netneurotools.spatial.local_morans_i

netneurotools.spatial.local_morans_i(annot, weight, use_sampvar=True)[source]

Calculate local Moran’s I for spatial autocorrelation.

Parameters:

annot (array-like, shape (n,)) – Array of annotations to calculate Moran’s I for.
weight (array-like, shape (n, n)) – Spatial weight matrix. Note that we do not explicitly check for symmetry in the weight matrix, nor zero-diagonal elements.
use_sampvar (bool, optional) – Whether to use sample variance (n - 1) in calculation. Default: True.

Returns:

local_morans_i – Local Moran’s I values for the given annotations and weight matrix.

Return type:

array, shape (n,)

Notes

Local Moran’s I is calculated as:

\[I_i = \frac{(x_i - \bar{x})}{\sum_{k=1}^n (x_k - \bar{x})^2/(n-1)} \sum_{j=1}^n w_{ij}(x_j - \bar{x})\]

where \(n\) is the number of observations, \(w_{ij}\) is the spatial weight between observations \(i\) and \(j\), \(x_i\) is the annotation for observation \(i\), and \(\bar{x}\) is the mean annotation value.

The value can be tested using the R pacakge spdep:

x <- rnorm(100)
m <- matrix(runif(100*100), nrow=100)
localmoran(x, mat2listw(m), mlvar=TRUE)