esda.Geary¶

class esda.Geary(y, w, transformation='r', permutations=999)[source]¶

Global Geary C Autocorrelation statistic

Parameters:

yarray: (n, 1) attribute vector
wW | Graph: spatial weights instance as W or Graph aligned with y
transformation{‘R’, ‘B’, ‘D’, ‘U’, ‘V’}: weights transformation, default is row-standardized. Other options include “B”: binary, “D”: doubly-standardized, “U”: untransformed (general weights), “V”: variance-stabilizing.
permutationsint: number of random permutations for calculation of pseudo-p_values

Notes

Technical details and derivations can be found in [CO81].

Examples

>>> import libpysal
>>> from esda.geary import Geary
>>> w = libpysal.io.open(libpysal.examples.get_path("book.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("book.txt"))
>>> y = np.array(f.by_col['y'])
>>> c = Geary(y,w,permutations=0)
>>> round(c.C,7)
0.3330108
>>> round(c.p_norm,7)
9.2e-05
>>>

Attributes:

yarray: original variable
wW | Graph: spatial weights
permutationsint: number of permutations
Cfloat: value of statistic
ECfloat: expected value
VCfloat: variance of G under normality assumption
z_normfloat: z-statistic for C under normality assumption
z_randfloat: z-statistic for C under randomization assumption
p_normfloat: p-value under normality assumption (one-tailed)
p_randfloat: p-value under randomization assumption (one-tailed)
simarray: (if permutations!=0) vector of I values for permutated samples
p_simfloat: (if permutations!=0) p-value based on permutations (one-tailed) null: sptial randomness alternative: the observed C is extreme it is either extremely high or extremely low
EC_simfloat: (if permutations!=0) average value of C from permutations
VC_simfloat: (if permutations!=0) variance of C from permutations
seC_simfloat: (if permutations!=0) standard deviation of C under permutations.
z_simfloat: (if permutations!=0) standardized C based on permutations
p_z_simfloat: (if permutations!=0) p-value based on standard normal approximation from permutations (one-tailed)

__init__(y, w, transformation='r', permutations=999)[source]¶

Methods

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

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

Function to compute a Geary 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, with default configurations, the derived columns will be named like ‘column_geary’ and ‘column_p_sim’
pvaluestr: a string denoting which pvalue should be returned. Refer to the the Geary statistic’s documentation for available p-values
outvalslist of strings: list of arbitrary attributes to return as columns from the Geary statistic
**stat_kwsdict: options to pass to the underlying statistic. For this, see the documentation for the Geary statistic.

Returns:

If inplace, None, and operation is conducted on dataframe in memory. Otherwise,
returns a copy of the dataframe with the relevant columns attached.

Notes

Technical details and derivations can be found in [CO81].