Geographic Data Science

The spatial lag
Dani Arribas-Bel

The spatial lag

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

Ysl = WY ysl − i = ∑jwijyj

  • 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…)

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