Re: collinear interaction but not for predictors

On 1 Dec 2005 14:55:46 -0800, "alphapoint05" <millerjm@xxxxxxx> wrote:

> Ok, centering solved the problem. But, now have a question regarding
> the substantive utility of interpreting multilcollinear interaction. If
> I have two predictors that are highly correlated, then I am concerned
> that they are measuring the same 'thing'. I either combine them or drop
> one from the analysis. I find out about the collinearity from checking
> diagnostics such as TOL and VIF. But, when I add the interaction term,
> aren't I adding redundant information?

You are asking whether the collinearity is increased by
adding the interaction term, when the two original
variables are highly correlated?

No, not necessarily.
If you enter the interaction as the 'centered product',
it adds information while being uncorrelated with the
two variables. For the contrast, (High-high and low-low)
get assigned high positive numbers; (middle-middle)
gets assigned near zero; and (high-low, low-high), the few
that there are, get assigned large negative numbers.


> In other words, shouldn't
> inspection of collinearity be limited to the noninteraction scenario?
> Is it even sensible to draw conclusions from collinearity diagnostics
> after including 2 predictors and their interaction?

What sense are you trying to draw? If you can code
them wisely, the interactions won't change the conclusions.

High collinearity is still a warning about robustness,
either for interpretation or for numerical methods of
solving.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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