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.

permutationspython:int

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

permutationpython:int

number of permutations

Ipython:float

value of bivariate Moran’s I

simarray

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

p_simpython: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_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_simpython:float

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

__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