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

Spatial measures

Able to capture different scales of segregation Depict different patters of residential segregation

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

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

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)

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

(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

(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)

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

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

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

Local dissimilarity index - Income(Gaussian function – bandwidth = 400 m)

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

Isolation of householders with more than 20 m.w.

(Gaussian function, bandwidth = 400 m)

INCREASE

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?

Compute local exposure/isolation indices using 12 different bandwidths (100 to 10000 meters)

Variable: head of household income/education (2000)

Local isolation index (Gaussian function – bandwidth = 6000 m)

Income higher than 20 mw Income inferior to 2 mw

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

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

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

Multi-Scale Analyses Using Spatial Measures of Segregation Flávia Feitosa New Frontiers in the...

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