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Segregation Measurement, Inferential Statistics, and Decomposition Analysis


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Segregation Analysis, Inference, and Decomposition with PySAL

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The PySAL segregation package is a tool for analyzing patterns of urban segregation. With only a few lines of code, segregation users can

Calculate over 40 segregation measures from simple to state-of-the art, including:

Test whether segregation estimates are statistically significant:

Decompose segregation comparisons into

  • differences arising from spatial structure
  • differences arising from demographic structure


Released versions of segregation are available on pip and anaconda


pip install segregation


conda install -c conda-forge segregation

You can also install the current development version from this repository

download anaconda:

cd into the directory and run the following commands

conda env create -f environment.yml
conda activate segregation
python develop

Getting started

For a complete guide to the segregation API, see the online documentation.

For code walkthroughs and sample analyses, see the example notebooks

Calculating Segregation Measures

Each index in the segregation module is implemented as a class, which is built from a pandas.DataFrame or a geopandas.GeoDataFrame. To estimate a segregation statistic, a user needs to call the segregation class she wishes to estimate, and pass three arguments:

  • the DataFrame containing population data
  • the name of the column with population counts for the group of interest
  • the name of the column with the total population for each enumeration unit

Every class in segregation has a statistic and a core_data attributes. The first is a direct access to the point estimation of the specific segregation measure and the second attribute gives access to the main data that the module uses internally to perform the estimates.

Single group measures

If, for example, a user was studying income segregation and wanted to know whether high-income residents tend to be more segregated from others. This user may want would want to fit a dissimilarity index (D) to a DataFrame called df to a specific group with columns like "hi_income", "med_income" and "low_income" that store counts of people in each income bracket, and a total column called "total_population". A typical call would be something like this:

from segregation.aspatial import Dissim
d_index = Dissim(df, "hi_income", "total_population")

To see the estimated D in the first generic example above, the user would have just to run d_index.statistic to see the fitted value.

If a user would want to fit a spatial dissimilarity index (SD), the call would be nearly identical, save for the fact that the DataFrame now needs to be a GeoDataFrame with an appropriate geometry column

from segregation.spatial import SpatialDissim
spatial_index = SpatialDissim(gdf, "hi_income", "total_population")

Some spatial indices can also accept either a PySAL W object, or a pandana Network object, which allows the user full control over how to parameterize spatial effects. The network functions can be particularly useful for teasing out differences in segregation measures caused by two cities that have two very different spatial structures, like for example Detroit MI (left) and Monroe LA (right):

For point estimation, all single-group indices available are summarized in the following table:

Measure Class/Function Spatial? Specific Arguments
Dissimilarity (D) Dissim No -
Gini (G) GiniSeg No -
Entropy (H) Entropy No -
Isolation (xPx) Isolation No -
Exposure (xPy) Exposure No -
Atkinson (A) Atkinson No b
Correlation Ratio (V) CorrelationR No -
Concentration Profile (R) ConProf No m
Modified Dissimilarity (Dct) ModifiedDissim No iterations
Modified Gini (Gct) ModifiedGiniSeg No iterations
Bias-Corrected Dissimilarity (Dbc) BiasCorrectedDissim No B
Density-Corrected Dissimilarity (Ddc) DensityCorrectedDissim No xtol
Minimun-Maximum Index (MM) MinMax No
Spatial Proximity Profile (SPP) SpatialProxProf Yes m
Spatial Dissimilarity (SD) SpatialDissim Yes w, standardize
Boundary Spatial Dissimilarity (BSD) BoundarySpatialDissim Yes standardize
Perimeter Area Ratio Spatial Dissimilarity (PARD) PerimeterAreaRatioSpatialDissim Yes standardize
Distance Decay Isolation (DDxPx) DistanceDecayIsolation Yes alpha, beta, metric
Distance Decay Exposure (DDxPy) DistanceDecayExposure Yes alpha, beta, metric
Spatial Proximity (SP) SpatialProximity Yes alpha, beta, metric
Absolute Clustering (ACL) AbsoluteClustering Yes alpha, beta, metric
Relative Clustering (RCL) RelativeClustering Yes alpha, beta, metric
Delta (DEL) Delta Yes -
Absolute Concentration (ACO) AbsoluteConcentration Yes -
Relative Concentration (RCO) RelativeConcentration Yes -
Absolute Centralization (ACE) AbsoluteCentralization Yes -
Relative Centralization (RCE) RelativeCentralization Yes -
Relative Centralization (RCE) RelativeCentralization Yes -
Spatial Minimun-Maximum (SMM) SpatialMinMax Yes network, w, decay, distance, precompute

Multigroup measures

segregation also facilitates the estimation of multigroup segregation measures.

