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

[Richard Williams <richardwilliams.ndu@gmail.com>]

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
WWW:    http://www.nd.edu/~rwilliam

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/