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pysal / mgwr

Multiscale Geographically Weighted Regression (MGWR)
https://mgwr.readthedocs.io/
BSD 3-Clause "New" or "Revised" License
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Multicollinearity in MGWR #9

Open TaylorOshan opened 6 years ago

TaylorOshan commented 6 years ago

Right now we currently have several popular diagnostics for local multicollinearity in gwr: local correlation coefficients, local vif, local condition number, and local variance decomposition proportions. The local CN in gwr is simply computed on the W-transformed design matrix, as is the local VDP, so I think we can get the mgwr equivalent easily by just computing them on the W-transformed matrix that uses a unique W-transform for each column of the design. I'm less certain about how to extend the local CC and VIF to the mgwr case. Fotheringham et al. have the local CC for gwr as

image so the denominator is quite easy to have separate weights for each of the covariates. But the numerator I am not sure about. The only thing I can think of is:

image

but I have no idea if that would be a valid covariance in the numerator or if there is another way to specify a weighted covariance with different weights for each covariate.

And I know the VIF for OLS can typically be computed from a matrix of the CC's but I don't think it would carry the same interpretation for GAM's.

TaylorOshan commented 6 years ago

local CN and VDP are available for MGWR