esda.moran — Moran’s I measures of spatial autocorrelation

New in version 1.0.

Moran’s I global and local measures of spatial autocorrelation

Moran’s I Spatial Autocorrelation Statistics

class pysal.esda.moran.Moran(y, w, transformation='r', permutations=999, two_tailed=True)[source]

Moran’s I Global Autocorrelation Statistic

Parameters:
  • y (array) – variable measured across n spatial units
  • w (W) – spatial weights instance
  • transformation (string) – weights transformation, default is row-standardized “r”. Other options include “B”: binary, “D”: doubly-standardized, “U”: untransformed (general weights), “V”: variance-stabilizing.
  • permutations (int) – number of random permutations for calculation of pseudo-p_values
  • two_tailed (boolean) – If True (default) analytical p-values for Moran are two tailed, otherwise if False, they are one-tailed.
y

array – original variable

w

W – original w object

permutations

int – number of permutations

I

float – value of Moran’s I

EI

float – expected value under normality assumption

VI_norm

float – variance of I under normality assumption

seI_norm

float – standard deviation of I under normality assumption

z_norm

float – z-value of I under normality assumption

p_norm

float – p-value of I under normality assumption

VI_rand

float – variance of I under randomization assumption

seI_rand

float – standard deviation of I under randomization assumption

z_rand

float – z-value of I under randomization assumption

p_rand

float – p-value of I under randomization assumption

two_tailed

boolean – If True p_norm and p_rand are two-tailed, otherwise they are one-tailed.

sim

array – (if permutations>0) vector of I values for permuted samples

p_sim

array – (if permutations>0) p-value based on permutations (one-tailed) null: spatial randomness alternative: the observed I is extreme if it is either extremely greater or extremely lower than the values obtained based on permutations

EI_sim

float – (if permutations>0) average value of I from permutations

VI_sim

float – (if permutations>0) variance of I from permutations

seI_sim

float – (if permutations>0) standard deviation of I under permutations.

z_sim

float – (if permutations>0) standardized I based on permutations

p_z_sim

float – (if permutations>0) p-value based on standard normal approximation from permutations

Examples

>>> import pysal
>>> w = pysal.open(pysal.examples.get_path("stl.gal")).read()
>>> f = pysal.open(pysal.examples.get_path("stl_hom.txt"))
>>> y = np.array(f.by_col['HR8893'])
>>> mi = Moran(y,  w)
>>> "%7.5f" % mi.I
'0.24366'
>>> mi.EI
-0.012987012987012988
>>> mi.p_norm
0.00027147862770937614

SIDS example replicating OpenGeoda

>>> w = pysal.open(pysal.examples.get_path("sids2.gal")).read()
>>> f = pysal.open(pysal.examples.get_path("sids2.dbf"))
>>> SIDR = np.array(f.by_col("SIDR74"))
>>> mi = pysal.Moran(SIDR,  w)
>>> "%6.4f" % mi.I
'0.2477'
>>> mi.p_norm
0.0001158330781489969

One-tailed

>>> mi_1 = pysal.Moran(SIDR,  w, two_tailed=False)
>>> "%6.4f" % mi_1.I
'0.2477'
>>> mi_1.p_norm
5.7916539074498452e-05
classmethod by_col(df, cols, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]

Function to compute a Moran statistic on a dataframe

Parameters:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • cols (string or list of string) – name or list of names of columns to use to compute the statistic
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran statistic
  • **stat_kws (keyword arguments) – options to pass to the underlying statistic. For this, see the documentation for the Moran 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.

See also

For, refer

class pysal.esda.moran.Moran_Local(y, w, transformation='r', permutations=999, geoda_quads=False)[source]

Local Moran Statistics

Parameters:
  • y (array) – (n,1), attribute array
  • w (W) – 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.
  • permutations (int) – number of random permutations for calculation of pseudo p_values
  • geoda_quads (boolean) – (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
y

array – original variable

w

W – original w object

permutations

int – number of random permutations for calculation of pseudo p_values

Is

array – local Moran’s I values

q

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

sim

array (permutations by n) – (if permutations>0) I values for permuted samples

p_sim

array – (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 extremelyi high or extremely low in the distribution of simulated Is.

