giddy.rank.Tau_Regional¶

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

Inter and intraregional decomposition of the classic Tau.

Parameters:	x : array (n, ), first variable. y : array (n, ), second variable. regimes : array (n, ), ids of which regime an observation belongs to. permutations : int number of random spatial permutations for computationally based inference.

Notes

The equation for calculating inter and intraregional Tau statistic can be found in [Rey16] Equation (27).

Examples

>>> import libpysal as ps
>>> import numpy as np
>>> from giddy.rank import Tau_Regional
>>> np.random.seed(10)
>>> 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]))
>>> r = y / y.mean(axis=0)
>>> regime = np.array(f.by_col['esquivel99'])
>>> res = Tau_Regional(y[:,0],y[:,-1],regime,permutations=999)
>>> res.tau_reg
array([[1.        , 0.25      , 0.5       , 0.6       , 0.83333333,
        0.6       , 1.        ],
       [0.25      , 0.33333333, 0.5       , 0.3       , 0.91666667,
        0.4       , 0.75      ],
       [0.5       , 0.5       , 0.6       , 0.4       , 0.38888889,
        0.53333333, 0.83333333],
       [0.6       , 0.3       , 0.4       , 0.2       , 0.4       ,
        0.28      , 0.8       ],
       [0.83333333, 0.91666667, 0.38888889, 0.4       , 0.6       ,
        0.73333333, 1.        ],
       [0.6       , 0.4       , 0.53333333, 0.28      , 0.73333333,
        0.8       , 0.8       ],
       [1.        , 0.75      , 0.83333333, 0.8       , 1.        ,
        0.8       , 0.33333333]])
>>> res.tau_reg_pvalues
array([[0.782, 0.227, 0.464, 0.638, 0.294, 0.627, 0.201],
       [0.227, 0.352, 0.391, 0.14 , 0.048, 0.252, 0.327],
       [0.464, 0.391, 0.587, 0.198, 0.107, 0.423, 0.124],
       [0.638, 0.14 , 0.198, 0.141, 0.184, 0.089, 0.217],
       [0.294, 0.048, 0.107, 0.184, 0.583, 0.25 , 0.005],
       [0.627, 0.252, 0.423, 0.089, 0.25 , 0.38 , 0.227],
       [0.201, 0.327, 0.124, 0.217, 0.005, 0.227, 0.322]])

Attributes:

Attributes:	n : int number of observations. S : array (n ,n), concordance matrix, s_{i,j}=1 if observation i and j are concordant, s_{i, j}=-1 if observation i and j are discordant, and s_{i,j}=0 otherwise. tau_reg : array (k, k), observed concordance matrix with diagonal elements measuring concordance between units within a regime and the off-diagonal elements denoting concordance between observations from a specific pair of different regimes. tau_reg_sim : array (permutations, k, k), concordance matrices for permuted samples (if permutations>0). tau_reg_pvalues : array (k, k), one-sided pseudo p-values for observed concordance matrix under the null that income mobility were random in its spatial distribution.

n : int: number of observations.
S : array: (n ,n), concordance matrix, s_{i,j}=1 if observation i and j are concordant, s_{i, j}=-1 if observation i and j are discordant, and s_{i,j}=0 otherwise.
tau_reg : array: (k, k), observed concordance matrix with diagonal elements measuring concordance between units within a regime and the off-diagonal elements denoting concordance between observations from a specific pair of different regimes.
tau_reg_sim : array: (permutations, k, k), concordance matrices for permuted samples (if permutations>0).
tau_reg_pvalues : array: (k, k), one-sided pseudo p-values for observed concordance matrix under the null that income mobility were random in its spatial distribution.

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