esda.Moran_BV¶

class esda.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 | 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.
permutations : int¶: number of random permutations for calculation of pseudo p_values

zx[source]¶

original x variable standardized by mean and std

Type:¶: array

zy[source]¶

original y variable standardized by mean and std

Type:¶: array

w[source]¶

original w object

Type:¶: W | Graph

permutation[source]¶

number of permutations

Type:¶: int

I[source]¶

value of bivariate Moran’s I

Type:¶: float

sim[source]¶

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

Type:¶: array

p_sim[source]¶

(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

Type:¶: float

EI_sim[source]¶

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

Type:¶: array

VI_sim[source]¶

(if permutations>0) variance of I from permutations

Type:¶: array

seI_sim[source]¶

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

Type:¶: array

z_sim[source]¶

(if permutations>0) standardized I based on permutations

Type:¶: array

p_z_sim[source]¶

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

Type:¶: float

Notes

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

Examples

>>> import libpysal, numpy

Set random number generator seed so we can replicate the example

>>> numpy.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 = numpy.array(f.by_col['SIDR74'])
>>> SIDR79 = numpy.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 import Moran_BV
>>> mbi = Moran_BV(SIDR79,  SIDR74,  w)

What is the bivariate Moran’s I value

>>> round(mbi.I, 3)
np.float64(0.156)

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

>>> round(mbi.p_z_sim, 3)
np.float64(0.001)

Methods

`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:¶

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 : W | Graph¶: spatial weights instance as W or Graph 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.

plot_scatter(ax=None, scatter_kwds=None, fitline_kwds=None)[source]¶

Plot a Moran scatterplot with optional coloring for significant points.

Parameters:¶

ax : matplotlib.axes.Axes, optional¶: Pre-existing axes for the plot, by default None.
scatter_kwds : dict, optional¶: Additional keyword arguments for scatter plot, by default None.
fitline_kwds : dict, optional¶: Additional keyword arguments for fit line, by default None.

Returns:¶

Axes object with the Moran scatterplot.

Return type:¶

matplotlib.axes.Axes

plot_simulation(ax=None, legend=False, fitline_kwds=None, **kwargs)[source]¶

Global Moran’s I simulated reference distribution.

Parameters:¶

ax : matplotlib.axes.Axes, optional¶: Pre-existing axes for the plot, by default None.
legend : bool, optional¶: Plot a legend, by default False
fitline_kwds : dict, optional¶: Additional keyword arguments for vertical Moran fit line, by default None.
**kwargs : keyword arguments, optional¶: Additional keyword arguments for KDE plot passed to seaborn.kdeplot, by default None.

Returns:¶

Axes object with the Moran scatterplot.

Return type:¶

matplotlib.axes.Axes

Notes

This requires optional dependencies matplotlib and seaborn.