See inserted comments ...
> Date: Tue, 7 Aug 2012 21:08:04 +0000
> From:
[hidden email]> Subject: Re: Multicolinearity.
> To:
[hidden email]>
> Certain authors like Baron and Kenny would argue this resulted because you did your interaction (moderation) analysis incorrectly.
I would say that the word "incorrectly" leaves the impression
that there is a single, simple "correct" answer. But there is no
doubt that multiplying two positive-valued variables induces an
artefactual correlation that is unwanted because it (a) leaves you
with coefficients that have no clear meaning, including (b) possible
collinearity and suppressor-variable relations.
> They would correctly argue that the same information contained in the interaction term is also contained in the two IV's themselves, and as such are correlated (first explicated in publication by Cohen as I understand it). This correlation will cause a multi-colinearity problem, and the model coefficients would be inaccurate. They would go on to say that by mean centering the IV's the correlation is reduced to the product term of the IV's (the interaction term) and as such you have reduced multicolinearity.
- The mean-centering is relevant only to computing the interaction.
- If your computer regression procedure is computing the interaction-term,
then you might need to center the original variables -- *if* you are wanting
to say anything about the main effects.
- The situation gets more complicated for 3-way interactions.
> More recent research has shown this not to be true,
I don't know what the "this" is referring to. But "more recent
research" is not going to refute the simple arithmetic that shows
the reduction of multicollinearity from centering.
> and so with normal OLS regression, your unfortunately stuck in a situation where you can't do what your trying to do and get valid results (which isn't to say that 100's if not 1000's of people don't still do this).
Hmm... It seems to me that you are casting aspersions on the usual
procedures, after a sloppy and misleading review. There are potentially
deep issues in looking at non-orthogonal designs, both for main effects
and for interactions. ... That is the context where I would agree that
there is some discussion about what sort are most valid, and when.
But most applications, and most results, do not require such deep thought.
>
> One solution is not to rely on OLS regression methods, and instead turn to a varying parameter model.
>
> Another point to consider is that most people often misinterpret the effects of the IV's, in the presence of the moderator, as a main effect, which has been shown to be incorrect. As Hayes and Matthes discuss, these are actually conditional effects. Your model with no interaction term has your main effects, but your model with the interaction term has the conditional effects of each IV, and the interaction is the difference in the conditional effect for a one point change in the interaction effect. First thing to consider is that you don't have two focal predictors and an interaction between the two, this doesn't fit with theory, and complicates interpretation. You have one focal predict, and a second moderator variable. In your example, you need to choose (based on theory), so let's say its Divergence, and then treat relevance as the proposed moderator variable. To interpret these correctly with regard to the interaction model, .666 is the change in Y for a 1 point in!
> crease in Divergence, when relevance is at 0. If you think about this, since you are showing that there is an interaction, then the value of M in this case (relevance) is meaningful, and having it at 0 doesn't make the interpretation of divergence all that useful on its own (unless you interpret it in light of the interaction effect, which is best done with plotting). One advantage of centering the IV's is that the coefficient value for divergence is now it's value when relevance is at the sample mean level. For an average amount of relevance, divergence changes Y by ### amount.
>
> Matthew J Poes
>...
[snip, original]
About the original -- centering the variables as multiplied for
the interaction will give the *usual*, most desired values
for coefficients. Does the Original Poster find these to be
good enough to answer his question?
Plotting the predictions will answer the more concrete question
of what the interaction "means".
--
Rich Ulrich