giddy.markov.prais¶

giddy.markov.prais(pmat)[source]¶

Prais conditional mobility measure.

Parameters:

pmatmatrix: (k, k), Markov probability transition matrix.

Returns:

prmatrix: (1, k), conditional mobility measures for each of the k classes.

Notes

Prais’ conditional mobility measure for a class is defined as:

\[pr_i = 1 - p_{i,i}\]

Examples

>>> import numpy as np
>>> import libpysal
>>> from giddy.markov import Markov,prais
>>> f = libpysal.io.open(libpysal.examples.get_path("usjoin.csv"))
>>> pci = np.array([f.by_col[str(y)] for y in range(1929,2010)])
>>> q5 = np.array([mc.Quantiles(y).yb for y in pci]).transpose()
>>> m = Markov(q5, summary=False)
>>> m.transitions
array([[729.,  71.,   1.,   0.,   0.],
       [ 72., 567.,  80.,   3.,   0.],
       [  0.,  81., 631.,  86.,   2.],
       [  0.,   3.,  86., 573.,  56.],
       [  0.,   0.,   1.,  57., 741.]])
>>> m.p
array([[0.91011236, 0.0886392 , 0.00124844, 0.        , 0.        ],
       [0.09972299, 0.78531856, 0.11080332, 0.00415512, 0.        ],
       [0.        , 0.10125   , 0.78875   , 0.1075    , 0.0025    ],
       [0.        , 0.00417827, 0.11977716, 0.79805014, 0.07799443],
       [0.        , 0.        , 0.00125156, 0.07133917, 0.92740926]])
>>> prais(m.p)
array([0.08988764, 0.21468144, 0.21125   , 0.20194986, 0.07259074])