import numpy as np
import pandas as pd
from libpysal import weights
from sklearn.base import BaseEstimator
from esda.crand import _prepare_bivariate, _prepare_univariate
from esda.crand import crand as _crand_plus
from esda.crand import njit as _njit
PERMUTATIONS = 999
[docs]
class Join_Counts_Local_BV(BaseEstimator):
"""Univariate Local Join Count Statistic"""
[docs]
def __init__(
self,
connectivity=None,
permutations=PERMUTATIONS,
n_jobs=1,
keep_simulations=True,
seed=None,
island_weight=0,
drop_islands=True,
):
"""
Initialize a Local_Join_Counts_BV estimator
Parameters
----------
connectivity : scipy.sparse matrix object
the connectivity structure describing
the relationships between observed units.
Need not be row-standardized.
permutations : int
number of random permutations for calculation of pseudo p_values
n_jobs : int
Number of cores to be used in the conditional randomisation.
If -1, all available cores are used.
keep_simulations : bool (default True)
If True, the entire matrix of replications under the null
is stored in memory and accessible; otherwise, replications
are not saved
seed : None/int
Seed to ensure reproducibility of conditional randomizations.
Must be set here, and not outside of the function, since numba
does not correctly interpret external seeds
nor numpy.random.RandomState instances.
island_weight:
value to use as a weight for the "fake" neighbor for every island.
If numpy.nan, will propagate to the final local statistic depending
on the `stat_func`. If 0, then the lag is always zero for islands.
drop_islands : bool (default True)
Whether or not to preserve islands as entries in the adjacency
list. By default, observations with no neighbors do not appear
in the adjacency list. If islands are kept, they are coded as
self-neighbors with zero weight. See ``libpysal.weights.to_adjlist()``.
"""
self.connectivity = connectivity
self.permutations = permutations
self.n_jobs = n_jobs
self.keep_simulations = keep_simulations
self.seed = seed
self.island_weight = island_weight
self.drop_islands = drop_islands
[docs]
def fit(self, x, z, case="CLC", n_jobs=1, permutations=999):
"""
Parameters
----------
x : numpy.ndarray
array containing binary (0/1) data
z : numpy.ndarray
array containing binary (0/1) data
Returns
-------
the fitted estimator.
Notes
-----
Technical details and derivations can be found in :cite:`AnselinLi2019`.
Examples
--------
>>> import libpysal
>>> w = libpysal.weights.lat2W(4, 4)
>>> x = np.ones(16)
>>> x[0:8] = 0
>>> z = [0,1,0,1,1,1,1,1,0,0,1,1,0,0,1,1]
>>> LJC_BV_C1 = Local_Join_Counts_BV(connectivity=w).fit(x, z, case="BJC")
>>> LJC_BV_C2 = Local_Join_Counts_BV(connectivity=w).fit(x, z, case="CLC")
>>> LJC_BV_C1.LJC
>>> LJC_BV_C1.p_sim
>>> LJC_BV_C2.LJC
>>> LJC_BV_C2.p_sim
Commpop data replicating GeoDa tutorial (Case 1)
>>> import libpysal
>>> import geopandas as gpd
>>> commpop = gpd.read_file(
... "https://github.com/jeffcsauer/GSOC2020/raw/master/"
... "validation/data/commpop.gpkg"
... )
>>> w = libpysal.weights.Queen.from_dataframe(commpop)
>>> LJC_BV_Case1 = Local_Join_Counts_BV(
... connectivity=w
... ).fit(commpop['popneg'], commpop['popplus'], case='BJC')
>>> LJC_BV_Case1.LJC
>>> LJC_BV_Case1.p_sim
Guerry data replicating GeoDa tutorial (Case 2)
>>> import libpysal
>>> import geopandas as gpd
>>> guerry = libpysal.examples.load_example('Guerry')
>>> guerry_ds = gpd.read_file(guerry.get_path('Guerry.shp'))
>>> guerry_ds['infq5'] = 0
>>> guerry_ds['donq5'] = 0
>>> guerry_ds.loc[(guerry_ds['Infants'] > 23574), 'infq5'] = 1
