Re: transformation of regressors to remove collinearity

On Mar 12, 8:33 pm, DZ <23...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
vontres...@xxxxxx wrote:
Collinearity is another way of saying that two or more predictors
are redundant. You really only need one since the others provide the
same information.  If there is high correllation between two
predictor variables, then they are supplying redundant information
and one of them can be deleted.

This would "fail" for certain forms of interactions, no matter how
high the correlation is. For example, if there are two binary
predictors, A:{A1, A2} and B:{B1, B2}, and the response is 0/1, then
there are values of the four possible Pr(Y | Ai & Bj) such that
the relative risks A1 vs. A2 and B1 vs. B2 can remain opposite (one
greater than 1, and the second one smaller), while Corr(A1, B1) is
approaching 1.

Also, sometimes the crucial information is the *difference* between
two variables.
.