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

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: indicator variable and interaction term different signs but both significant Date Sun, 07 Apr 2013 02:25:52 -0500

```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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```