esda.Moran_Rate¶

class esda.Moran_Rate(e, b, w, adjusted=True, transformation='r', permutations=999, two_tailed=True)[source]¶

Adjusted Moran’s I Global Autocorrelation Statistic for Rate Variables [AR99]

Parameters:

earray: an event variable measured across n spatial units
barray: a population-at-risk variable measured across n spatial units
wW | Graph: spatial weights instance as W or Graph aligned with e and b
adjustedbool: whether or not Moran’s I needs to be adjusted for rate variable
transformation{‘R’, ‘B’, ‘D’, ‘U’, ‘V’}: weights transformation, default is row-standardized “r”. Other options include “B”: binary, “D”: doubly-standardized, “U”: untransformed (general weights), “V”: variance-stabilizing.
two_tailedbool: If True (default), analytical p-values for Moran’s I are two-tailed, otherwise they are one tailed.
permutationsint: number of random permutations for calculation of pseudo p_values

Examples

>>> import libpysal
>>> w = libpysal.io.open(libpysal.examples.get_path("sids2.gal")).read()
>>> f = libpysal.io.open(libpysal.examples.get_path("sids2.dbf"))
>>> e = np.array(f.by_col('SID79'))
>>> b = np.array(f.by_col('BIR79'))
>>> from esda.moran import Moran_Rate
>>> mi = Moran_Rate(e, b,  w, two_tailed=False)
>>> "%6.4f" % mi.I
'0.1662'
>>> "%6.4f" % mi.p_norm
'0.0042'

Attributes:

yarray: rate variable computed from parameters e and b if adjusted is True, y is standardized rates otherwise, y is raw rates
wW | Graph: original w object
permutationsint: number of permutations
Ifloat: value of Moran’s I
EIfloat: expected value under normality assumption
VI_normfloat: variance of I under normality assumption
seI_normfloat: standard deviation of I under normality assumption
z_normfloat: z-value of I under normality assumption
p_normfloat: p-value of I under normality assumption
VI_randfloat: variance of I under randomization assumption
seI_randfloat: standard deviation of I under randomization assumption
z_randfloat: z-value of I under randomization assumption
p_randfloat: p-value of I under randomization assumption
two_tailedbool: If True, p_norm and p_rand are two-tailed p-values, otherwise they are one-tailed.
simarray: (if permutations>0) vector of I values for permuted samples
p_simarray: (if permutations>0) p-value based on permutations (one-sided) null: spatial randomness alternative: the observed I is extreme if it is either extremely greater or extremely lower than the values obtained from permutaitons
EI_simfloat: (if permutations>0) average value of I from permutations
VI_simfloat: (if permutations>0) variance of I from permutations
seI_simfloat: (if permutations>0) standard deviation of I under permutations.
z_simfloat: (if permutations>0) standardized I based on permutations
p_z_simfloat: (if permutations>0) p-value based on standard normal approximation from

__init__(e, b, w, adjusted=True, transformation='r', permutations=999, two_tailed=True)[source]¶

Methods

`__init__`(e, b, w[, adjusted, ...])
`by_col`(df, events, populations[, w, ...])	Function to compute a Moran_Rate statistic on a dataframe

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

Function to compute a Moran_Rate statistic on a dataframe

Parameters:

dfpandas.DataFrame: a pandas dataframe with a geometry column
eventsstr or list of strings: one or more names where events are stored
populationsstr or list of strings: one or more names where the populations corresponding to the events are stored. If one population column is provided, it is used for all event columns. If more than one population column is provided but there is not a population for every event column, an exception will be raised.
wW | Graph: spatial weights instance as W or Graph 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_moran_rate’
pvaluestr: a string denoting which pvalue should be returned. Refer to the the Moran_Rate statistic’s documentation for available p-values
outvalslist of strings: list of arbitrary attributes to return as columns from the Moran_Rate statistic
**stat_kwskeyword arguments: options to pass to the underlying statistic. For this, see the documentation for the Moran_Rate 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.