In this case, the call is nearly identical to the single-group, only now we pass a list of column names rather than a single string; reprising the income segregation example above, an example call might look like this

from segregation.aspatial import MultiDissim
index = MultiDissim(df, ['hi_income', 'med_income', 'low_income'])

Available multi-group indices are summarized in the table below:

Measure Class/Function Spatial? Specific Arguments
Multigroup Dissimilarity MultiDissim No -
Multigroup Gini MultiGiniSeg No -
Multigroup Normalized Exposure MultiNormalizedExposure No -
Multigroup Information Theory MultiInformationTheory No -
Multigroup Relative Diversity MultiRelativeDiversity No -
Multigroup Squared Coefficient of Variation MultiSquaredCoefficientVariation No -
Multigroup Diversity MultiDiversity No normalized
Simpson’s Concentration SimpsonsConcentration No -
Simpson’s Interaction SimpsonsInteraction No -
Multigroup Divergence MultiDivergence No -

Local measures

Also, it is possible to calculate local measures of segregation. A statistics attribute will contain the values of these indexes. Note: in this case the attribute is in the plural since, many statistics are fitted, one for each enumeration unit Local segregation indices have the same signature as their global cousins and are summarized in the table below:

Measure Class/Function Spatial? Specific Arguments
Location Quotient MultiLocationQuotient No -
Local Diversity MultiLocalDiversity No -
Local Entropy MultiLocalEntropy No -
Local Simpson’s Concentration MultiLocalSimpsonConcentration No -
Local Simpson’s Interaction MultiLocalSimpsonInteraction No -
Local Centralization LocalRelativeCentralization Yes -

Testing for Statistical Significance

Once the segregation indexes are fitted, the user can perform inference to shed light for statistical significance in regional analysis. The summary of the inference framework is presented in the table below:

Inference Type Class/Function Function main Inputs Function Outputs
Single Value SingleValueTest seg_class, iterations_under_null, null_approach, two_tailed p_value, est_sim, statistic
Two Values TwoValueTest seg_class_1, seg_class_2, iterations_under_null, null_approach p_value, est_sim, est_point_diff

Another useful analysis that can be performed with the segregation module is a decompositional approach where two different indexes can be broken down into their spatial component (c_s) and attribute component (c_a). This framework is summarized in the table below:

Framework Class/Function Function main Inputs Function Outputs
Decomposition DecomposeSegregation index1, index2, counterfactual_approach c_a, c_s

In this case, the difference in measured D statistics between Detroit and Monroe is attributable primarily to their demographic makeup, rather than the spatial structure of the two cities. (Note, this is to be expected since D is not a spatial index)


PySAL-segregation is under active development and contributors are welcome.

If you have any suggestion, feature request, or bug report, please open a new issue on GitHub. To submit patches, please follow the PySAL development guidelines and open a pull request. Once your changes get merged, you’ll automatically be added to the Contributors List.


If you are having issues, please talk to us in the gitter room.


The project is licensed under the BSD license.


Award #1831615 RIDIR: Scalable Geospatial Analytics for Social Science Research

Renan Xavier Cortes is grateful for the support of Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazil (CAPES) - Process number 88881.170553/2018-01


To cite segregation, we recommend the following

  author       = {Renan Xavier Cortes and
                  eli knaap and
                  Sergio Rey and
                  Wei Kang and
                  Philip Stephens and
                  James Gaboardi and
                  Levi John Wolf and
                  Antti Härkönen and
                  Dani Arribas-Bel},
  title        = {PySAL/segregation: Segregation Analysis, Inference, & Decomposition},
  month        = feb,
  year         = 2020,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3265359},
  url          = {}