esda.MoranLocalConditional¶

class esda.MoranLocalConditional(permutations=999, unit_scale=True, transformer=None, alternative='two-sided')[source]¶

Fit a local moran statistic for y after regressing out the effects of confounding X on y. A “stronger” version of the MoranLocalPartial statistic, as defined by [Wolf, 2024]

Compute the Multivariable Local Moran statistics under partial dependence [Wolf, 2024]

Parameters:¶

permutations : int¶: the number of permutations to run for the inference, driven by conditional randomization.
unit_scale : bool¶: whether to enforce unit variance in the local statistics. This normalizes the variance of the data at inupt, ensuring that the covariance statistics are not overwhelmed by any single covariate’s large variance.
partial_labels : bool, default=True: whether to calculate the classification based on the part-regressive quadrant classification or the univariate quadrant classification, like a classical Moran’s I. When mvquads is True, the variables are labelled as: - label 1: observations with large y - rho * x that also have large Wy values. - label 2: observations with small y - rho * x values that also have large Wy values. - label 3: observations with small y - rho * x values that also have small Wy values. - label 4: observations with large y - rho * x values that have small Wy values.
alternative : str (default: 'two-sided')¶: the alternative hypothesis for the inference. One of ‘two-sided’, ‘greater’, ‘lesser’, ‘directed’, or ‘folded’. See the esda.significance.calculate_significance() documentation for more information.

connectivity[source]¶

Type:¶: The weights matrix inputted, but row standardized

D[source]¶

not None, this will be [1 y X]

Type:¶: The “design” matrix used in computation. If X is

R[source]¶

always be the same shape as D and contain [1, Wy, Wy, ….]

Type:¶: the “response” matrix used in computation. Will

DtDi[source]¶

the P x P matrix describing the variance and covariance of y and X.

Type:¶: empirical parameter covariance matrix

P[source]¶

Type:¶: the number of parameters. 1 if X is not provided.

association_[source]¶

the first column, lmos[:,1] is the LISAs corresponding to the relationship between Wy and y conditioning on X.

Type:¶: the N,P matrix of multivariable LISA statistics.

reference_distribution_[source]¶: the (N, permutations, P+1) realizations from the conditional randomization to generate reference distributions for each Local Moran statistic. rlmos_[:,:,1] pertain to the reference distribution of y and Wy.

significance_[source]¶

part-regressive relationships. quads[:,0] pertains to the relationship between y and Wy. The mean is not classified, since it’s just binary above/below mean usually.

Type:¶: the (N, P) matrix of quadrant classifications for the

partials_[source]¶

The ith slice of partials_[:,:,i] contains the partial regressive contribution of that covariate, with the first column indicating the part-regressive outcome and the second indicating the part-regressive design. The partial regression matrix starts at zero, so partials_[:,:,0] corresponds to the partial regression describing the relationship between y and Wy.

Type:¶: the (N,2,P+1) matrix of part-regressive contributions.

labels_[source]¶

part-regressive relationships. See the partial_labels argument for more information.

Type:¶: the (N,) array of quadrant classifications for the

Methods

`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
`fit`(X, y, W)
`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:¶

df : pandas.DataFrame¶: a pandas dataframe with a geometry column
cols : string or list of string¶: name or list of names of columns to use to compute the statistic
w : W | Graph¶: spatial weights instance as W or Graph aligned with the dataframe. If not provided, this is searched for in the dataframe’s metadata
inplace : bool¶: 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 : string¶: a string denoting which pvalue should be returned. Refer to the the Moran_Local statistic’s documentation for available p-values
outvals : list of strings¶: 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.

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:¶

gdf : geopandas.GeoDataFrame¶: geodataframe used to conduct the local Moran analysis
crit_value : float, optional¶: critical value to determine statistical significance, by default 0.05
kwargs : dict, optional¶: additional keyword arguments passed to the geopandas explore method

Returns:¶

interactive map with LISA clusters

Return type:¶

Folium.Map

fit(X, y, W)[source]¶

Parameters:¶

y : (N,1) array¶: array of data that is the targeted “outcome” covariate to compute the multivariable Moran’s I
X : (N,3) array¶: array of data that is used as “confounding factors” to account for their covariance with Y.
W : (N,N) weights object¶: spatial weights instance as W or Graph aligned with y. Immediately row-standardized.

Return type:¶

A fitted MoranLocalConditional() estimator

get_cluster_labels(crit_value=0.05)[source]¶

Return LISA cluster labels for each observation.

Parameters:¶

crit_value : float, optional¶: crititical significance value for statistical inference, by default 0.05

Returns:¶

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

Return type:¶

numpy.array

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

Create static map of LISA indicators

Parameters:¶

gdf : geopandas.GeoDataFrame¶: geodataframe used to conduct the local Moran analysis
crit_value : float, optional¶: critical value to determine statistical significance, by default 0.05
kwargs : dict, optional¶: additional keyword arguments passed to the geopandas explore method

Returns:¶

matplotlib axis

Return type:¶

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, losh_scaling_factor=False, losh_inference=None, a=2)[source]¶

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

Parameters:¶

gdf : geopandas.GeoDataFrame¶: geodataframe used to conduct the local Moran analysis
attribute : str¶: Column name of attribute which should be depicted in Choropleth map.
crit_value : float, 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’.
quadrant : int, 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_kwds : keyword arguments, optional¶: Keywords used for creating and designing the scatter points, by default None.
fitline_kwds : keyword arguments, optional¶: Keywords used for creating and designing the moran fitline in the scatterplot, by default None.
legend_kwds : dict¶: Keyword arguments passed to geopandas.GeodataFrame.plot legend_kwds allowing repositioning of the legend in LISA cluster plot and choropleth.
losh_scaling_factor : bool | int | float, by default False¶: Scale the scatterplot observations by LOSH. When set to a number, it is treated as the multiplicative factor applied to exp(LOSH.Hi) when converting LOSH values into marker areas.
losh_inference : str, optional¶: Inference method for LOSH. See LOSH for supported options. Applies only if losh_scaling_factor is not False.
a : int or float, default=2¶: Residual exponent passed to esda.losh.LOSH.fit(). The default corresponds to a variance-based LOSH measure. Applies only if losh_scaling_factor is not False.

Returns:¶

axs

Return type:¶

array of Matplotlib axes

plot_scatter(crit_value=0.05, ax=None, scatter_kwds=None, fitline_kwds=None, losh_scaling_factor=False, losh_inference=None, a=2)[source]¶

Plot a Moran scatterplot with optional coloring for significant points.

Parameters:¶

crit_value : float, optional¶: Critical value to determine statistical significance, by default 0.05.
ax : matplotlib.axes.Axes, optional¶: Pre-existing axes for the plot, by default None.
scatter_kwds : dict, optional¶: Additional keyword arguments for scatter plot, by default None.
fitline_kwds : dict, optional¶: Additional keyword arguments for fit line, by default None.
losh_scaling_factor : bool | int | float, by default False¶: Scale the observations by LOSH. When set to a number, it is treated as the multiplicative factor applied to exp(LOSH.Hi) when converting LOSH values into marker areas.
losh_inference : str, optional¶: Inference method for LOSH. See LOSH for supported options. Applies only if losh_scaling_factor is not False.
a : int or float, default=2¶: Residual exponent passed to esda.losh.LOSH.fit(). The default corresponds to a variance-based LOSH measure. Applies only if losh_scaling_factor is not False.

Returns:¶

Axes object with the Moran scatterplot.

Return type:¶

matplotlib.axes.Axes