Hi Leonardo,
In the model that you're referring to, are X and Z continuous variables?
In the 1st model (w/o the X.*Z term), a contrast testing the difference
of b1 and b2 is testing whether the "main" effect of each variable
differs. Whether such a contrast is meaningful depends on the
variables, and requires that X and Z both be scaled in a meaningful
fashion relative to each other. In this model, b1 and b2 have nothing
to do with the "interaction" of X and Z (where "interaction" is defined
as the product of X and Z).
In your 2nd model (with the X.*Z term) you have included an interaction
term. Note however that interpreting "interaction" effects between
continuous variables is a tricky endeavor. See for example:
http://www.nd.edu/~rwilliam/stats2/l55.pdf
http://www.ats.ucla.edu/stat/sas/faq/spplot/reg_int_cont.htm
Hope that helps.
cheers,
-MH
On Thu, 2011-09-15 at 15:46 +0100, Leonardo Cerliani wrote:
> dear FSL people,
> I have what I think is a basic question (*very* basic, sorry about that...) which came to my mind while digging in the posts about interaction effects in multiple regression, and I would appreciate a lot to have your advice on it.
>
> Suppose I have the following model:
> Yhat = b0 + b1*X + b2*Z + error
>
> and I want to test for an interaction between X and Z. Now, what is the difference between:
>
> 1. using an interaction EV
> Yhat = b0 + b1*X + b2*Z + b3*(X.*Z)+ error
> and contrast matrix [0 0 0 1]
>
> 2. evaluating the difference in the regression slopes with the contrast matrix [0 1 -1] and [0 -1 1] in the original model
>
> thanks a lot for your reply,
> all the best!
>
> leonardo
|