# pysal.explore.giddy.markov.kullback¶

pysal.explore.giddy.markov.kullback(F)[source]

Kullback information based test of Markov Homogeneity.

Parameters: F : array (s, r, r), values are transitions (not probabilities) for s strata, r initial states, r terminal states. Results : dictionary (key - value) Conditional homogeneity - (float) test statistic for homogeneity of transition probabilities across strata. Conditional homogeneity pvalue - (float) p-value for test statistic. Conditional homogeneity dof - (int) degrees of freedom = r(s-1)(r-1).

Notes

Based on [KKK62]. Example below is taken from Table 9.2 .

Examples

>>> import numpy as np
>>> from pysal.explore.giddy.markov import kullback
>>> s1 = np.array([
...         [ 22, 11, 24,  2,  2,  7],
...         [ 5, 23, 15,  3, 42,  6],
...         [ 4, 21, 190, 25, 20, 34],
...         [0, 2, 14, 56, 14, 28],
...         [32, 15, 20, 10, 56, 14],
...         [5, 22, 31, 18, 13, 134]
...     ])
>>> s2 = np.array([
...     [3, 6, 9, 3, 0, 8],
...     [1, 9, 3, 12, 27, 5],
...     [2, 9, 208, 32, 5, 18],
...     [0, 14, 32, 108, 40, 40],
...     [22, 14, 9, 26, 224, 14],
...     [1, 5, 13, 53, 13, 116]
...     ])
>>>
>>> F = np.array([s1, s2])
>>> res = kullback(F)
>>> "%8.3f"%res['Conditional homogeneity']
' 160.961'
>>> "%d"%res['Conditional homogeneity dof']
'30'
>>> "%3.1f"%res['Conditional homogeneity pvalue']
'0.0'