esda.MoranLocalPartial

class esda.MoranLocalPartial(permutations=999, unit_scale=True, partial_labels=True, alternative='two-sided')

__init__(permutations=999, unit_scale=True, partial_labels=True, alternative='two-sided')

Compute the Multivariable Local Moran statistics under partial dependence [Wol24]

Parameters

permutationsint

the number of permutations to run for the inference, driven by conditional randomization.

unit_scalebool

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_labelsbool, 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.

alternativestr (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.

Attributes:

connectivityThe weights matrix inputted, but row standardized

DThe “design” matrix used in computation. If X is

not None, this will be [1 y X]

Rthe “response” matrix used in computation. Will

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

DtDiempirical parameter covariance matrix

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

Pthe number of parameters. 1 if X is not provided.

association_the N,P matrix of multivariable LISA statistics.

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

reference_distribution_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_the (N, P) matrix of quadrant classifications for the

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.

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

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.

labels_the (N,) array of quadrant classifications for the

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

Methods

__init__([permutations, unit_scale, ...])	Compute the Multivariable Local Moran statistics under partial dependence [Wol24]
fit(X, y, W)	Fit the partial local Moran statistic on input data

Attributes

association_	The association between y and the local average of y, removing the correlation due to x and the local average of y
labels_	The classifications (in terms of cluster-type and outlier-type) for the association_ statistics.
partials_	The components of the local statistic.
reference_distribution_	Simulated distribution of association_, assuming that there is
significance_	The pseudo-p-value built using map randomization for the structural relationship between y and its local average, removing the correlation due to the relationship between x and the local average of y.

property association_

The association between y and the local average of y, removing the correlation due to x and the local average of y

fit(X, y, W)

Fit the partial local Moran statistic on input data

Parameters:

X(N,p) array

array of data that is used as “confounding factors” to account for their covariance with Y.

y(N,1) array

array of data that is the targeted “outcome” covariate to compute the multivariable Moran’s I

W(N,N) weights object

spatial weights instance as W or Graph aligned with y. Immediately row-standardized.

Returns:

selfobject

this MoranLocalPartial() statistic after fitting to data

property labels_

The classifications (in terms of cluster-type and outlier-type) for the association_ statistics. If the quads requested are mvquads, then the classification is done with respect to the left and right components (first and second columns of partials_).

If the quads requested are uvquads, then this will only be computed with respect to the outcome and the local average. The cluster typology is:

• 1: above-average left component (either y or D @ DtDi),

  above-average right component (local average of y)

• 2: below-average left component (either y or D @ DtDi),

  above-average right component (local average of y)

• 3: below-average left component (either y or D @ DtDi)

  below-average right component (local average of y)

• 4: above-average left component (either y or D @ DtDi)

  below-average right component (local average of y)

property partials_

The components of the local statistic. The first column is the structural exogenous component of the data, and the second is the local average of y.

property reference_distribution_

Simulated distribution of association_, assuming that there is

• no structural relationship between y and its local average;

• the same observed structural relationship between y and x.

property significance_

The pseudo-p-value built using map randomization for the structural relationship between y and its local average, removing the correlation due to the relationship between x and the local average of y.