Geographic Data Science

The spatial lag

Product of a spatial weights matrix W and a given variably Y

Y_sl = WY y_sl − i = ∑_jw_ijy_j

• Measure that captures the behaviour of a variable in the neighborhood of a given observation i.
• If W is standardized, the spatial lag is the average value of the variable in the neighborhood

• Common way to introduce space formally in a statistical framework

• Heavily used in both ESDA and spatial regression to delineate neighborhoods. Examples:

  • Moran’s I
  • LISAs
  • Spatial models (lag, error…)