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 []

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

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

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