esda.Moran

class esda.Moran(y, w, transformation='r', permutations=999, two_tailed=True)

Moran’s I Global Autocorrelation Statistic

Parameters:

wW | Graph

spatial weights instance as W or Graph aligned with y

Other options include “B”: binary, “D”: doubly-standardized, “O”: restore original transformation (applicable only if w is passed as W) (general weights), “V”: variance-stabilizing.

pseudo-p_values

tailed, otherwise if False, they are one-tailed.

Attributes:

wW | Graph

original w object

are one-tailed.

vector of I values for permuted samples

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

average value of I from permutations

variance of I from permutations

standard deviation of I under permutations.

standardized I based on permutations

p-value based on standard normal approximation from permutations

Notes

Technical details and derivations can be found in [CO81].

Examples

>>> import libpysal
>>> w = libpysal.io.open(libpysal.examples.get_path("stl.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("stl_hom.txt"))
>>> y = np.array(f.by_col['HR8893'])
>>> from esda.moran import Moran
>>> mi = Moran(y,  w)
>>> round(mi.I, 3)
0.244
>>> mi.EI
-0.012987012987012988
>>> mi.p_norm
0.00027147862770937614

SIDS example replicating OpenGeoda

>>> w = libpysal.io.open(libpysal.examples.get_path("sids2.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("sids2.dbf"))
>>> SIDR = np.array(f.by_col("SIDR74"))
>>> mi = Moran(SIDR,  w)
>>> round(mi.I, 3)
0.248
>>> mi.p_norm
0.0001158330781489969

One-tailed

>>> mi_1 = Moran(SIDR,  w, two_tailed=False)
>>> round(mi_1.I, 3)
0.248
>>> round(mi_1.p_norm, 4)
0.0001

__init__(y, w, transformation='r', permutations=999, two_tailed=True)

Methods

__init__(y, w[, transformation, ...])
by_col(df, cols[, w, inplace, pvalue, outvals])	Function to compute a Moran statistic on a dataframe
plot_scatter([ax, scatter_kwds, fitline_kwds])	Plot a Moran scatterplot with optional coloring for significant points.
plot_simulation([ax, legend, fitline_kwds])	Global Moran's I simulated reference distribution.

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

Function to compute a Moran statistic on a dataframe

Parameters:

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

return a series contaning the results of the computation. If operating inplace, the derived columns will be named ‘column_moran’

the Moran statistic’s documentation for available p-values

Moran statistic

documentation for the Moran statistic.

Returns:

the relevant columns attached.

plot_scatter(ax=None, scatter_kwds=None, fitline_kwds=None)

Plot a Moran scatterplot with optional coloring for significant points.

Parameters:

axmatplotlib.axes.Axes, optional

Pre-existing axes for the plot, by default None.

Returns:

matplotlib.axes.Axes

Axes object with the Moran scatterplot.

plot_simulation(ax=None, legend=False, fitline_kwds=None, **kwargs)

Global Moran’s I simulated reference distribution.

Parameters:

axmatplotlib.axes.Axes, optional

Pre-existing axes for the plot, by default None.

by default None.

Returns:

matplotlib.axes.Axes

Axes object with the Moran scatterplot.

Notes

This requires optional dependencies matplotlib and seaborn.

Examples

>>> import libpysal
>>> w = libpysal.io.open(libpysal.examples.get_path("stl.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("stl_hom.txt"))
>>> y = np.array(f.by_col['HR8893'])
>>> from esda.moran import Moran
>>> mi = Moran(y,  w)

Default plot:

>>> mi.plot_simulation()

Customized styling that turns the distribution into a pink line and line indicating I to a black line:

>>> mi.plot_simulation(fitline_kwds={"color": "k"}, color="pink", shade=False)