Spatial Pattern Diagnostics¶

Question: How does spatial dependence change as the neighbourhood expands?

A single global statistic collapses all scales into one number. The correlogram reveals the scale structure of spatial dependence by computing an autocorrelation statistic at a series of increasing distances or neighbourhood sizes.

Key concepts:

• Distance-band correlogram — computes the statistic for all pairs of observations within each successive distance band. Reveals whether autocorrelation drops off smoothly, has a secondary peak, or oscillates.

• KNN correlogram — steps through \(k = 1, 2, \ldots\) nearest neighbours. Useful when observations are unevenly spaced and fixed distance bands would produce empty or overloaded bands.

• Nonparametric (LOWESS) — fits a locally weighted regression of pairwise products against pairwise distances, providing a smooth curve without pre-defined bins.

The correlogram accepts any esda global statistic (Moran’s \(I\), Geary’s \(C\), Getis-Ord \(G\)), so the profile shape changes depending on which aspect of spatial association is being measured.