esda.Gamma

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

Gamma index for spatial autocorrelation

Parameters:
wW

spatial weights instance can be binary or row-standardized

operation{‘c’, ‘s’, ‘a’}

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

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

Notes

For further technical details see [HGC81].

Examples

use same example as for join counts to show similarity

>>> import libpysal, numpy as np
>>> from esda.gamma 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
20.0
>>> round(g.g_z, 3)
3.188
>>> round(g.p_sim_g, 3)
0.003
>>> g.min_g
0.0
>>> g.max_g
20.0
>>> g.mean_g
11.093093093093094
>>> np.random.seed(12345)
>>> g1 = Gamma(y,w,operation='s')
>>> g1.g
8.0
>>> round(g1.g_z, 3)
-3.706
>>> g1.p_sim_g
0.001
>>> g1.min_g
14.0
>>> g1.max_g
48.0
>>> g1.mean_g
25.623623623623622
>>> np.random.seed(12345)
>>> g2 = Gamma(y,w,operation='a')
>>> g2.g
8.0
>>> round(g2.g_z, 3)
-3.706
>>> g2.p_sim_g
0.001
>>> g2.min_g
14.0
>>> g2.max_g
48.0
>>> g2.mean_g
25.623623623623622
>>> np.random.seed(12345)
>>> g3 = Gamma(y,w,standardize=True)
>>> g3.g
32.0
>>> round(g3.g_z, 3)
3.706
>>> g3.p_sim_g
0.001
>>> g3.min_g
-48.0
>>> g3.max_g
20.0
>>> g3.mean_g
-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
20.0
>>> round(g4.g_z, 3)
3.188
>>> round(g4.p_sim_g, 3)
0.003
Attributes:
wW

original w object

op{‘c’, ‘s’, ‘a’}

attribute similarity function, as per parameters attribute similarity function

vector of Gamma index values for permuted samples

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

__init__(y, w, operation='c', standardize=False, permutations=999)[source]

Methods

__init__(y, w[, operation, standardize, ...])

by_col(df, cols[, w, inplace, pvalue, outvals])

Attributes

p_sim

new name to fit with Moran module

classmethod by_col(df, cols, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]
property p_sim

new name to fit with Moran module