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: spatial weights instance
adjustedboolean: 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_tailedboolean: 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: 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_tailedboolean: 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

Methods

by_col(df, events, populations[, w, …])

Function to compute a Moran_Rate statistic on a dataframe

__init__(self, e, b, w, adjusted=True, transformation='r', permutations=999, two_tailed=True)[source]¶: Initialize self. See help(type(self)) for accurate signature.

Methods

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