esda.LocalCrossPlot¶

class esda.LocalCrossPlot(connectivity=None, permuations=999, star=False, n_jobs=-1, seed=None, island_weight=0, inference=None, a=2)[source]¶

Combine local statistics into a G-I-LOSH cross plot.

The local G-I-LOSH cross plot is a joint diagnostic that places standardized Getis-Ord \(G_i\) values on the x-axis and standardized Local Moran statistics on the y-axis while scaling symbol sizes by local spatial heteroscedasticity (LOSH), proposed by Westerholt [2026]. This provides a compact view of local clustering, local association, and local variance structure in a single graphic.

For details refer to Westerholt [2026].

Parameters:¶

connectivity : W | Graph, optional¶

Spatial weights object aligned with the observed values.

permuations : int, default=999¶

Number of random permutations used when fitting Moran_Local and G_Local.

star : bool, default=False¶

Whether to include the focal observation in the Getis-Ord local statistic.

n_jobs : int, default=-1¶

Number of parallel workers for permutation-based inference in the local Moran and local Getis-Ord statistics.

seed : int, optional¶

Random seed forwarded to permutation-based local statistics.

island_weight : float, default=0¶

Weight assigned to the synthetic neighbor used for islands in the local Moran and local Getis-Ord calculations.

inference : str, optional¶

Inference method for LOSH. See LOSH for supported options.

a : int or float, default=2¶

Residual exponent passed to esda.losh.LOSH.fit(). The default corresponds to a variance-based LOSH measure.

connectivity[source]¶

Spatial weights object used to fit the component estimators.

Type:¶

W | Graph or None

permutations[source]¶

Number of permutations used for local Moran and local Getis-Ord inference.

Type:¶

int

losh_[source]¶

Fitted LOSH estimator.

Type:¶

LOSH

moran_local_[source]¶

Fitted local Moran estimator.

Type:¶

Moran_Local

g_local_[source]¶

Fitted local Getis-Ord estimator.

Type:¶

G_Local

Methods

fit(y)	Fit the component local statistics used in the plot.
from_estimators(g_local, moran_local, losh)	Construct a plotter from pre-fitted component estimators.
plot([crit_value, losh_scaling_factor, ...])	Draw the local cross plot.

fit(y)[source]¶

Fit the component local statistics used in the plot.

Parameters:¶

y : array_like¶

One-dimensional array of observed values aligned with connectivity.

Return type:¶

LocalCrossPlot

Notes

Fitting computes and stores:

• LOSH for local spatial heteroscedasticity,

• Moran_Local for local spatial association,

• G_Local for local concentration.

classmethod from_estimators(g_local, moran_local, losh)[source]¶

Construct a plotter from pre-fitted component estimators.

Parameters:¶

g_local : G_Local¶

Fitted local Getis-Ord estimator.

moran_local : Moran_Local¶

Fitted local Moran estimator.

losh : LOSH¶

Fitted LOSH estimator.

Returns:¶

Plotter populated with the provided estimators.

Return type:¶

LocalCrossPlot

Notes

This constructor is useful when the component estimators have already been fit elsewhere or when custom settings were used for each statistic independently.

plot(crit_value=0.05, losh_scaling_factor=10, linewidth=0.5, ax=None, legend=False)[source]¶

Draw the local cross plot.

Parameters:¶

crit_value : float, default=0.05¶

The critical value for significance.

losh_scaling_factor : float, default=10¶

Multiplicative factor applied to exp(losh_.Hi) when converting LOSH values into marker areas.

linewidth : float, default=0.5¶

Line width for marker outlines.

ax : matplotlib.axes.Axes, optional¶

Axes on which to draw the plot. If omitted, a new figure and axes are created.

Returns:¶

Axes containing the plot.

Return type:¶

matplotlib.axes.Axes

Notes

The plot uses the following encodings:

• x-axis: standardized local Getis-Ord \(G_i^*\),

• y-axis: permutation-standardized Local Moran statistic,

• marker size: exp(LOSH),

• marker color: significance/sign combinations of local Getis-Ord and Local Moran results.