Local Spatial Structure¶

Question: Where are clusters or spatial outliers located?

Local methods assign each observation its own statistic, identifying which specific units are driving the global pattern — or where the global pattern breaks down.

Choosing a method:

• Local Moran’s I (LISA) — decomposes Moran’s \(I\) into per-unit contributions. Produces four quadrant labels: High-High (hot spot), Low-Low (cold spot), High-Low and Low-High (spatial outliers).

• Local Geary — analogous to global Geary’s C at the unit level. Distinguishes clusters (similar neighbours) from outliers (dissimilar neighbours) without using the global mean as a reference.

• \(G_i\) (Getis-Ord local) — identifies hotspots and coldspots based on raw value concentration; does not detect spatial outliers. Preferred when magnitude rather than relative position matters.

• LOSH — measures local variance rather than the local mean. Most useful in combination with a mean statistic to detect transitional or boundary zones.

• Local Join Counts — the local version of join count analysis for binary variables; detects co-location of positive events.

• Multivariate Moran — extends local Moran to relationships between two or more variables.

All local statistics carry multiple-comparison risk; applying a false-discovery-rate correction (e.g., esda.fdr) before mapping is recommended.