esda.Gamma

class esda.Gamma(y, w, operation='c', standardize=False, permutations=999)[source]

Gamma index for spatial autocorrelation

Parameters:
y : array

variable measured across n spatial units

w : W | Graph

spatial weights instance as W or Graph aligned with y can be binary or row-standardized

operation : {'c', 's', 'a'}

attribute similarity function where, ‘c’ cross product ‘s’ squared difference ‘a’ absolute difference

standardize : {False, True}

standardize variables first False, keep as is True, standardize to mean zero and variance one

permutations : int

number of random permutations for calculation of pseudo-p_values

y[source]

original variable

Type:

array

w[source]

original w object

Type:

W

op[source]

attribute similarity function, as per parameters attribute similarity function

Type:

{‘c’, ‘s’, ‘a’}

stand[source]

standardization

Type:

{False, True}

permutations[source]

number of permutations

Type:

int

gamma[source]

value of Gamma index

Type:

float

sim_g[source]

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

Type:

array

p_sim_g[source]

(if permutations>0) p-value based on permutations (one-sided) null: spatial randomness alternative: the observed Gamma is more extreme than under randomness implemented as a two-sided test

Type:

array

mean_g[source]

average of permuted Gamma values

Type:

float

min_g[source]

minimum of permuted Gamma values

Type:

float

max_g[source]

maximum of permuted Gamma values

Type:

float

Examples

use same example as for join counts to show similarity

>>> import libpysal, numpy as np
>>> from esda import Gamma
>>> w = libpysal.weights.lat2W(4, 4)
>>> y=np.ones(16)
>>> y[0:8]=0
>>> np.random.seed(12345)
>>> g = Gamma(y, w)
>>> g.g
np.float64(20.0)
>>> round(g.g_z, 3)
np.float64(3.188)
>>> round(g.p_sim_g, 3)
np.float64(0.003)
>>> g.min_g
np.float64(0.0)
>>> g.max_g
np.float64(20.0)
>>> g.mean_g
np.float64(11.093093093093094)
>>> np.random.seed(12345)
>>> g1 = Gamma(y, w, operation='s')
>>> g1.g
np.float64(8.0)
>>> round(g1.g_z, 3)
np.float64(-3.706)
>>> g1.p_sim_g
np.float64(0.001)
>>> g1.min_g
np.float64(14.0)
>>> g1.max_g
np.float64(48.0)
>>> g1.mean_g
np.float64(25.623623623623622)
>>> np.random.seed(12345)
>>> g2 = Gamma(y, w, operation='a')
>>> g2.g
np.float64(8.0)
>>> round(g2.g_z, 3)
np.float64(-3.706)
>>> g2.p_sim_g
np.float64(0.001)
>>> g2.min_g
np.float64(14.0)
>>> g2.max_g
np.float64(48.0)
>>> g2.mean_g
np.float64(25.623623623623622)
>>> np.random.seed(12345)
>>> g3 = Gamma(y, w, standardize=True)
>>> g3.g
np.float64(32.0)
>>> round(g3.g_z, 3)
np.float64(3.706)
>>> g3.p_sim_g
np.float64(0.001)
>>> g3.min_g
np.float64(-48.0)
>>> g3.max_g
np.float64(20.0)
>>> g3.mean_g
np.float64(-3.2472472472472473)
>>> np.random.seed(12345)
>>> def func(z, i, j):
...     q = z[i] * z[j]
...     return q
...
>>> g4 = Gamma(y, w, operation=func)
>>> g4.g
np.float64(20.0)
>>> round(g4.g_z, 3)
np.float64(3.188)
>>> round(g4.p_sim_g, 3)
np.float64(0.003)

Notes

For further technical details see [Hubert et al., 1981].

Attributes

p_sim

new name to fit with Moran module
property p_sim[source]

new name to fit with Moran module