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:
wW | Graph

spatial weights instance as W or Graph aligned with y

transformation{‘R’, ‘B’, ‘D’, ‘U’, ‘V’}

weights transformation, default is row-standardized “r”. Other options include “B”: binary, “D”: doubly-standardized, “O”: restore original transformation (applicable only if w is passed as W), “V”: variance-stabilizing.

p_values

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

all available cores are used.

keep_simulationsBoolean

(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.

Attributes:
wW | Graph

original w object

values indicate quandrant location 1 HH, 2 LH, 3 LL, 4 HL

I values for permuted samples

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.

average values of local Is from permutations

variance of Is from permutations

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.

from []. Varies according only to cardinality. We recommend using VI_sim, not VI, for analysis. This VI is only provided for reproducibility.

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.

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.

standard deviations of Is under permutations.

z_simarrray

(if permutations>0) standardized Is based on permutations

p-values based on standard normal approximation from permutations (one-sided) for two-sided tests, these values should be multiplied by 2

all available cores are used.

keep_simulationsBoolean

(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.

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.

__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.

explore(gdf[, crit_value])

Create interactive map of LISA indicators

get_cluster_labels([crit_value])

Return LISA cluster labels for each observation.

plot(gdf[, crit_value])

Create static map of LISA indicators

plot_combination(gdf, attribute[, ...])

Produce three-plot visualisation of Moran Scatteprlot, LISA cluster and Choropleth maps, with Local Moran region and quadrant masking

plot_scatter([crit_value, ax, scatter_kwds, ...])

Plot a Moran scatterplot with optional coloring for significant points.
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:
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

return a series contaning the results of the computation. If operating inplace, the derived columns will be named ‘column_moran_local’

the Moran_Local statistic’s documentation for available p-values

Moran_Local statistic

documentation for the Moran_Local statistic.

Returns:
the relevant columns attached.
explore(gdf, crit_value=0.05, **kwargs)[source]

Create interactive map of LISA indicators

Parameters:
Returns:
Folium.Map

interactive map with LISA clusters

get_cluster_labels(crit_value=0.05)[source]

Return LISA cluster labels for each observation.

Parameters:
Returns:
local Moran analysis

plot(gdf, crit_value=0.05, **kwargs)[source]

Create static map of LISA indicators

Parameters:
Returns:
ax

matplotlib axis

plot_combination(gdf, attribute, crit_value=0.05, region_column=None, mask=None, mask_color='#636363', quadrant=None, legend=True, scheme='Quantiles', cmap='YlGnBu', figsize=(15, 4), scatter_kwds=None, fitline_kwds=None, legend_kwds=None)[source]

Produce three-plot visualisation of Moran Scatteprlot, LISA cluster and Choropleth maps, with Local Moran region and quadrant masking

Parameters:
region_column: string, optional

Column name containing mask region of interest, by default None

mask: str, float, int, optional

Identifier or name of the region to highlight, by default None Use the same dtype to specifiy as in original dataset.

mask_color: str, optional

Color of mask, by default ‘#636363’.

Choropleth maps, by default None

figsize: tuple, optional

W, h of figure, by default (15,4)

legend: boolean, optional

If True, legend for maps will be depicted, by default True

scheme: str, optional

Name of mapclassify classifier to be used, by default ‘Quantiles’

cmap: str, optional

Name of matplotlib colormap used for plotting the Choropleth. By default ‘YlGnBu’.

None.

in the scatterplot, by default None.

allowing repositioning of the legend in LISA cluster plot and choropleth.

Returns:
plot_scatter(crit_value=0.05, ax=None, scatter_kwds=None, fitline_kwds=None)[source]

Plot a Moran scatterplot with optional coloring for significant points.

Parameters:
axmatplotlib.axes.Axes, optional

Pre-existing axes for the plot, by default None.

Returns:
matplotlib.axes.Axes

Axes object with the Moran scatterplot.