esda.Spatial_Pearson_Local

class esda.Spatial_Pearson_Local(connectivity=None, permutations=999)

Local Spatial Pearson Statistic

__init__(connectivity=None, permutations=999)

Initialize a spatial local pearson estimator

Parameters:

connectivity: scipy.sparse matrix object

the connectivity structure describing the relationships between observed units. Will be row-standardized.

permutations: int

the number of permutations to conduct for inference. if < 1, no permutational inference will be conducted.

significance_: numpy.ndarray (2,2)

permutation-based p-values for the fraction of times the observed correlation was more extreme than the simulated correlations.

Attributes

———-

associations_: numpy.ndarray (n_samples,)

array containg the estimated Lee spatial pearson correlation coefficients, where element [0,1] is the spatial correlation coefficient, and elements [0,0] and [1,1] are the “spatial smoothing factor”

reference_distribution_: numpy.ndarray (n_permutations, n_samples)

distribution of correlation matrices for randomly-shuffled maps.

significance_: numpy.ndarray (n_samples,)

permutation-based p-values for the fraction of times the observed correlation was more extreme than the simulated correlations.

Notes

Technical details and derivations can be found in [Lee01].

Methods

__init__([connectivity, permutations])	Initialize a spatial local pearson estimator
fit(x, y)	Bivariate local pearson's R based on Eq.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
set_fit_request(*[, x])	Request metadata passed to the fit method.
set_params(**params)	Set the parameters of this estimator.

fit(x, y)

Bivariate local pearson’s R based on Eq. 22 in Lee (2001), using site-wise conditional randomization from Moran_Local_BV.

\[L_i = \dfrac{ n \cdot \Big[ig(\sum_i w_{ij}(x_j - ar{x})ig) ig(\sum_i w_{ij}(y_j - ar{y})ig) \Big] } { \sqrt{\sum_i (x_i - ar{x})^2} \sqrt{\sum_i (y_i - ar{y})^2}} = \dfrac{ n \cdot ( ilde{x}_j - ar{x}) ( ilde{y}_j - ar{y}) } { \sqrt{\sum_i (x_i - ar{x})^2} \sqrt{\sum_i (y_i - ar{y})^2}}\]

Lee, Sang Il. (2001), “Developing a bivariate spatial association measure: An integration of Pearson’s r and Moran’s I.” Journal of Geographical Systems, 3(4):369-385.

Parameters:

xnumpy.ndarray

array containing continuous data

ynumpy.ndarray

array containing continuous data

Returns:

the fitted estimator.

set_fit_request(*, x: bool | None | str = '$UNCHANGED$') → Spatial_Pearson_Local

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

xstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for x parameter in fit.

Returns:

selfobject

The updated object.