Multigroup aspatial indexes of segregation

This is an example notebook of functionalities for multigroup aspatial indexes of the segregation module. Firstly, we need to import the packages we need:



In [1]:

    
%%capture

import pysal.lib
from pysal.explore import segregation
import geopandas as gpd

Then it's time to load some data to estimate segregation. We use the data of 2000 Census Tract Data for the metropolitan area of Sacramento, CA, USA.

We use a geopandas dataframe available in PySAL examples repository.

For more information about the data: https://github.com/pysal/pysal.lib/tree/master/pysal.lib/examples/sacramento2



In [2]:

    
input_df = gpd.read_file(pysal.lib.examples.get_path("sacramentot2.shp"))
input_df.columns









    Out[2]:





Index(['FIPS', 'MSA', 'TOT_POP', 'POP_16', 'POP_65', 'WHITE_', 'BLACK_',
       'ASIAN_', 'HISP_', 'MULTI_RA', 'MALES', 'FEMALES', 'MALE1664',
       'FEM1664', 'EMPL16', 'EMP_AWAY', 'EMP_HOME', 'EMP_29', 'EMP_30',
       'EMP16_2', 'EMP_MALE', 'EMP_FEM', 'OCC_MAN', 'OCC_OFF1', 'OCC_INFO',
       'HH_INC', 'POV_POP', 'POV_TOT', 'HSG_VAL', 'FIPSNO', 'POLYID',
       'geometry'],
      dtype='object')

The groups of interest are White, Black, Asian and Hispanic population. Therefore, we create an auxiliary list with only the necessary columns for fitting the index.



In [3]:

    
groups_list = ['WHITE_', 'BLACK_', 'ASIAN_','HISP_']

We also can plot the spatial distribution of the composition of each of these groups over the tracts of Sacramento:



In [4]:

    
import matplotlib.pyplot as plt

for i in range(len(groups_list)):
    input_df['comp_' + groups_list[i]] = input_df[groups_list[i]] / input_df['TOT_POP']

fig, axes = plt.subplots(ncols = 2, nrows = 2, figsize = (17, 10))


input_df.plot(column = 'comp_' + groups_list[0],
              cmap = 'OrRd',
              legend = True, ax = axes[0,0])
axes[0,0].set_title('Composition of ' + groups_list[0])
axes[0,0].set_xticks([])
axes[0,0].set_yticks([])
axes[0,0].set_facecolor('white')


input_df.plot(column = 'comp_' + groups_list[1],
              cmap = 'OrRd',
              legend = True, ax = axes[0,1])
axes[0,1].set_title('Composition of ' + groups_list[1])
axes[0,1].set_xticks([])
axes[0,1].set_yticks([])
axes[0,1].set_facecolor('white')


input_df.plot(column = 'comp_' + groups_list[2],
              cmap = 'OrRd',
              legend = True, ax = axes[1,0])
axes[1,0].set_title('Composition of ' + groups_list[2])
axes[1,0].set_xticks([])
axes[1,0].set_yticks([])
axes[1,0].set_facecolor('white')

input_df.plot(column = 'comp_' + groups_list[3],
              cmap = 'OrRd',
              legend = True, ax = axes[1,1])
axes[1,1].set_title('Composition of ' + groups_list[3])
axes[1,1].set_xticks([])
axes[1,1].set_yticks([])
axes[1,1].set_facecolor('white')

Multigroup Dissimilarity Index



In [5]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiDissim



In [6]:

    
index = MultiDissim(input_df, groups_list)
type(index)









    Out[6]:





segregation.aspatial.multigroup_aspatial_indexes.MultiDissim



In [7]:

    
index.statistic









    Out[7]:





0.41340872573177806

Multigroup Gini Index



In [8]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiGiniSeg



In [9]:

    
index = MultiGiniSeg(input_df, groups_list)
type(index)









    Out[9]:





segregation.aspatial.multigroup_aspatial_indexes.MultiGiniSeg



In [10]:

    
index.statistic









    Out[10]:





0.5456349992598081

Multigroup Normalized Exposure Index



In [11]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiNormalizedExposure



In [12]:

    
index = MultiNormalizedExposure(input_df, groups_list)
type(index)









    Out[12]:





segregation.aspatial.multigroup_aspatial_indexes.MultiNormalizedExposure



In [13]:

    
index.statistic









    Out[13]:





0.18821879029994157

Multigroup Information Theory Index



In [14]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiInformationTheory



In [15]:

    
index = MultiInformationTheory(input_df, groups_list)
type(index)









    Out[15]:





segregation.aspatial.multigroup_aspatial_indexes.MultiInformationTheory



In [16]:

    
index.statistic









    Out[16]:





0.1710160297858887

Multigroup Relative Diversity Index



In [17]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiRelativeDiversity



In [18]:

    
index = MultiRelativeDiversity(input_df, groups_list)
type(index)









    Out[18]:





segregation.aspatial.multigroup_aspatial_indexes.MultiRelativeDiversity



In [19]:

    
index.statistic









    Out[19]:





0.15820019878220337

Multigroup Squared Coefficient of Variation Index



In [20]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiSquaredCoefficientVariation



In [21]:

    
index = MultiSquaredCoefficientVariation(input_df, groups_list)
type(index)









    Out[21]:





segregation.aspatial.multigroup_aspatial_indexes.MultiSquaredCoefficientVariation



In [22]:

    
index.statistic









    Out[22]:





0.11875484641127525

Multigroup Diversity Index



In [23]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiDiversity



In [24]:

    
index = MultiDiversity(input_df, groups_list)
type(index)









    Out[24]:





segregation.aspatial.multigroup_aspatial_indexes.MultiDiversity



In [25]:

    
index.statistic









    Out[25]:





0.9733112243997906



In [26]:

    
# Normalized version of the multigroup diversity index
normalized_index = MultiDiversity(input_df, groups_list, normalized = True)
normalized_index.statistic









    Out[26]:





0.7020956383415715

Simpson's Concentration Index (lambda)



In [27]:

    
%%capture
from pysal.explore.segregation.aspatial import SimpsonsConcentration



In [28]:

    
index = SimpsonsConcentration(input_df, groups_list)
type(index)









    Out[28]:





segregation.aspatial.multigroup_aspatial_indexes.SimpsonsConcentration



In [29]:

    
index.statistic









    Out[29]:





0.49182413151957904

Simpson's Interaction Index (I)



In [30]:

    
%%capture
from pysal.explore.segregation.aspatial import SimpsonsInteraction



In [31]:

    
index = SimpsonsInteraction(input_df, groups_list)
type(index)









    Out[31]:





segregation.aspatial.multigroup_aspatial_indexes.SimpsonsInteraction



In [32]:

    
index.statistic









    Out[32]:





0.508175868480421

Multigroup Divergence Index



In [33]:

    
%%capture
from pysal.explore.segregation.aspatial import MultiDivergence



In [34]:

    
index = MultiDivergence(input_df, groups_list)
type(index)









    Out[34]:





segregation.aspatial.multigroup_aspatial_indexes.MultiDivergence



In [35]:

    
index.statistic









    Out[35]:





0.16645182134289443