"""Perimeter-Area Ratio Dissimilarity Index."""
__author__ = "Renan X. Cortes <renanc@ucr.edu>, Sergio J. Rey <sergio.rey@ucr.edu> and Elijah Knaap <elijah.knaap@ucr.edu>"
import numpy as np
from sklearn.metrics.pairwise import manhattan_distances
from .._base import SingleGroupIndex, SpatialExplicitIndex, _return_length_weighted_w
from .dissim import _dissim
def _perimeter_area_ratio_spatial_dissim(
data, group_pop_var, total_pop_var, standardize=True
):
"""Calculation of Perimeter/Area Ratio Spatial Dissimilarity index.
Parameters
----------
data : a geopandas DataFrame with a geometry column.
group_pop_var : string
The name of variable in data that contains the population size of the group of interest
total_pop_var : string
The name of variable in data that contains the total population of the unit
standardize : boolean
A condition for standardisation of the weights matrices.
If True, the values of cij in the formulas gets standardized and the overall sum is 1.
Returns
----------
statistic : float
Perimeter/Area Ratio Spatial Dissimilarity Index
core_data : a geopandas DataFrame
A geopandas DataFrame that contains the columns used to perform the estimate.
Notes
-----
Originally based on Wong, David WS. "Spatial indices of segregation." Urban studies 30.3 (1993): 559-572.
However, Tivadar, Mihai. "OasisR: An R Package to Bring Some Order to the World of Segregation Measurement." Journal of Statistical Software 89.1 (2019): 1-39.
points out that in Wong’s original there is an issue with the formula which is an extra division by 2 in the spatial interaction component.
This function follows the formula present in the first Appendix of Tivadar, Mihai. "OasisR: An R Package to Bring Some Order to the World of Segregation Measurement." Journal of Statistical Software 89.1 (2019): 1-39.
References: :cite:`wong1993spatial` and :cite:`tivadar2019oasisr`.
"""
if type(standardize) is not bool:
raise TypeError("std is not a boolean object")
D = _dissim(data, group_pop_var, total_pop_var)[0]
# If a unit has zero population, the group of interest frequency is zero
data = data.assign(
pi=np.where(
data[total_pop_var] == 0, 0, data[group_pop_var] / data[total_pop_var]
)
)
if not standardize:
cij = _return_length_weighted_w(data).sparse.toarray()
else:
cij = _return_length_weighted_w(data).sparse.toarray()
cij = cij / cij.sum()
peri = data.length
ai = data.area
aux_sum = np.add(
np.array(list((peri / ai))),
np.array(list((peri / ai))).reshape((len(list((peri / ai))), 1)),
)
max_pa = max(peri / ai)
num = np.multiply(
np.multiply(manhattan_distances(data[["pi"]]), cij), aux_sum
).sum()
den = 2 * max_pa
PARD = D - (num / den)
PARD
core_data = data[[group_pop_var, total_pop_var, data.geometry.name]]
return PARD, core_data
[docs]class PARDissim(SingleGroupIndex, SpatialExplicitIndex):
"""Perimeter-Area Ratio Dissimilarity 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
standardize : boolean
A condition for row standardisation of the weights matrices. If True, the values of cij in the formulas gets row standardized.
For the sake of comparison, the seg R package of Hong, Seong-Yun, David O'Sullivan, and Yukio Sadahiro. "Implementing spatial segregation measures in R." PloS one 9.11 (2014): e113767.
works by default with row standardization.
Attributes
----------
statistic : float
PARDissim Index
core_data : a pandas DataFrame
A pandas DataFrame that contains the columns used to perform the estimate.
Notes
-----
Originally based on Wong, David WS. "Spatial indices of segregation." Urban studies 30.3 (1993): 559-572.
However, Tivadar, Mihai. "OasisR: An R Package to Bring Some Order to the World of Segregation Measurement." Journal of Statistical Software 89.1 (2019): 1-39.
points out that in Wong’s original there is an issue with the formula which is an extra division by 2 in the spatial interaction component.
This function follows the formula present in the first Appendix of Tivadar, Mihai. "OasisR: An R Package to Bring Some Order to the World of Segregation Measurement." Journal of Statistical Software 89.1 (2019): 1-39.
References: :cite:`wong1993spatial` and :cite:`tivadar2019oasisr`.
"""
[docs] def __init__(
self, data, group_pop_var, total_pop_var, w=None, standardize=True, **kwargs
):
"""Init."""
SingleGroupIndex.__init__(self, data, group_pop_var, total_pop_var)
SpatialExplicitIndex.__init__(self,)
self.standardize = standardize
aux = _perimeter_area_ratio_spatial_dissim(
self.data, self.group_pop_var, self.total_pop_var, self.standardize
)
self.statistic = aux[0]
self.core_data = aux[1]
self._function = _perimeter_area_ratio_spatial_dissim