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


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: indicator variable and interaction term different signs but both significant
Date   Sun, 07 Apr 2013 15:58:40 -0500

At 07:34 AM 4/7/2013, David Hoaglin wrote:
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.

Thanks David, but I admit I am still confused. According to the model, it is 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." If MV = 0 is an uninteresting or impossible value, that is pretty much a worthless thing to know, but it is still a correct statement.

Part of what I like about my phrasing (which appears to be a more or less common phrasing) is that I believe it helps make clear (perhaps along with some graphs) why you generally shouldn't make a big deal of the coefficient for the dummy variable, in this case OC_D. It is simply the predicted difference between the two groups at a specific point, MV = 0, a point that may not even be possible in practice. Lines go off to infinity in both directions, and if the lines are non-parallel (as when there are interactions) there will be an infinite number of possible differences between the two lines, most of which will be totally uninteresting. I used to have students making statements like "once you control for female * income, the effect of female switches from positive to negative" and they tried to come up with profound theoretical explanations for that.

I agree with you about being careful about extrapolating beyond the range of the data, but if MV = 0 isn't even theoretically possible it is kind of a moot point. Testing the statistical significance of any predicted values you compute should also give you some protection.

The main thing, though, is that I am confused by your preferred wording: "The appropriate general interpretation of an estimated coefficient is that it tells how the dependent variable changes per unit change in that predictor after adjusting for simultaneous linear change in the other predictors in the data at hand." Why exactly is that a superior wording? I'm not even totally sure what that means. Are you just trying to warn against extrapolating beyond the observed range of the data? If so I think there is probably a more straightforward way of phrasing it. And, I don't think it is clear what "simultaneous linear change in the other predictors" is supposed to mean. Nor do I think the wording makes it clear what substantive interpretation you should give to the coefficient for OC_D.

I think we are in agreement on most points, i.e. we both think there is little point on making a big deal of when MV = 0 when that may not be interesting or even possible -- but I don't understand why you think your preferred wording is better and other wordings are incorrect. But I'd be interested in hearing you elaborate.

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
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