EI_sim

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

VI_sim

array – (if permutations>0) variance of Is from permutations

seI_sim

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

z_sim

arrray – (if permutations>0) standardized Is based on permutations

p_z_sim

array – (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

Examples

>>> import pysal as ps
>>> import numpy as np
>>> np.random.seed(10)
>>> w = ps.open(ps.examples.get_path("desmith.gal")).read()
>>> f = ps.open(ps.examples.get_path("desmith.txt"))
>>> y = np.array(f.by_col['z'])
>>> lm = ps.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 = ps.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

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:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • cols (string or list of string) – name or list of names of columns to use to compute the statistic
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran_Local statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran_Local statistic
  • **stat_kws (keyword arguments) – 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.

See also

For, refer

class pysal.esda.moran.Moran_BV(x, y, w, transformation='r', permutations=999)[source]

Bivariate Moran’s I

Parameters:
  • x (array) – x-axis variable
  • y (array) – wy will be on y axis
  • w (W) – 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.
  • permutations (int) – number of random permutations for calculation of pseudo p_values
zx

array – original x variable standardized by mean and std

zy

array – original y variable standardized by mean and std

w

W – original w object

permutation

int – number of permutations

I

float – value of bivariate Moran’s I

sim

array – (if permutations>0) vector of I values for permuted samples

p_sim

float – (if permutations>0) p-value based on permutations (one-sided) null: spatial randomness alternative: the observed I is extreme it is either extremely high or extremely low

EI_sim

array – (if permutations>0) average value of I from permutations

VI_sim

array – (if permutations>0) variance of I from permutations

seI_sim

array – (if permutations>0) standard deviation of I under permutations.

z_sim

array – (if permutations>0) standardized I based on permutations

p_z_sim

float – (if permutations>0) p-value based on standard normal approximation from permutations

Notes

Inference is only based on permutations as analytical results are none too reliable.

Examples

>>> import pysal
>>> import numpy as np

Set random number generator seed so we can replicate the example

>>> np.random.seed(10)

Open the sudden infant death dbf file and read in rates for 74 and 79 converting each to a numpy array

>>> f = pysal.open(pysal.examples.get_path("sids2.dbf"))
>>> SIDR74 = np.array(f.by_col['SIDR74'])
>>> SIDR79 = np.array(f.by_col['SIDR79'])

Read a GAL file and construct our spatial weights object

>>> w = pysal.open(pysal.examples.get_path("sids2.gal")).read()

Create an instance of Moran_BV

>>> mbi = Moran_BV(SIDR79,  SIDR74,  w)

What is the bivariate Moran’s I value

>>> print mbi.I
0.156131961696

Based on 999 permutations, what is the p-value of our statistic

>>> mbi.p_z_sim
0.0014186617421765302
classmethod by_col(df, x, y=None, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]

Function to compute a Moran_BV statistic on a dataframe

Parameters:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • X (list of strings) – column name or list of column names to use as X values to compute the bivariate statistic. If no Y is provided, pairwise comparisons among these variates are used instead.
  • Y (list of strings) – column name or list of column names to use as Y values to compute the bivariate statistic. if no Y is provided, pariwise comparisons among the X variates are used instead.
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran_BV statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran_BV statistic
  • **stat_kws (keyword arguments) – options to pass to the underlying statistic. For this, see the documentation for the Moran_BV 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.

See also

For, refer

pysal.esda.moran.Moran_BV_matrix(variables, w, permutations=0, varnames=None)[source]

Bivariate Moran Matrix

Calculates bivariate Moran between all pairs of a set of variables.

Parameters:
  • variables (list) – sequence of variables
  • w (W) – a spatial weights object
  • permutations (int) – number of permutations
  • varnames (list) – strings for variable names. If specified runtime summary is printed
Returns:

results – (i, j) is the key for the pair of variables, values are the Moran_BV objects.

Return type:

dictionary

Examples

>>> import pysal

open dbf

>>> f = pysal.open(pysal.examples.get_path("sids2.dbf"))

pull of selected variables from dbf and create numpy arrays for each

>>> varnames = ['SIDR74',  'SIDR79',  'NWR74',  'NWR79']
>>> vars = [np.array(f.by_col[var]) for var in varnames]

create a contiguity matrix from an external gal file

>>> w = pysal.open(pysal.examples.get_path("sids2.gal")).read()

create an instance of Moran_BV_matrix

>>> res = Moran_BV_matrix(vars,  w,  varnames = varnames)

check values

>>> print round(res[(0,  1)].I,7)
0.1936261
>>> print round(res[(3,  0)].I,7)
0.3770138
class pysal.esda.moran.Moran_Local_BV(x, y, w, transformation='r', permutations=999, geoda_quads=False)[source]

