esda.Moran_BV

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

Bivariate Moran’s I

Parameters:
wW | Graph

spatial weights instance as W or Graph aligned with x and y

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

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

p_values

Attributes:
wW | Graph

original w object

vector of I values for permuted samples

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

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

Inference is only based on permutations as analytical results are not too reliable.

Examples

>>> import libpysal
>>> 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 = libpysal.io.open(libpysal.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 = libpysal.io.open(libpysal.examples.get_path("sids2.gal")).read()

Create an instance of Moran_BV

>>> from esda.moran import Moran_BV
>>> mbi = Moran_BV(SIDR79,  SIDR74,  w)

What is the bivariate Moran’s I value

>>> round(mbi.I, 3)
0.156

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

>>> round(mbi.p_z_sim, 3)
0.001
__init__(x, y, w, transformation='r', permutations=999)[source]

Methods

__init__(x, y, w[, transformation, permutations])

by_col(df, x[, y, w, inplace, pvalue, outvals])

Function to compute a Moran_BV 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, 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:
the bivariate statistic. If no Y is provided, pairwise comparisons among these variates are used instead.

the bivariate statistic. if no Y is provided, pariwise comparisons among the X variates are used instead.

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_local’

the Moran_BV statistic’s documentation for available p-values

Moran_BV statistic

documentation for the Moran_BV statistic.

Returns:
the relevant columns attached.
plot_scatter(ax=None, scatter_kwds=None, fitline_kwds=None)[source]

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)[source]

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.