esda.Moran_Local

class esda.Moran_Local(y, w, transformation='r', permutations=999, geoda_quads=False, n_jobs=1, keep_simulations=True, seed=None, island_weight=0)[source]

Local Moran Statistics.

Parameters:
yarray

(n,1), attribute array

wW | Graph

spatial weights instance as W or Graph aligned with y

transformation{‘R’, ‘B’, ‘D’, ‘U’, ‘V’}

weights transformation, default is row-standardized “r”. Other options include “B”: binary, “D”: doubly-standardized, “U”: untransformed (general weights), “V”: variance-stabilizing.

permutationsint

number of random permutations for calculation of pseudo p_values

geoda_quadsbool

(default=False) If True use GeoDa scheme: HH=1, LL=2, LH=3, HL=4 If False use PySAL Scheme: HH=1, LH=2, LL=3, HL=4

n_jobsint

Number of cores to be used in the conditional randomisation. If -1, all available cores are used.

keep_simulationsBoolean

(default=True) If True, the entire matrix of replications under the null is stored in memory and accessible; otherwise, replications are not saved

seedNone/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.

Notes

For technical details see [Ans95].

Examples

>>> import libpysal
>>> import numpy as np
>>> np.random.seed(10)
>>> w = libpysal.io.open(libpysal.examples.get_path("desmith.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("desmith.txt"))
>>> y = np.array(f.by_col['z'])
>>> from esda.moran import Moran_Local
>>> lm = Moran_Local(y, w, transformation = "r", permutations = 99)
>>> lm.q
array([4, 4, 4, 2, 3, 3, 1, 4, 3, 3])
>>> lm.p_z_sim[0]
0.24669152541631179
>>> lm = Moran_Local(y, w, transformation = "r", permutations = 99,                             geoda_quads=True)
>>> lm.q
array([4, 4, 4, 3, 2, 2, 1, 4, 2, 2])

Note random components result is slightly different values across architectures so the results have been removed from doctests and will be moved into unittests that are conditional on architectures.

Attributes:
yarray

original variable

wW | Graph

original w object

permutationsint

number of random permutations for calculation of pseudo p_values

Isarray

local Moran’s I values

qarray

(if permutations>0) values indicate quandrant location 1 HH, 2 LH, 3 LL, 4 HL

simarray (permutations by n)

(if permutations>0) I values for permuted samples

p_simarray

(if permutations>0) p-values based on permutations (one-sided) null: spatial randomness alternative: the observed Ii is further away or extreme from the median of simulated values. It is either extremely high or extremely low in the distribution of simulated Is.

EI_simarray

(if permutations>0) average values of local Is from permutations

VI_simarray

(if permutations>0) variance of Is from permutations

EIarray

analytical expectation of Is under total permutation, from []. Is the same at each site, and equal to the expectation of I itself when transformation=’r’. We recommend using EI_sim, not EI, for analysis. This EI is only provided for reproducibility.

VIarray

analytical variance of Is under total permutation, from []. Varies according only to cardinality. We recommend using VI_sim, not VI, for analysis. This VI is only provided for reproducibility.

EIcarray

analytical expectation of Is under conditional permutation, from [SOT98]. Varies strongly by site, since it conditions on z_i. We recommend using EI_sim, not EIc, for analysis. This EIc is only provided for reproducibility.

VIcarray

analytical variance of Is under conditional permutation, from [SOT98]. Varies strongly by site, since it conditions on z_i. We recommend using VI_sim, not VIc, for analysis. This VIc is only provided for reproducibility.

seI_simarray

(if permutations>0) standard deviations of Is under permutations.

z_simarrray

(if permutations>0) standardized Is based on permutations

p_z_simarray

(if permutations>0) p-values based on standard normal approximation from permutations (one-sided) for two-sided tests, these values should be multiplied by 2

n_jobsint

Number of cores to be used in the conditional randomisation. If -1, all available cores are used.

keep_simulationsBoolean

(default=True) If True, the entire matrix of replications under the null is stored in memory and accessible; otherwise, replications are not saved

seedNone/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.

__init__(y, w, transformation='r', permutations=999, geoda_quads=False, n_jobs=1, keep_simulations=True, seed=None, island_weight=0)[source]

Methods

__init__(y, w[, transformation, ...])

by_col(df, cols[, w, inplace, pvalue, outvals])

Function to compute a Moran_Local statistic on a dataframe.

explore(gdf[, crit_value])

Create interactive map of LISA indicators

get_cluster_labels([crit_value])

Return LISA cluster labels for each observation.

classmethod by_col(df, cols, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]

Function to compute a Moran_Local statistic on a dataframe.

Parameters:
dfpandas.DataFrame

a pandas dataframe with a geometry column

colsstr or list of str

name or list of names of columns to use to compute the statistic

wW | Graph

spatial weights instance as W or Graph aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata

inplacebool

a boolean denoting whether to operate on the dataframe inplace or to return a series contaning the results of the computation. If operating inplace, the derived columns will be named ‘column_moran_local’

pvaluestr

a string denoting which pvalue should be returned. Refer to the the Moran_Local statistic’s documentation for available p-values

outvalslist of strings

list of arbitrary attributes to return as columns from the Moran_Local statistic

**stat_kwsdict

options to pass to the underlying statistic. For this, see the documentation for the Moran_Local statistic.

Returns:
If inplace, None, and operation is conducted on dataframe
in memory. Otherwise, returns a copy of the dataframe with
the relevant columns attached.
explore(gdf, crit_value=0.05, **kwargs)[source]

Create interactive map of LISA indicators

Parameters:
gdfgeopandas.GeoDataFrame

geodataframe used to conduct the local Moran analysis

crit_valuefloat, optional

critical value to determine statistical significance, by default 0.05

kwargsdict, optional

additional keyword arguments passed to the geopandas explore method

Returns:
Folium.Map

interactive map with LISA clusters

get_cluster_labels(crit_value=0.05)[source]

Return LISA cluster labels for each observation.

Parameters:
crit_valuefloat, optional

crititical significance value for statistical inference, by default 0.05

Returns:
numpy.array

an array of cluster labels aligned with the input data used to conduct the local Moran analysis