esda.Moran_Local¶
- class esda.Moran_Local(y, w, transformation='r', permutations=999, geoda_quads=False, n_jobs=1, keep_simulations=True, seed=None, island_weight=0)[source]¶
Local Moran Statistics.
- Parameters:
- y
array
(n,1), attribute array
- w
W
weight instance assumed to be aligned with y
- 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.
- permutations
int
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
- n_jobs
int
Number of cores to be used in the conditional randomisation. If -1, all available cores are used.
- keep_simulations
Boolean
(default=True) If True, the entire matrix of replications under the null is stored in memory and accessible; otherwise, replications are not saved
- seedNone/int
Seed to ensure reproducibility of conditional randomizations. Must be set here, and not outside of the function, since numba does not correctly interpret external seeds nor numpy.random.RandomState instances.
- island_weight:
value to use as a weight for the “fake” neighbor for every island. If numpy.nan, will propagate to the final local statistic depending on the stat_func. If 0, then the lag is always zero for islands.
- y
Notes
For technical details see [Ans95].
Examples
>>> import libpysal >>> import numpy as np >>> np.random.seed(10) >>> w = libpysal.io.open(libpysal.examples.get_path("desmith.gal")).read() >>> f = libpysal.io.open(libpysal.examples.get_path("desmith.txt")) >>> y = np.array(f.by_col['z']) >>> from esda.moran import Moran_Local >>> lm = Moran_Local(y, w, transformation = "r", permutations = 99) >>> lm.q array([4, 4, 4, 2, 3, 3, 1, 4, 3, 3]) >>> lm.p_z_sim[0] 0.24669152541631179 >>> lm = Moran_Local(y, w, transformation = "r", permutations = 99, geoda_quads=True) >>> lm.q array([4, 4, 4, 3, 2, 2, 1, 4, 2, 2])
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.
- Attributes:
- y
array
original variable
- w
W
original w object
- permutations
int
number of random permutations for calculation of pseudo p_values
- Is
array
local Moran’s I values
- q
array
(if permutations>0) values indicate quandrant location 1 HH, 2 LH, 3 LL, 4 HL
- sim
array
(permutations
by
n
) (if permutations>0) I values for permuted samples
- p_sim
array
(if permutations>0) p-values based on permutations (one-sided) null: spatial randomness alternative: the observed Ii is further away or extreme from the median of simulated values. It is either extremely high or extremely low in the distribution of simulated Is.
- EI_sim
array
(if permutations>0) average values of local Is from permutations
- VI_sim
array
(if permutations>0) variance of Is from permutations
- EI
array
analytical expectation of Is under total permutation, from []. Is the same at each site, and equal to the expectation of I itself when transformation=’r’. We recommend using EI_sim, not EI, for analysis. This EI is only provided for reproducibility.
- VI
array
analytical variance of Is under total permutation, from []. Varies according only to cardinality. We recommend using VI_sim, not VI, for analysis. This VI is only provided for reproducibility.
- EIc
array
analytical expectation of Is under conditional permutation, from [SOT98]. Varies strongly by site, since it conditions on z_i. We recommend using EI_sim, not EIc, for analysis. This EIc is only provided for reproducibility.
- VIc
array
analytical variance of Is under conditional permutation, from [SOT98]. Varies strongly by site, since it conditions on z_i. We recommend using VI_sim, not VIc, for analysis. This VIc is only provided for reproducibility.
- seI_sim
array
(if permutations>0) standard deviations of Is under permutations.
- z_sim
arrray
(if permutations>0) standardized Is based on permutations
- p_z_sim
array
(if permutations>0) p-values based on standard normal approximation from permutations (one-sided) for two-sided tests, these values should be multiplied by 2
- n_jobs
int
Number of cores to be used in the conditional randomisation. If -1, all available cores are used.
- keep_simulations
Boolean
(default=True) If True, the entire matrix of replications under the null is stored in memory and accessible; otherwise, replications are not saved
- seedNone/int
Seed to ensure reproducibility of conditional randomizations. Must be set here, and not outside of the function, since numba does not correctly interpret external seeds nor numpy.random.RandomState instances.
- y
- __init__(y, w, transformation='r', permutations=999, geoda_quads=False, n_jobs=1, keep_simulations=True, seed=None, island_weight=0)[source]¶
Methods
__init__
(y, w[, transformation, ...])by_col
(df, cols[, w, inplace, pvalue, outvals])Function to compute a Moran_Local statistic on a dataframe.
- classmethod by_col(df, cols, w=None, inplace=False, pvalue='sim', outvals=None, **stat_kws)[source]¶
Function to compute a Moran_Local statistic on a dataframe.
- Parameters:
- df
pandas.DataFrame
a pandas dataframe with a geometry column
- cols
str
orlist
ofstr
name or list of names of columns to use to compute the statistic
- w
pysal
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, the derived columns will be named ‘column_moran_local’
- pvalue
str
a string denoting which pvalue should be returned. Refer to the the Moran_Local statistic’s documentation for available p-values
- outvals
list
ofstrings
list of arbitrary attributes to return as columns from the Moran_Local statistic
- **stat_kws
dict
options to pass to the underlying statistic. For this, see the documentation for the Moran_Local statistic.
- df
- Returns: