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])	Configure whether metadata should be requested to be 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

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the 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.

Added in version 1.3.

Parameters:

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

Metadata routing for x parameter in fit.

Returns:

selfobject

The updated object.