Bivariate Local Moran Statistics

Parameters:
  • x (array) – x-axis variable
  • y (array) – (n,1), wy will be on y axis
  • w (W) – 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.
  • permutations (int) – number of random permutations for calculation of pseudo p_values
  • geoda_quads (boolean) – (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
zx

array – original x variable standardized by mean and std

zy

array – original y variable standardized by mean and std

w

W – original w object

permutations

int – number of random permutations for calculation of pseudo p_values

Is

float – value of Moran’s I

q

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

sim

array – (if permutations>0) vector of I values for permuted samples

p_sim

array – (if permutations>0) p-value 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 extremelyi high or extremely low in the distribution of simulated Is.

EI_sim

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

VI_sim

array – (if permutations>0) variance of Is from permutations

seI_sim

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

z_sim

arrray – (if permutations>0) standardized Is based on permutations

p_z_sim

array – (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

Examples

>>> import pysal as ps
>>> import numpy as np
>>> np.random.seed(10)
>>> w = ps.open(ps.examples.get_path("sids2.gal")).read()
>>> f = ps.open(ps.examples.get_path("sids2.dbf"))
>>> x = np.array(f.by_col['SIDR79'])
>>> y = np.array(f.by_col['SIDR74'])
>>> lm = ps.Moran_Local_BV(x, y, w, transformation = "r",                                permutations = 99)
>>> lm.q[:10]
array([3, 4, 3, 4, 2, 1, 4, 4, 2, 4])
>>> lm.p_z_sim[0]
0.0017240031348827456
>>> lm = ps.Moran_Local_BV(x, y, w, transformation = "r",                                permutations = 99, geoda_quads=True)
>>> lm.q[:10]
array([2, 4, 2, 4, 3, 1, 4, 4, 3, 4])

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

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

Function to compute a Moran_Local_BV statistic on a dataframe

Parameters:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • X (list of strings) – column name or list of column names to use as X values to compute the bivariate statistic. If no Y is provided, pairwise comparisons among these variates are used instead.
  • Y (list of strings) – column name or list of column names to use as Y values to compute the bivariate statistic. if no Y is provided, pariwise comparisons among the X variates are used instead.
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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_bv’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran_Local_BV statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran_Local_BV statistic
  • **stat_kws (keyword arguments) – options to pass to the underlying statistic. For this, see the documentation for the Moran_Local_BV 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.

See also

For, refer

class pysal.esda.moran.Moran_Rate(e, b, w, adjusted=True, transformation='r', permutations=999, two_tailed=True)[source]

Adjusted Moran’s I Global Autocorrelation Statistic for Rate Variables [Assuncao1999]

Parameters:
  • e (array) – an event variable measured across n spatial units
  • b (array) – a population-at-risk variable measured across n spatial units
  • w (W) – spatial weights instance
  • adjusted (boolean) – whether or not Moran’s I needs to be adjusted for rate variable
  • 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.
  • two_tailed (boolean) – If True (default), analytical p-values for Moran’s I are two-tailed, otherwise they are one tailed.
  • permutations (int) – number of random permutations for calculation of pseudo p_values
y

array – rate variable computed from parameters e and b if adjusted is True, y is standardized rates otherwise, y is raw rates

w

W – original w object

permutations

int – number of permutations

I

float – value of Moran’s I

EI

float – expected value under normality assumption

VI_norm

float – variance of I under normality assumption

seI_norm

float – standard deviation of I under normality assumption

z_norm

float – z-value of I under normality assumption

p_norm

float – p-value of I under normality assumption

VI_rand

float – variance of I under randomization assumption

seI_rand

float – standard deviation of I under randomization assumption

z_rand

float – z-value of I under randomization assumption

p_rand

float – p-value of I under randomization assumption

two_tailed

boolean – If True, p_norm and p_rand are two-tailed p-values, otherwise they are one-tailed.

sim

array – (if permutations>0) vector of I values for permuted samples

p_sim

array – (if permutations>0) p-value based on permutations (one-sided) null: spatial randomness alternative: the observed I is extreme if it is either extremely greater or extremely lower than the values obtained from permutaitons

EI_sim

float – (if permutations>0) average value of I from permutations

VI_sim

float – (if permutations>0) variance of I from permutations

seI_sim

float – (if permutations>0) standard deviation of I under permutations.