>>> guerry_ds.loc[(guerry_ds['Donatns'] > 10973), 'donq5'] = 1
>>> w = libpysal.weights.Queen.from_dataframe(guerry_ds)
>>> LJC_BV_Case2 = Local_Join_Counts_BV(
... connectivity=w
... ).fit(guerry_ds['infq5'], guerry_ds['donq5'], case='CLC')
>>> LJC_BV_Case2.LJC
>>> LJC_BV_Case2.p_sim
"""
# Need to ensure that the np.array() are of dtype='float' for numba
x = np.array(x, dtype="float")
z = np.array(z, dtype="float")
w = self.connectivity
# Fill the diagonal with 0s
w = weights.util.fill_diagonal(w, val=0)
w.transform = "b"
self.x = x
self.z = z
self.n = len(x)
self.w = w
self.case = case
n_jobs = self.n_jobs
self.LJC = self._statistic(x, z, w, case, self.drop_islands)
if permutations:
if case == "BJC":
self.p_sim, self.rjoins = _crand_plus(
z=np.column_stack((x, z)),
w=self.w,
observed=self.LJC,
permutations=permutations,
keep=True,
n_jobs=n_jobs,
stat_func=_ljc_bv_case1,
island_weight=self.island_weight,
)
# Set p-values for those with LJC of 0 to NaN
self.p_sim[self.LJC == 0] = "NaN"
elif case == "CLC":
self.p_sim, self.rjoins = _crand_plus(
z=np.column_stack((x, z)),
w=self.w,
observed=self.LJC,
permutations=permutations,
keep=True,
n_jobs=n_jobs,
stat_func=_ljc_bv_case2,
island_weight=self.island_weight,
)
# Set p-values for those with LJC of 0 to NaN
self.p_sim[self.LJC == 0] = "NaN"
else:
raise NotImplementedError(
f"The requested LJC method ({case}) is not currently supported!"
)
return self
@staticmethod
def _statistic(x, z, w, case, drop_islands):
# Create adjacency list. Note that remove_symmetric=False - this is
# different from the esda.Join_Counts() function.
adj_list = w.to_adjlist(remove_symmetric=False, drop_islands=drop_islands)
# First, set up a series that maps the values to the weights table
zseries_x = pd.Series(x, index=w.id_order)
zseries_z = pd.Series(z, index=w.id_order)
# Map the values to the focal (i) values
focal_x = zseries_x.loc[adj_list.focal].values
focal_z = zseries_z.loc[adj_list.focal].values
# Map the values to the neighbor (j) values
neighbor_x = zseries_x.loc[adj_list.neighbor].values
neighbor_z = zseries_z.loc[adj_list.neighbor].values
if case == "BJC":
BJC = (
(focal_x == 1) & (focal_z == 0) & (neighbor_x == 0) & (neighbor_z == 1)
)
adj_list_BJC = pd.DataFrame(
adj_list.focal.values, BJC.astype("uint8")
).reset_index()
adj_list_BJC.columns = ["BJC", "ID"]
adj_list_BJC = adj_list_BJC.groupby(by="ID").sum()
return np.array(adj_list_BJC.BJC.values, dtype="float")
elif case == "CLC":
CLC = (
(focal_x == 1) & (focal_z == 1) & (neighbor_x == 1) & (neighbor_z == 1)
)
adj_list_CLC = pd.DataFrame(
adj_list.focal.values, CLC.astype("uint8")
).reset_index()
adj_list_CLC.columns = ["CLC", "ID"]
adj_list_CLC = adj_list_CLC.groupby(by="ID").sum()
return np.array(adj_list_CLC.CLC.values, dtype="float")
else:
raise NotImplementedError(
f"The requested LJC method ({case}) is not currently supported!"
)
# --------------------------------------------------------------
# Conditional Randomization Function Implementations
# --------------------------------------------------------------
# Note: scaling not used
@_njit(fastmath=True)
def _ljc_bv_case1(i, z, permuted_ids, weights_i, scaling):
zx = z[:, 0]
zy = z[:, 1]
other_weights = weights_i[1:]
zyi, zyrand = _prepare_univariate(i, zy, permuted_ids, other_weights)
return zx[i] * (zyrand @ other_weights)
@_njit(fastmath=True)
def _ljc_bv_case2(i, z, permuted_ids, weights_i, scaling):
zy = z[:, 1]
other_weights = weights_i[1:]
zxi, zxrand, zyi, zyrand = _prepare_bivariate(i, z, permuted_ids, other_weights)
zf = zxrand * zyrand
return zy[i] * (zf @ other_weights)