esda.Gamma

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

Gamma index for spatial autocorrelation

Parameters:

yarray

variable measured across n spatial units

wW | 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

permutationsint

number of random permutations for calculation of pseudo-p_values

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:

yarray

original variable

wW

original w object

op{‘c’, ‘s’, ‘a’}

attribute similarity function, as per parameters attribute similarity function

stand{False, True}

standardization

permutationsint

number of permutations

gammafloat

value of Gamma index

sim_garray

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

p_sim_garray

(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

mean_gfloat

average of permuted Gamma values

min_gfloat

minimum of permuted Gamma values

max_gfloat

maximum of permuted Gamma values

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

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)

property p_sim

new name to fit with Moran module