netneurotools.spatial.morans_i

netneurotools.spatial.morans_i(annot, weight, use_numba=False)[source]

Calculate 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_numba (bool, optional) – Whether to use numba for calculation. Default: True (if numba is installed).

Returns:

morans_i – Moran’s I value for the given annotations and weight matrix.

Return type:

float

Notes

Moran’s I is calculated as:

\[I = \frac{n}{\sum_{i=1}^{n} \sum_{j=1}^{n} w_{ij}} \frac{\sum_{i=1}^{n} \sum_{j=1}^{n} w_{ij} (x_i - \bar{x})(x_j - \bar{x})}{\sum_{i=1}^{n} (x_i - \bar{x})^2}\]

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)
w <- mat2listw(m)
moran(v, w, 100, Szero(w))
# or
moran.test(x, w)