esda.Moran_BV¶

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

Bivariate Moran’s I

Parameters:

xarray: x-axis variable
yarray: wy will be on y axis
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

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

Attributes:

zxarray: original x variable standardized by mean and std
zyarray: original y variable standardized by mean and std
wW: original w object
permutationint: number of permutations
Ifloat: value of bivariate Moran’s I
simarray: (if permutations>0) vector of I values for permuted samples
p_simfloat: (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_simarray: (if permutations>0) average value of I from permutations
VI_simarray: (if permutations>0) variance of I from permutations
seI_simarray: (if permutations>0) standard deviation of I under permutations.
z_simarray: (if permutations>0) standardized I based on permutations
p_z_simfloat: (if permutations>0) p-value based on standard normal approximation from permutations

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

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:

dfpandas.DataFrame: a pandas dataframe with a geometry column
Xlist 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.
Ylist 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.
wpysal weights object: a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
inplacebool: 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’
pvaluestr: a string denoting which pvalue should be returned. Refer to the the Moran_BV statistic’s documentation for available p-values
outvalslist of strings: list of arbitrary attributes to return as columns from the Moran_BV statistic
**stat_kwskeyword arguments: options to pass to the underlying statistic. For this, see the documentation for the Moran_BV statistic.

Returns: