"""Entropy Segregation Index."""
__author__ = "Renan X. Cortes <renanc@ucr.edu>, Sergio J. Rey <sergio.rey@ucr.edu> and Elijah Knaap <elijah.knaap@ucr.edu>"
import geopandas as gpd
import numpy as np
np.seterr(divide="ignore", invalid="ignore")
from .._base import SingleGroupIndex, SpatialImplicitIndex
def _entropy(data, group_pop_var, total_pop_var):
"""Calculate Entropy index.
Parameters
----------
data : pandas.DataFrame or geopandas.GeoDataFrame
Dataframe or geodataframe if spatial index holding data for location of interest
group_pop_var : string
Variable containing the population count of the group of interest
total_pop_var : string
Variable in data that contains the total population count of the unit
Returns
----------
statistic : float
Entropy index statistic value
core_data : pandas.DataFrame
A pandas DataFrame that contains the columns used to perform the estimate.
Notes
-----
Based on Massey, Douglas S., and Nancy A. Denton. "The dimensions of residential segregation." Social forces 67.2 (1988): 281-315.
Reference: :cite:`massey1988dimensions`.
"""
x = np.array(data[group_pop_var])
t = np.array(data[total_pop_var])
if any(t < x):
raise ValueError(
"Group of interest population must equal or lower than the total population of the units."
)
T = t.sum()
P = x.sum() / T
# If a unit has zero population, the group of interest frequency is zero
pi = np.where(t == 0, 0, x / t)
E = P * np.log(1 / P) + (1 - P) * np.log(1 / (1 - P))
Ei = pi * np.log(1 / pi) + (1 - pi) * np.log(1 / (1 - pi))
Ei = np.nan_to_num(Ei) # replace nan with 0
H = np.nansum(
t * (E - Ei) / (E * T)
) # If some pi is zero, numpy will treat as zero
if not isinstance(data, gpd.GeoDataFrame):
core_data = data[[group_pop_var, total_pop_var]]
else:
core_data = data[[group_pop_var, total_pop_var, data.geometry.name]]
return H, core_data
[docs]
class Entropy(SingleGroupIndex, SpatialImplicitIndex):
"""Entropy Index.
Parameters
----------
data : pandas.DataFrame or geopandas.GeoDataFrame, required
dataframe or geodataframe if spatial index holding data for location of interest
group_pop_var : str, required
name of column on dataframe holding population totals for focal group
total_pop_var : str, required
name of column on dataframe holding total overall population
w : libpysal.weights.KernelW, optional
lipysal spatial kernel weights object used to define an egohood
network : pandana.Network
pandana Network object representing the study area
distance : int
Maximum distance (in units of geodataframe CRS) to consider the extent of the egohood
decay : str
type of decay function to apply. Options include
precompute : bool
Whether to precompute the pandana Network object
Attributes
----------
statistic : float
Entropy Index
core_data : a pandas DataFrame
A pandas DataFrame that contains the columns used to perform the estimate.
Notes
-----
Based on Massey, Douglas S., and Nancy A. Denton. "The dimensions of residential segregation." Social forces 67.2 (1988): 281-315.
Reference: :cite:`massey1988dimensions`.
"""
[docs]
def __init__(
self,
data,
group_pop_var,
total_pop_var,
w=None,
network=None,
distance=None,
decay=None,
function="triangular",
precompute=None,
**kwargs
):
"""Init."""
SingleGroupIndex.__init__(self, data, group_pop_var, total_pop_var)
if any([w, network, distance]):
SpatialImplicitIndex.__init__(
self, w, network, distance, decay, function, precompute
)
aux = _entropy(self.data, self.group_pop_var, self.total_pop_var)
self.statistic = aux[0]
self.data = aux[1]
self._function = _entropy