A neighbor is “somebody” who is:

- Next door →
**Contiguity**-based*W*s - Close →
**Distance**-based*W*s - In the same “place” as us →
**Block**weights - …

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

**Sharing boundaries** to any extent

- Rook
- Queen
- …

Weight is (inversely) proportional to distance between observations

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

Weights are assigned based on discretionary rules loosely related to geography

For example:

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

No neighbors receive zero weight: *w*_{ij} = 0

Neighbors, it depends, *w*_{ij} can be:

One

*w*_{ij}= 1 → BinarySome proportion (0 <

*w*_{ij}< 1, continuous) which can be a function of:- Distance
- Strength of interaction (e.g. commuting flows, trade, etc.)
- …

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

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:

where *w*_{i·} is the sum of a row.

A course on Geographic Data Science by Dani Arribas-Bel is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.