Asymetric Interaction - is this possible?

[tino]

Dear all,

my thought might be a bit naive, but please consider the follwing problem:

Asssume you are interested in the effect of x on y conditional on z. From a regression perspective, we would most likely use a product term in the form x*z to test this interactive relation (while also including x and z as separate predictors). However, the multiplicative approach implies that we could also use z*x, which would mean that the effect of z on y depends on x.

Although this seems straightforward from a statistical ppoint of view, from a theoretical perspective it might be important to distinguish whether x is moderated by z (Theory A) or z moderated by x (Theory B).

I am not aware of any method or approach to distinguish between such theoretical differences using a product term approach in multiple regression; are there any methodological alternatives?

Many thanks for your responses,
Tino

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[Bruce Weaver]

Tino, can you provide a substantive example where the x-y relationship is moderated by z, but the z-y relationship is not moderated by x?  Thanks.

tino wrote

Dear all,

my thought might be a bit naive, but please consider the follwing problem:

Asssume you are interested in the effect of x on y conditional on z. From a regression perspective, we would most likely use a product term in the form x*z to test this interactive relation (while also including x and z as separate predictors). However, the multiplicative approach implies that we could also use z*x, which would mean that the effect of z on y depends on x.

Although this seems straightforward from a statistical ppoint of view, from a theoretical perspective it might be important to distinguish whether x is moderated by z (Theory A) or z moderated by x (Theory B).

I am not aware of any method or approach to distinguish between such theoretical differences using a product term approach in multiple regression; are there any methodological alternatives?

Many thanks for your responses,
Tino

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[Steve Simon, P.Mean Consulting]

On 7/23/2014 9:58 AM, Tino Nsenene wrote:

 > Asssume you are interested in the effect of x on y conditional on z.
 > From a regression perspective, we would most likely use a product
 > term in the form x*z to test this interactive relation (while also
 > including x and z as separate predictors). However, the
 > multiplicative approach implies that we could also use z*x, which
 > would mean that the effect of z on y depends on x.
 >
 > Although this seems straightforward from a statistical ppoint of
 > view, from a theoretical perspective it might be important to
 > distinguish whether x is moderated by z (Theory A) or z moderated by
 > x (Theory B).
 >
 > I am not aware of any method or approach to distinguish between such
 > theoretical differences using a product term approach in multiple
 > regression; are there any methodological alternatives?

If you think carefully about the definition of moderator variables, it
is not an either/or situation. Both Theory A and Theory B can co-exist.
Perhaps you are confusing this with mediator variables.

Steve Simon, [hidden email], Standard Disclaimer.
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