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

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

At 11:07 PM 4/6/2013, David Hoaglin wrote:

> Richard gave the following interpretation of the coefficient of OC_D
> in the initial model: "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."  The
> phrase "and the values of other variables are the same for both,"
> however, does not reflect the way multiple regression works.  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.  (I realize that various books have
> interpretations similar to the one that Richard gave, but that does
> not make those interpretations correct in general.)  Since OC_D is an
> indicator variable, its coefficient gives the difference, on average,
> between overconfident managers and rational managers after adjusting
> for the contributions of the other predictors.  One of those other
> predictors is OC_MV, so the resulting interpretation for the
> coefficient of OC_D is the one that I gave above.

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!


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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EMAIL:  Richard.A.Williams.5@ND.Edu
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