In the case of a constant coefficient, where the VIF is greater than 10, what does that mean? Do all the variables in the model exhibit multicollinearity? How can multicollinearity be reduced? Multicollinearity could be reduced by removing variables with VIF >10. But I don't know what to do with the constant coefficient.
Thank you very much
Multicollinearity is the property of near singularity which is associated with the entire experimental design in general ( the complete Design matrix) and not of any particular explanatory variables or the intercept.
You can use biased regression tools such as Principal Component Regression or Ridge regression to estimate model parameters while dealing with Multicollinearity.
Multicollinearity can be reduced by altering the experimental design, if possible.... this would change the variation partitioning structure associated with the Design matrix and make it less ill conditioned.
I recommend the following book in this context:
Mathematical Analysis of Spectral Orthogonality by Kalivas and Lang.
The intercept/constant in a standard regression shouldn't have a VIF because it is constant you can't calculate the R^2 from being predicted by the other predictors. So this is either an error or an unusually parameterized regression model of some kind (I can't immediately think what). If the latter you'll need to provide more details.
Looking further - your package may be reporting an uncentred VIF in place of or in addition to a centred VIF. There is an apparently unresolved debate in the literature about when or why that's useful. For practical purpose in most regressions it seems likely that high uncentred VIF may not be problematic. I've never seen uncentred VIF used in a published paper ...
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