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: | Weights | Use when | |---|---| | Queen/Rook contiguity | Irregular polygons (admin units, parcels) | | K-nearest neighbors | Points; islands present (contiguity leaves them unconnected) | | Distance band | Physical process with known range | | Kernel (distance-decayed) | Smooth influence, GWR-style local models | ```python 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 outlier...