pysal.explore.esda.G_Local

class pysal.explore.esda.G_Local(y, w, transform='R', permutations=999, star=False)[source]

Generalized Local G Autocorrelation

Parameters:
y : array

variable

w : W

DistanceBand, weights instance that is based on threshold distance and is assumed to be aligned with y

transform : {‘R’, ‘B’}

the type of w, either ‘B’ (binary) or ‘R’ (row-standardized)

permutations : int

the number of random permutations for calculating pseudo p values

star : boolean

whether or not to include focal observation in sums (default: False)

Notes

To compute moments of Gs under normality assumption, PySAL considers w is either binary or row-standardized. For binary weights object, the weight value for self is 1 For row-standardized weights object, the weight value for self is 1/(the number of its neighbors + 1).

For technical details see [GO10] and [OG10].

Examples

>>> import pysal.lib
>>> import numpy
>>> numpy.random.seed(10)

Preparing a point data set

>>> points = [(10, 10), (20, 10), (40, 10), (15, 20), (30, 20), (30, 30)]

Creating a weights object from points

>>> w = pysal.lib.weights.DistanceBand(points,threshold=15)

Prepareing a variable

>>> y = numpy.array([2, 3, 3.2, 5, 8, 7])

Applying Getis and Ord local G test using a binary weights object

>>> from pysal.explore.esda.getisord import G_Local
>>> lg = G_Local(y,w,transform='B')

Examining the results

>>> lg.Zs
array([-1.0136729 , -0.04361589,  1.31558703, -0.31412676,  1.15373986,
        1.77833941])
>>> round(lg.p_sim[0], 3)
0.101
>>> numpy.random.seed(10)

Applying Getis and Ord local G* test using a binary weights object >>> lg_star = G_Local(y,w,transform=’B’,star=True)

Examining the results >>> lg_star.Zs array([-1.39727626, -0.28917762, 0.65064964, -0.28917762, 1.23452088,

2.02424331])
>>> round(lg_star.p_sim[0], 3)
0.101
>>> numpy.random.seed(12345)

Applying Getis and Ord local G test using a row-standardized weights object >>> lg = G_Local(y,w,transform=’R’)

Examining the results >>> lg.Zs array([-0.62074534, -0.01780611, 1.31558703, -0.12824171, 0.28843496,

1.77833941])
>>> round(lg.p_sim[0], 3)
0.103
>>> numpy.random.seed(10)

Applying Getis and Ord local G* test using a row-standardized weights object

>>> lg_star = G_Local(y,w,transform='R',star=True)

Examining the results >>> lg_star.Zs array([-0.62488094, -0.09144599, 0.41150696, -0.09144599, 0.24690418,

1.28024388])
>>> round(lg_star.p_sim[0], 3)
0.101
Attributes:
y : array

original variable

w : DistanceBand W

original weights object

permutations : int

the number of permutations

Gs : array

of floats, the value of the orginal G statistic in Getis & Ord (1992)

EGs : float

expected value of Gs under normality assumption the values is scalar, since the expectation is identical across all observations

VGs : array

of floats, variance values of Gs under normality assumption

Zs : array

of floats, standardized Gs

p_norm : array

of floats, p-value under normality assumption (one-sided) for two-sided tests, this value should be multiplied by 2

sim : array

of arrays of floats (if permutations>0), vector of I values for permutated samples

p_sim : array

of floats, p-value based on permutations (one-sided) null - spatial randomness alternative - the observed G is extreme it is either extremely high or extremely low

EG_sim : array

of floats, average value of G from permutations

VG_sim : array

of floats, variance of G from permutations

seG_sim : array

of floats, standard deviation of G under permutations.

z_sim : array

of floats, standardized G based on permutations

p_z_sim : array

of floats, p-value based on standard normal approximation from permutations (one-sided)

Methods

by_col(df, cols[, w, inplace, pvalue, outvals]) Function to compute a G_Local statistic on a dataframe
calc  
__init__(y, w, transform='R', permutations=999, star=False)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(y, w[, transform, permutations, star]) Initialize self.
by_col(df, cols[, w, inplace, pvalue, outvals]) Function to compute a G_Local statistic on a dataframe
calc()