giddy.rank.SpatialTau¶

class giddy.rank.SpatialTau(x, y, w, permutations=0)[source]¶

Spatial version of Kendall’s rank correlation statistic.

Kendall’s Tau is based on a comparison of the number of pairs of n observations that have concordant ranks between two variables. The spatial Tau decomposes these pairs into those that are spatial neighbors and those that are not, and examines whether the rank correlation is different between the two sets relative to what would be expected under spatial randomness.

Parameters:	x : array (n, ), first variable. y : array (n, ), second variable. w : W spatial weights object. permutations : int number of random spatial permutations for computationally based inference.

Notes

Algorithm has two stages. The first calculates classic Tau using a list based implementation of the algorithm from [Chr05]. Second stage calculates concordance measures for neighboring pairs of locations using a modification of the algorithm from [PTVF07]. See [Rey14] for details.

Examples

>>> import libpysal as ps
>>> import numpy as np
>>> from giddy.rank import SpatialTau
>>> f=ps.io.open(ps.examples.get_path("mexico.csv"))
>>> vnames=["pcgdp%d"%dec for dec in range(1940,2010,10)]
>>> y=np.transpose(np.array([f.by_col[v] for v in vnames]))
>>> regime=np.array(f.by_col['esquivel99'])
>>> w=ps.weights.block_weights(regime)
>>> np.random.seed(12345)
>>> res=[SpatialTau(y[:,i],y[:,i+1],w,99) for i in range(6)]
>>> for r in res:
...     ev = r.taus.mean()
...     "%8.3f %8.3f %8.3f"%(r.tau_spatial, ev, r.tau_spatial_psim)
... 
'   0.397    0.659    0.010'
'   0.492    0.706    0.010'
'   0.651    0.772    0.020'
'   0.714    0.752    0.210'
'   0.683    0.705    0.270'
'   0.810    0.819    0.280'

Attributes:

Attributes:	tau : float The classic Tau statistic. tau_spatial : float Value of Tau for pairs that are spatial neighbors. taus : array (permtuations, 1), values of simulated tau_spatial values under random spatial permutations in both periods. (Same permutation used for start and ending period). pairs_spatial : int Number of spatial pairs. concordant : float Number of concordant pairs. concordant_spatial : float Number of concordant pairs that are spatial neighbors. extraX : float Number of extra X pairs. extraY : float Number of extra Y pairs. discordant : float Number of discordant pairs. discordant_spatial : float Number of discordant pairs that are spatial neighbors. taus : float spatial tau values for permuted samples (if permutations>0). tau_spatial_psim : float one-sided pseudo p-value for observed tau_spatial under the null of spatial randomness of rank exchanges (if permutations>0).

tau : float: The classic Tau statistic.
tau_spatial : float: Value of Tau for pairs that are spatial neighbors.
taus : array: (permtuations, 1), values of simulated tau_spatial values under random spatial permutations in both periods. (Same permutation used for start and ending period).
pairs_spatial : int: Number of spatial pairs.
concordant : float: Number of concordant pairs.
concordant_spatial : float: Number of concordant pairs that are spatial neighbors.
extraX : float: Number of extra X pairs.
extraY : float: Number of extra Y pairs.
discordant : float: Number of discordant pairs.
discordant_spatial : float: Number of discordant pairs that are spatial neighbors.
taus : float: spatial tau values for permuted samples (if permutations>0).
tau_spatial_psim : float: one-sided pseudo p-value for observed tau_spatial under the null of spatial randomness of rank exchanges (if permutations>0).

__init__(x, y, w, permutations=0)[source]¶: Initialize self. See help(type(self)) for accurate signature.