# Decomposition framework of the PySAL segregation module

This is a notebook that explains a step-by-step procedure to perform decomposition on comparative segregation measures.

First, let’s import all the needed libraries.

import pandas as pd
import pickle
import numpy as np
import matplotlib.pyplot as plt

from pysal.explore import segregation
from pysal.explore.segregation.decomposition import DecomposeSegregation



In this example, we are going to use census data that the user must download its own copy, following similar guidelines explained in https://github.com/spatialucr/geosnap/tree/master/geosnap/data where you should download the full type file of 2010. The zipped file download will have a name that looks like LTDB_Std_All_fullcount.zip. After extracting the zipped content, the filepath of the data should looks like this:

#filepath = '~/LTDB_Std_2010_fullcount.csv'



df = pd.read_csv(filepath, encoding = "ISO-8859-1", sep = ",")



We are going to work with the variable of the nonhispanic black people (nhblk10) and the total population of each unit (pop10). So, let’s read the map of all census tracts of US and select some specific columns for the analysis:

# This file can be download here: https://drive.google.com/open?id=1gWF0OCn6xuR_WrEj7Ot2jY6KI2t6taIm
with open('data/tracts_US.pkl', 'rb') as input:

map_gpd['INTGEOID10'] = pd.to_numeric(map_gpd["GEOID10"])
gdf_pre = map_gpd.merge(df, left_on = 'INTGEOID10', right_on = 'tractid')
gdf = gdf_pre[['GEOID10', 'geometry', 'pop10', 'nhblk10']]



In this notebook, we use the Metropolitan Statistical Area (MSA) of US (we’re also using the word ‘cities’ here to refer them). So, let’s read the correspondence table that relates the tract id with the corresponding Metropolitan area…

# You can download this file here: https://drive.google.com/open?id=10HUUJSy9dkZS6m4vCVZ-8GiwH0EXqIau
with open('data/tract_metro_corresp.pkl', 'rb') as input:



..and merge them with the previous data.

merged_gdf = gdf.merge(tract_metro_corresp, left_on = 'GEOID10', right_on = 'geoid10')



We now build the composition variable (compo) which is the division of the frequency of the chosen group and total population. Let’s inspect the first rows of the data.

merged_gdf['compo'] = np.where(merged_gdf['pop10'] == 0, 0, merged_gdf['nhblk10'] / merged_gdf['pop10'])


GEOID10 geometry pop10 nhblk10 geoid10 metro_id numeric_id geoid name compo
0 01001020801 POLYGON ((-86.456273 32.405837, -86.4570349999... 3081 293 01001020801 33860 33860 33860 Montgomery, AL 0.095099
1 01001020802 POLYGON ((-86.412497 32.589422, -86.412442 32.... 10435 1420 01001020802 33860 33860 33860 Montgomery, AL 0.136080
2 01001020200 POLYGON ((-86.467354 32.459308, -86.46764 32.4... 2170 1226 01001020200 33860 33860 33860 Montgomery, AL 0.564977
3 01001020700 POLYGON ((-86.46106999999999 32.42709, -86.461... 2891 452 01001020700 33860 33860 33860 Montgomery, AL 0.156347
4 01001020600 POLYGON ((-86.470524 32.456117, -86.4700469999... 3668 776 01001020600 33860 33860 33860 Montgomery, AL 0.211559

Now, we chose two different metropolitan areas to compare the degree of segregation.

## Map of the composition of the Metropolitan area of Los Angeles

la_2010 = merged_gdf.loc[(merged_gdf.name == "Los Angeles-Long Beach-Anaheim, CA")]
la_2010.plot(column = 'compo', figsize = (10, 10), cmap = 'OrRd', legend = True)
plt.axis('off')


(-119.02865769999998, -117.3360503, 32.6463769, 34.9269651)


## Map of the composition of the Metropolitan area of New York

ny_2010 = merged_gdf.loc[(merged_gdf.name == 'New York-Newark-Jersey City, NY-NJ-PA')]
ny_2010.plot(column = 'compo', figsize = (20, 10), cmap = 'OrRd', legend = True)
plt.axis('off')


(-75.5381038, -71.59841419999998, 39.36886419999999, 41.70820779999999)


We first compare the Gini index of both cities. Let’s import the Gini_Seg class from segregation, fit both indexes and check the difference in point estimation.

from pysal.explore.segregation.aspatial import GiniSeg

G_la = GiniSeg(la_2010, 'nhblk10', 'pop10')
G_ny = GiniSeg(ny_2010, 'nhblk10', 'pop10')

G_la.statistic - G_ny.statistic


-0.10652888790131243


Let’s decompose these difference according to Rey, S. et al “Comparative Spatial Segregation Analytics”. Forthcoming. You can check the options available in this decomposition below:

help(DecomposeSegregation)


