esda.Gamma¶
- class esda.Gamma(y, w, operation='c', standardize=False, permutations=999)[source]¶
Gamma index for spatial autocorrelation
- Parameters:
- 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
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:
- w
W
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
Methods
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Attributes
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