Geographic Data Science

What is a neighbor?

A neighbor is “somebody” who is:

• Next door → Contiguity-based Ws
• Close → Distance-based Ws
• In the same “place” as us → Block weights
• …

See Anselin & Rey (2014) for an in-detail discussion and more types of W.

Contiguity-based weights

Sharing boundaries to any extent

• Rook
• Queen
• …

Distance-based weights

Weight is (inversely) proportional to distance between observations

• Inverse distance (threshold)
• KNN (fixed number of neighbors)
• …

Block weights

Weights are assigned based on discretionary rules loosely related to geography

For example:

• LSOAs into MSOAs
• Post-codes within city boundaries
• Counties within states
• …

How much of a neighbor?

No neighbors receive zero weight: w_ij = 0

Neighbors, it depends, w_ij can be:

• One w_ij = 1 → Binary

• Some proportion (0 < w_ij < 1, continuous) which can be a function of:

  • Distance
  • Strength of interaction (e.g. commuting flows, trade, etc.)
  • …

Choice of W

Should be based on and reflect the underlying channels of interaction for the question at hand.

Examples:

• Processes propagated by inmediate contact (e.g. disease contagion) → Contiguity weights
• Accessibility → Distance weights
• Effects of county differences in laws → Block weights

Standardization

In some applications (e.g. spatial autocorrelation) it is common to standardize W

The most widely used standardization is row-based: divide every element by the sum of the row:

$$\bar{w_{ij}} = \dfrac{w_{ij}}{w_{i\cdotp}}$$

where w_i· is the sum of a row.