Geographic Data Science

Global Spatial Autocorrelation Dani Arribas-Bel

Global Spatial Autocorr.

“Clustering”

Overall trend where the distribution of values follows a particular pattern over space

[Positive] Similar values close to each other (high-high, low-low)

[Negative] Similar values far from each other (high-low)

How to measure it???

Graphical device that displays a variable on the horizontal axis against its spatial lag on the vertical one
Variable and spatial weights matrix are preferably standardized
Asssessment of the overall association between a variable in a given location and in its neighborhood

Formal test of global spatial autocorrelation

Statistically identify the presence of clustering in a variable

Slope of the Moran plot

Inference based on how likely it is to obtain a map like observed from a purely random pattern

$I = \dfrac{N} {\sum_{i} \sum_{j} w_{ij}} \dfrac {\sum_{i} \sum_{j} w_{ij}(Z_i) (Z_j)} {\sum_{i} (Z_i)^2}$