z_sim

float – (if permutations>0) standardized I based on permutations

p_z_sim

float – (if permutations>0) p-value based on standard normal approximation from

Examples

>>> import pysal
>>> w = pysal.open(pysal.examples.get_path("sids2.gal")).read()
>>> f = pysal.open(pysal.examples.get_path("sids2.dbf"))
>>> e = np.array(f.by_col('SID79'))
>>> b = np.array(f.by_col('BIR79'))
>>> mi = pysal.esda.moran.Moran_Rate(e, b,  w, two_tailed=False)
>>> "%6.4f" % mi.I
'0.1662'
>>> "%6.4f" % mi.p_norm
'0.0042'
classmethod by_col(df, events, populations, w=None, inplace=False, pvalue='sim', outvals=None, swapname='', **stat_kws)[source]

Function to compute a Moran_Rate statistic on a dataframe

Parameters:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • events (string or list of strings) – one or more names where events are stored
  • populations (string or list of strings) – one or more names where the populations corresponding to the events are stored. If one population column is provided, it is used for all event columns. If more than one population column is provided but there is not a population for every event column, an exception will be raised.
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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_rate’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran_Rate statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran_Rate statistic
  • **stat_kws (keyword arguments) – options to pass to the underlying statistic. For this, see the documentation for the Moran_Rate 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.

See also

For, refer

class pysal.esda.moran.Moran_Local_Rate(e, b, w, adjusted=True, transformation='r', permutations=999, geoda_quads=False)[source]

Adjusted Local Moran Statistics for Rate Variables [Assuncao1999]

Parameters:
  • e (array) – (n,1), an event variable across n spatial units
  • b (array) – (n,1), a population-at-risk variable across n spatial units
  • w (W) – weight instance assumed to be aligned with y
  • adjusted (boolean) – whether or not local Moran statistics need to be adjusted for rate variable
  • 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.
  • permutations (int) – number of random permutations for calculation of pseudo p_values
  • geoda_quads (boolean) – (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
y

array – rate variables computed from parameters e and b if adjusted is True, y is standardized rates otherwise, y is raw rates

w

W – original w object

permutations

int – number of random permutations for calculation of pseudo p_values

I

float – value of Moran’s I

q

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

sim

array – (if permutations>0) vector of I values for permuted samples

p_sim

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

EI_sim

float – (if permutations>0) average value of I from permutations

VI_sim

float – (if permutations>0) variance of I from permutations

seI_sim

float – (if permutations>0) standard deviation of I under permutations.

z_sim

float – (if permutations>0) standardized I based on permutations

p_z_sim

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

Examples

>>> import pysal as ps
>>> import numpy as np
>>> np.random.seed(10)
>>> w = ps.open(ps.examples.get_path("sids2.gal")).read()
>>> f = ps.open(ps.examples.get_path("sids2.dbf"))
>>> e = np.array(f.by_col('SID79'))
>>> b = np.array(f.by_col('BIR79'))
>>> lm = ps.esda.moran.Moran_Local_Rate(e, b, w,                                                transformation = "r",                                                permutations = 99)
>>> lm.q[:10]
array([2, 4, 3, 1, 2, 1, 1, 4, 2, 4])
>>> lm.p_z_sim[0]
0.39319552026912641
>>> lm = ps.esda.moran.Moran_Local_Rate(e, b, w,                                                transformation = "r",                                                permutations = 99,                                                geoda_quads=True)
>>> lm.q[:10]
array([3, 4, 2, 1, 3, 1, 1, 4, 3, 4])

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

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

Function to compute a Moran_Local_Rate statistic on a dataframe

Parameters:
  • df (pandas.DataFrame) – a pandas dataframe with a geometry column
  • events (string or list of strings) – one or more names where events are stored
  • populations (string or list of strings) – one or more names where the populations corresponding to the events are stored. If one population column is provided, it is used for all event columns. If more than one population column is provided but there is not a population for every event column, an exception will be raised.
  • w (pysal weights object) – a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
  • inplace (bool) – 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_rate’
  • pvalue (string) – a string denoting which pvalue should be returned. Refer to the the Moran_Local_Rate statistic’s documentation for available p-values
  • outvals (list of strings) – list of arbitrary attributes to return as columns from the Moran_Local_Rate statistic
  • **stat_kws (keyword arguments) – options to pass to the underlying statistic. For this, see the documentation for the Moran_Local_Rate 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.

See also

For, refer