RESIDENCE
Final RemarksFinal 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.
Thank you for the attention!!!
Multi-Scale Analyses Using Multi-Scale Analyses Using Spatial Measures of Spatial Measures of SegregationSegregation
Flávia Feitosa
New Frontiers in the Field of Segregation Measurement and AnalysisMonte Verita, July 1-6 2007