Metrics¶

Spatial autocorrelation¶

THe following metrics measures spatial autocorrelation based on both feature locations and feature values simultaneously.

Moran’s I¶

Moran’s I, based on cross-products, measures value association and is calculated for n observations on a variable x at locations i, j as:

$moran$

Given a set of features and an associated attribute, it evaluates whether the pattern expressed is clustered, dispersed, or random.

Moran’s I is between -1 and 1 (as long as the weight matrix is row-standardized).

Values close to 0 indicate no spatial autocorrelation.
Values close to 1 indicate strong positive spatial autocorrelation. I.e. regions close to each other behave similar in terms of the variable of interest.
Values close to -1 indicate strong negative spatial autocorrelation

Geary’s C¶

Geary’s C tests statistics for spatial autocorrelation by using the sum of squared differences between pairs of data of variable x as a measure of covariation. Geary’s ratio is between 0 and 2.

$geary$

Values close to 1 indicate no spatial autocorrelation.
Values close to 0 indicate strong positive autocorrelation.
Values close to 2 indicate strong negative spatial autocorrelation.