esda.G¶

class esda.G(y, w, permutations=999)[source]¶

Global G Autocorrelation Statistic

Parameters:

yarray (n,1): Attribute values
wW | Graph: spatial weights instance as W or Graph aligned with y
permutationsint: the number of random permutations for calculating pseudo p_values

Notes

Moments are based on normality assumption.

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

Examples

>>> import libpysal
>>> 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 = libpysal.weights.DistanceBand(points,threshold=15)
>>> w.transform = "B"

Preparing a variable

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

Applying Getis and Ord G test

>>> from esda.getisord import G
>>> g = G(y,w)

Examining the results

>>> round(g.G, 3)
0.557

>>> round(g.p_norm, 3)
0.173

Attributes:

yarray: original variable
wW: spatial weights instance as W or Graph aligned with y
permutationint: the number of permutations
Gfloat: the value of statistic
EGfloat: the expected value of statistic
VGfloat: the variance of G under normality assumption
z_normfloat: standard normal test statistic
p_normfloat: p-value under normality assumption (one-sided)
simarray: (if permutations > 0) vector of G values for permutated samples
p_simfloat: 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_simfloat: average value of G from permutations
VG_simfloat: variance of G from permutations
seG_simfloat: standard deviation of G under permutations.
z_simfloat: standardized G based on permutations
p_z_simfloat: p-value based on standard normal approximation from permutations (one-sided)

Methods

`__init__`(y, w[, permutations])
`by_col`(df, cols[, w, inplace, pvalue, outvals])	Function to compute a G statistic on a dataframe

classmethod by_col(df, cols, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]¶

Function to compute a G statistic on a dataframe

Parameters:

dfpandas.DataFrame: a pandas dataframe with a geometry column
colsstr or list of str: name or list of names of columns to use to compute the statistic
wpysal weights object: a weights object aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
inplacebool: a boolean denoting whether to operate on the dataframe inplace or to return a series contaning the results of the computation. If operating inplace, the derived columns will be named ‘column_g’
pvaluestr: a string denoting which pvalue should be returned. Refer to the the G statistic’s documentation for available p-values
outvalslist of strings: list of arbitrary attributes to return as columns from the G statistic
**stat_kwsdict: options to pass to the underlying statistic. For this, see the documentation for the G statistic.

Returns: