James,
If W and Z were different, it would not be meaningful to compare the
b0's from the two models, because their definitions are different. In
the first model, b0 is the slope of Y against X after adjusting for Z,
whereas in the second model b0 is the slope of Y against X after
adjusting for W. Similarly, the definitions of a are different.
You don't say why you aren't using a single model, with an indicator
variable for, say, the high level of the other variable and an
interaction between that indicator and X. Then you could test whether
the coefficient of that interaction term is 0.
I see your comment about nonlinear models, but your models are not
nonlinear. Even if you had a nonlinear model, the interaction might
not be any more difficult to interpret.
David Hoaglin
On Thu, May 2, 2013 at 11:25 AM, James Bernard <jamesstatalist@gmail.com> wrote:
> Richard,
>
> W and Z can be different or the same. In my case, they are the same. I
> am comparing b0 of in two models where they are tested on a sample
> split by low and high of another variable.
>
> Interaction term is not easily interpretable in non-linear models
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