netneurotools.spatial.lees_i

netneurotools.spatial.lees_i(annot_1, annot_2, weight, use_numba=False)

Calculate Lee’s I for spatial autocorrelation.

Parameters:

• annot_1 (array-like, shape (n,)) – Array of annotations to calculate Lee’s I for.

• annot_2 (array-like, shape (n,)) – Array of annotations to calculate Lee’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:

lees_i – Lee’s I value for the given annotations and weight matrix.

Return type:

float

Notes

Lee’s I is calculated as:

\[L(x,y) = \frac{n}{\sum_{i=1}^n(\sum_{j=1}^n w_{ij})^2} \frac{\sum_{i=1}^n(\sum_{j=1}^n w_{ij}(x_i - \bar{x})) (\sum_{j=1}^n w_{ij}(y_i - \bar{y}))} {\sqrt{\sum_{i=1}^n(x_i - \bar{x})^2}\sqrt{\sum_{i=1}^n(y_i - \bar{y})^2}}\]

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. \(x\) and \(y\) are the annotations for the two variables.

The value can be tested using the R pacakge spdep:

x <- rnorm(100)
y <- rnorm(100)
m <- matrix(runif(100*100), nrow=100)
lee(x, y, mat2listw(m), 100)
# or
lee.test(x, y, mat2listw(m))