esda.Moran_Local_Rate

class esda.Moran_Local_Rate(e, b, w, adjusted=True, transformation='r', permutations=999, geoda_quads=False)[source]

Adjusted Local Moran Statistics for Rate Variables [AR99].

Parameters
earray

(n,1), an event variable across n spatial units

barray

(n,1), a population-at-risk variable across n spatial units

wW

weight instance assumed to be aligned with y

adjustedbool

whether or not local Moran statistics need 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.

permutationsint

number of random permutations for calculation of pseudo p_values

geoda_quadsbool

(default=False) If True use GeoDa scheme: HH=1, LL=2, LH=3, HL=4 If False use PySAL Scheme: HH=1, LH=2, LL=3, HL=4

Attributes
———-
yarray

rate variables 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 random permutations for calculation of pseudo p_values

Ifloat

value of Moran’s I

qarray

(if permutations>0) values indicate quandrant location 1 HH, 2 LH, 3 LL, 4 HL

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 Ii is further away or extreme from the median of simulated Iis. It is either extremely high or extremely low in the distribution of simulated Is

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 permutations (one-sided) for two-sided tests, these values should be multiplied by 2

Examples

>>> import libpysal
>>> import numpy as np
>>> np.random.seed(10)
>>> 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_Local_Rate
>>> lm = Moran_Local_Rate(e, b, w, transformation = "r", permutations = 99)
>>> lm.q[:10]
array([2, 4, 3, 1, 2, 1, 1, 4, 2, 4])
>>> lm = Moran_Local_Rate(e, b, w,  transformation = "r",  permutations = 99,  geoda_quads=True)
>>> lm.q[:10]
array([3, 4, 2, 1, 3, 1, 1, 4, 3, 4])

Note random components result is slightly different values across architectures so the results have been removed from doctests and will be moved into unittests that are conditional on architectures

__init__(self, e, b, w, adjusted=True, transformation='r', permutations=999, geoda_quads=False)[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_Local_Rate statistic on a dataframe

calc(self, w, z)