pysal.explore.esda.Gamma

class pysal.explore.esda.Gamma(y, w, operation='c', standardize='no', permutations=999)[source]

Gamma index for spatial autocorrelation

Parameters:
y : array

variable measured across n spatial units

w : W

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

standardize : {‘no’, ‘yes’}

standardize variables first ‘no’ keep as is ‘yes’ or ‘y’ standardize to mean zero and variance one

permutations : int

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 pysal.lib, numpy as np
>>> from pysal.explore.esda.gamma import Gamma
>>> w = pysal.lib.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='y')
>>> 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:
y : array

original variable

w : W

original w object

op : {‘c’, ‘s’, ‘a’}

attribute similarity function, as per parameters attribute similarity function

stand : {‘no’, ‘yes’}

standardization

permutations : int

number of permutations

gamma : float

value of Gamma index

sim_g : array

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

p_sim_g : array

(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_g : float

average of permuted Gamma values

min_g : float

minimum of permuted Gamma values

max_g : float

maximum of permuted Gamma values

Methods

by_col  
__init__(y, w, operation='c', standardize='no', permutations=999)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(y, w[, operation, standardize, …]) Initialize self.
by_col(df, cols[, w, inplace, pvalue, outvals])

Attributes

p_sim new name to fit with Moran module