Help on class DecomposeSegregation in module segregation.decomposition.decompose_segregation:

class DecomposeSegregation(builtins.object)
|  Decompose segregation differences into spatial and attribute components.
|
|  Given two segregation indices of the same type, use Shapley decomposition
|  to measure whether the differences between index measures arise from
|  differences in spatial structure or population structure
|
|  Parameters
|  ----------
|  index1 : segregation.SegIndex class
|      First SegIndex class to compare.
|  index2 : segregation.SegIndex class
|      Second SegIndex class to compare.
|  counterfactual_approach : str, one of
|                            ["composition", "share", "dual_composition"]
|      The technique used to generate the counterfactual population
|      distributions.
|
|  Attributes
|  ----------
|
|  c_s : float
|      Shapley's Spatial Component of the decomposition
|
|  c_a : float
|      Shapley's Attribute Component of the decomposition
|
|  Methods
|  ----------
|
|  plot : Visualize features of the Decomposition performed
|      plot_type : str, one of ['cdfs', 'maps']
|
|      'cdfs' : visualize the cumulative distribution functions of the compositions/shares
|      'maps' : visualize the spatial distributions for original data and counterfactuals generated and Shapley's components (only available for GeoDataFrames)
|
|  Examples
|  --------
|  Several examples can be found at https://github.com/pysal/segregation/blob/master/notebooks/decomposition_wrapper_example.ipynb.
|
|  Methods defined here:
|
|  __init__(self, index1, index2, counterfactual_approach='composition')
|      Initialize self.  See help(type(self)) for accurate signature.
|
|  plot(self, plot_type='cdfs')
|      Plot the Segregation Decomposition Profile
|
|  ----------------------------------------------------------------------
|  Data descriptors defined here:
|
|  __dict__
|      dictionary for instance variables (if defined)
|
|  __weakref__
|      list of weak references to the object (if defined)



## Composition Approach (default)

The difference of -0.10653 fitted previously, can be decomposed into two components. The Spatial component and the attribute component. Let’s estimate both, respectively.

DS_composition = DecomposeSegregation(G_la, G_ny)
DS_composition.c_s


0.029575766160051364

DS_composition.c_a


-0.1361046540613638


So, the first thing to notice is that attribute component, i.e., given by a difference in the population structure (in this case, the composition) plays a more important role in the difference, since it has a higher absolute value.

The difference in the composition can be inspected in the plotting method with the type cdfs:

DS_composition.plot(plot_type = 'cdfs')



If your data is a GeoDataFrame, it is also possible to visualize the counterfactual compositions with the argument plot_type = 'maps'

The first and second contexts are Los Angeles and New York, respectively.

DS_composition.plot(plot_type = 'maps')



Note that in all plotting methods, the title presents each component of the decomposition performed.

## Share Approach

The share approach takes into consideration the share of each group in each city. Since this approach takes into consideration the focus group and the complementary group share to build the “counterfactual” total population of each unit, it is of interest to inspect all these four cdf’s.

ps.: The share is the population frequency of each group in each unit over the total population of that respectively group.

DS_share = DecomposeSegregation(G_la, G_ny, counterfactual_approach = 'share')
DS_share.plot(plot_type = 'cdfs')



We can see that curve between the contexts are closer to each other which represent a drop in the importance of the population structure (attribute component) to -0.062. However, this attribute still overcomes the spatial component (-0.045) in terms of importance due to both absolute magnitudes.

DS_share.plot(plot_type = 'maps')



We can see that the counterfactual maps of the composition (outside of the main diagonal), in this case, are slightly different from the previous approach.

## Dual Composition Approach

The dual_composition approach is similar to the composition approach. However, it uses also the counterfactual composition of the cdf of the complementary group.

DS_dual = DecomposeSegregation(G_la, G_ny, counterfactual_approach = 'dual_composition')
DS_dual.plot(plot_type = 'cdfs')



It is possible to see that the component values are very similar with slight changes from the composition approach.

DS_dual.plot(plot_type = 'maps')



The counterfactual distributions are virtually the same (but not equal) as the one from the composition approach.

## Inspecting a different index: Relative Concentration

from pysal.explore.segregation.spatial import RelativeConcentration

RCO_la = RelativeConcentration(la_2010, 'nhblk10', 'pop10')
RCO_ny = RelativeConcentration(ny_2010, 'nhblk10', 'pop10')

RCO_la.statistic - RCO_ny.statistic


-0.4252237137424809

RCO_DS_composition = DecomposeSegregation(RCO_la, RCO_ny)
RCO_DS_composition.c_s


-0.37586237172215886

RCO_DS_composition.c_a


-0.049361342020322


It is possible to note that, in this case, the spatial component is playing a much more relevant role in the decomposition.