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:

yarray: (n,1), attribute array
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.
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
n_jobsint: Number of cores to be used in the conditional randomisation. If -1, 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:

yarray: original variable
wW | Graph: original w object
zarray: zero-mean, unit standard deviation normalized y
permutationsint: number of random permutations for calculation of pseudo p_values
Isarray: local Moran’s I values
qarray: (if permutations>0) values indicate quandrant location 1 HH, 2 LH, 3 LL, 4 HL
simarray (permutations by n): (if permutations>0) I values for permuted samples
p_simarray: (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_simarray: (if permutations>0) average values of local Is from permutations
VI_simarray: (if permutations>0) variance of Is from permutations
EIarray: 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.
VIarray: 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.
EIcarray: 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.
VIcarray: 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_simarray: (if permutations>0) standard deviations of Is under permutations.
z_simarrray: (if permutations>0) standardized Is based on permutations
p_z_simarray: (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_jobsint: Number of cores to be used in the conditional randomisation. If -1, 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:

dfpandas.DataFrame: a pandas dataframe with a geometry column
colsstr or list of str: name or list of names of columns to use to compute the statistic
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
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’
pvaluestr: a string denoting which pvalue should be returned. Refer to the the Moran_Local statistic’s documentation for available p-values
outvalslist of strings: list of arbitrary attributes to return as columns from the Moran_Local statistic
**stat_kwsdict: options to pass to the underlying statistic. For this, see the documentation for the Moran_Local statistic.

Returns:

If inplace, None, and operation is conducted on dataframe
in memory. Otherwise, returns a copy of the dataframe with
the relevant columns attached.

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

Create interactive map of LISA indicators

Parameters:

gdfgeopandas.GeoDataFrame: geodataframe used to conduct the local Moran analysis
crit_valuefloat, optional: critical value to determine statistical significance, by default 0.05
kwargsdict, optional: additional keyword arguments passed to the geopandas explore method

Returns:

Folium.Map: interactive map with LISA clusters

get_cluster_labels(crit_value=0.05)[source]¶

Return LISA cluster labels for each observation.

Parameters:

crit_valuefloat, optional: crititical significance value for statistical inference, by default 0.05

Returns:

numpy.array: an array of cluster labels aligned with the input data used to conduct the local Moran analysis

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

Create static map of LISA indicators

Parameters:

gdfgeopandas.GeoDataFrame: geodataframe used to conduct the local Moran analysis
crit_valuefloat, optional: critical value to determine statistical significance, by default 0.05
kwargsdict, optional: additional keyword arguments passed to the geopandas explore method

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:

gdfgeopandas.GeoDataFrame: geodataframe used to conduct the local Moran analysis
attributestr: Column name of attribute which should be depicted in Choropleth map.
crit_valuefloat, optional: critical value to determine statistical significance, by default 0.05
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’.
quadrantint, optional: Quadrant 1-4 in scatterplot masking values in LISA cluster and 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’.
scatter_kwdskeyword arguments, optional: Keywords used for creating and designing the scatter points, by default None.
fitline_kwdskeyword arguments, optional: Keywords used for creating and designing the moran fitline in the scatterplot, by default None.
legend_kwdsdict: Keyword arguments passed to geopandas.GeodataFrame.plot legend_kwds allowing repositioning of the legend in LISA cluster plot and choropleth.

Returns:

axsarray of Matplotlib axes

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:

crit_valuefloat, optional: Critical value to determine statistical significance, by default 0.05.
axmatplotlib.axes.Axes, optional: Pre-existing axes for the plot, by default None.
scatter_kwdsdict, optional: Additional keyword arguments for scatter plot, by default None.
fitline_kwdsdict, optional: Additional keyword arguments for fit line, by default None.

Returns:

matplotlib.axes.Axes: Axes object with the Moran scatterplot.