As I'm reading through Modern Spatial Econometrics in Practice, we assume
the spatial weights matrix to be sparse. At one point they note that the
contiguity matrix for the US counties is 0.18% non-zero. But what %
non-zero is too dense?
I am wondering if there is any research or papers that document what a
recommended upper bound of sparsity should be for one of these models? Is
10% non-zero too much or sufficient? I suspect the answer is, like most
things, "it depends."
But, thinking of a situation where someone might use a distance band to
specify neighbors they might create a bandwidth that can encompass 50% or
more of points if using max(knn=1) to specify the distance. I suspect using
a kernel or IDW could reduce the weights close to zero making the impact
minimal.
Nonetheless, I'm curious if others have thought about this or written about
it!
Thanks,
Josiah
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