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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Sun, 7 Apr 2013 00:07:14 -0400 |

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 * * 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/

**References**:**st: indicator variable and interaction term different signs but both significant***From:*Nahla Betelmal <nahlaib@gmail.com>

**Re: st: indicator variable and interaction term different signs but both significant***From:*Anthony Fulginiti <fulginit@usc.edu>

**Re: st: indicator variable and interaction term different signs but both significant***From:*Nahla Betelmal <nahlaib@gmail.com>

**Re: st: indicator variable and interaction term different signs but both significant***From:*Richard Williams <richardwilliams.ndu@gmail.com>

**Re: st: indicator variable and interaction term different signs but both significant***From:*Nahla Betelmal <nahlaib@gmail.com>

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