Most analyses that use aerial geometries utilize row standardized weights because there is not good theoretical reason to apply diifferent weights.
If, however, we have a good reason to use polygon centroids or, probably more approrpiately, using point data, we can use kernel weights. Kernel weights are used to introduce a decay function ito our weighting.
Say we have a point with 8 neighbors which are not at a uniform distance away. How much weight should we give each location in our subsequent calculations? Should we really be allocating equal weight? Or, should we recognize that things that are closer likely have more impact than those that are further away
A good use case of say gaussian kernel weights is if we have a hexagonal grid of incidents that are fairly small. First order neighbors may be limiting and we want to include 2nd or third order neighbors, but those should have less weight.
Most analyses that use aerial geometries utilize row standardized weights because there is not good theoretical reason to apply diifferent weights.
If, however, we have a good reason to use polygon centroids or, probably more approrpiately, using point data, we can use kernel weights. Kernel weights are used to introduce a decay function ito our weighting.
Say we have a point with 8 neighbors which are not at a uniform distance away. How much weight should we give each location in our subsequent calculations? Should we really be allocating equal weight? Or, should we recognize that things that are closer likely have more impact than those that are further away
A good use case of say gaussian kernel weights is if we have a hexagonal grid of incidents that are fairly small. First order neighbors may be limiting and we want to include 2nd or third order neighbors, but those should have less weight.