esda.Moran_Local¶

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

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 [Anselin1995]. 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 [Anselin1995]. 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)[source]¶

Methods

`__init__`(y, w[, transformation, …])
`by_col`(df, cols[, w, inplace, pvalue, outvals])	Function to compute a Moran_Local statistic on a dataframe