spatial-statistics

Spatial Statistics

Purpose: answer "is it clustered, where, and why" with defensible inference. The core discipline: spatial data violates independence assumptions, so standard statistics silently overstate significance — every analysis here starts with weights design and ends with residual diagnostics.

Spatial weights (W) — the analysis IS the weights

Every result downstream depends on W; choose it for substantive reasons and run a sensitivity check with one alternative:

from libpysal.weights import Queen

w = Queen.from_dataframe(gdf, use_index=True)
print(f"islands: {w.islands}")   # unconnected units break stats — fix or document
w.transform = "r"                # row-standardize (default for Moran/lag models)

Always report: weights type, parameters, number of islands, and whether results survive an alternative W.

Global → local workflow

1. Global Moran's I (esda.Moran, permutation inference ≥999) — answers "any clustering at all?" Report I, p_sim, and the permutation distribution, not the analytical p.
2. LISA / local Moran (esda.Moran_Local) — maps WHERE: High-High, Low-Low clusters, High-Low/Low-High outliers. Correct for multiple testing (FDR at minimum) before coloring a map — uncorrected LISA maps overstate clusters and this is the field's most common abuse.
3. Getis-Ord Gi* (esda.G_Local, star=True) — hot/cold spots of intensity (a distinct question from Moran clusters — Gi* finds concentrations of high values, LISA finds similarity structure).
4. Rates, not counts, for population-based phenomena; use Empirical Bayes smoothing (esda.smoothing) for small-population units before any of the above — raw rates in sparse units are noise.