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: weight instance assumed to be 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: 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
wpysal weights object: a weights object 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