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

[David Hoaglin <dchoaglin@gmail.com>]

Nahla,

The discussion has been giving a lot of attention to MV = 0.  I don't
recall seeing information on the minimum and maximum values of MV, but
MV = 0 may be far from the values of MV in your data.  The behavior of
the model would be clearer if you centered MV at a suitable value,
near the middle of the data.

Since you have OC_MV in the model, you should focus on the coefficient
of OC_MV, in conjunction with the coefficient of MV.  The coefficient
of MV (.000584 in your simplified model) is a slope of the dependent
variable against MV for rational managers (OC_D = 0), and the
coefficient of OC_MV (.012836) is the additional slope of the
dependent variable against MV for overconfident managers.  That is,
the slope against MV for overconfident managers is .000584 + .012836.
In the presence of OC_MV, the coefficient of OC_D is the change in the
intercept term that accompanies the slope against MV for the
overconfident managers.

When you removed those other five predictors, the fit of the model
became substantially poorer (e.g., R-squared dropped from .37 to .11).
 That drop may reflect the contributions of private_D and same_D in
the initial model, but the situation could be more complicated.  A
P-value in the initial output tells you only about the significance of
that predictor when all the other predictors are already in the model.
 It would be informative to remove "non-significant" predictors one at
a time.

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.

Bottom line: Center MV, focus on the coefficients of OC_MV and MV, and
be sure to report the list of variables whose contributions you are
adjusting for.

David Hoaglin

On Sat, Apr 6, 2013 at 7:53 PM, Nahla Betelmal <nahlaib@gmail.com> wrote:
> Hi Richard,
>
> Thank you for the help and for the file.
>
> let me get this straight, if MV=0 , overconfident managers would
> manage earnings LESS than other managers (accept as it is
> statistically significant). However, When MV has other values the
> overconfident manage might manage earnings more or less than others.
>
> I understand that interpretation of OC_D has no practical meaning as
> MV cant be zero, however, I wonder if the interpretation of the
> interaction term (OC_MV) depends on the sign of OC_D. As you can see
> they have different signs.
>
> Does the fact OC_D has a negative sign and OC_MV has a positive one ,
> mean : a) overconfident managers will manage earnings more when MV is
> high, or b) overconfident mangers will manage earnings less especially
> when MV is high!!
>
> Also, can you explain what do you mean by "To me the critical thing
> seems to be that the effect of MV is about 3 times as large for
> overconfident managers as it is for regular managers" I did not get
> that.
>
> The other variables have theoretical background, however, I drooped
> them to see what happens.
>
>
> Linear regression                                      Number of obs =      56
>                                                        F(  3,    52) =    2.90
>                                                        Prob > F      =  0.0433
>                                                        R-squared     =  0.1116
>                                                        Root MSE      =  .09448
>
> ------------------------------------------------------------------------------
>              |               Robust
> Earnings Mgt |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>    MV |    .000584   .0015479     0.38   0.707    -.0025221    .0036901
>   OC_D |  -.0728009   .0320739    -2.27   0.027     -.137162   -.0084398
>  OC_MV |    .012836   .0048402     2.65   0.011     .0031235    .0225485
>   _cons |   .0156561   .0125722     1.25   0.219    -.0095719    .0408841
>
>
> Thank you again
>
> Nahla
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