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Re: st: indicator variable and interaction term different signs but both significant


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: indicator variable and interaction term different signs but both significant
Date   Sun, 7 Apr 2013 08:34:52 -0400

Richard,

That statement may be all right in Nahla's analysis.  The difficulty
lies in the phrase "and the values of other variables are the same for
both."  OC_MV = 0 because MV = 0; that is a special case.  We don't
know that the data contain overconfident managers and rational
managers for whom the values of size, leverage, litigation, private_D,
and same_D are the same (or nearly enough the same).  If so, no
problem.  If not, the statement is an extrapolation, not supported by
the data.  It is up to Nahla (and to analysts generally) to avoid
extrapolating (too far) beyond the data.  Many people (and textbooks)
give that sort of interpretation without any evidence of checking on
extrapolation.

My bottom line was that Nahla should focus on the interaction term (or
in the present example the X^2 term), rather than the "main effect."
The general interpretation is still correct for the coefficient of X,
but it is not meaningful to consider the effect of X without including
the contribution of X^2.  The discussion in your handout is good
guidance on such issues.

David Hoaglin

On Sun, Apr 7, 2013 at 3:25 AM, Richard Williams
<richardwilliams.ndu@gmail.com> wrote:
>
>
> I have to admit that I don't understand what is wrong with my statement, at
> least in the case of this specific example. To be clear, if MV = 0, the
> interaction term OC_MV will also equal 0. So, go ahead and plug in whatever
> values you want for the other variables, compute the predicted values for a
> regular manager and an overconfident manager, and it will indeed always be
> the case that "The coefficient for OC_D is the predicted difference between
> an overconfident manager and a regular manager when MV = 0 and the values of
> other variables are the same for both." They have to be since the
> calculations of the predicted values are identical for both, except that for
> regular managers the coefficient for OC_D gets multiplied by 0 whereas for
> overconfident managers it gets multiplied by 1.
>
> I would agree that things like other interaction terms or X^2 terms make
> life more complicated, e.g. two cases can't have different values of X while
> having the same value of X^2. But, that isn't the case here. I also don't
> think it makes much sense in such a case to talk about the effect of X
> separate from the effect of X^2, so I am not clear how the language on
> "after adjusting for simultaneous linear change in the other predictors at
> hand" really helps any. Even if it were more technically correct, I don't
> think it is at all clear what it means. You have to break down and use a few
> sentences when you have interaction terms and squared terms and things like
> that!
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