Spatial Autocorrelation
Definition
Spatial autocorrelation measures the degree to which nearby observations are similar or dissimilar. Positive autocorrelation means clustering of alike values; negative implies checkerboard patterns. Global statistics like Moran’s I summarize overall structure, while local indicators show where clusters or outliers occur. Understanding autocorrelation matters for valid inference and for designing sampling strategies.
Application
Epidemiology tests whether disease risk clusters; economics examines spatial spillovers; ecology studies species aggregation; and real estate assesses price patterns. Autocorrelation also informs kriging and spatial regression, which explicitly model spatial dependence.
FAQ
Why can ignoring autocorrelation inflate significance in regression?
Residuals that are spatially correlated violate independence assumptions, making p‑values too optimistic. Spatial lag or error models correct for this by absorbing dependence.
How is the spatial weights matrix chosen and why does it matter?
Weights encode neighborhood structure (k‑nearest, distance bands, contiguity). Different choices change results; sensitivity tests ensure conclusions are robust.
What does a Moran scatterplot reveal beyond the I statistic?
It shows each observation’s value versus the spatially lagged mean, identifying high‑high, low‑low clusters and high‑low, low‑high outliers for targeted action.
When might negative autocorrelation appear in real data?
Land‑use zoning that separates incompatible uses, alternating agricultural fields, or predator‑prey territories can create alternating patterns.