Re: st: Interpretation of factor variables

[David Hoaglin <dchoaglin@gmail.com>]

Dear Yu,

In writing  "i.Dummy i.Dummy#c.Continuous" in the Stata command, you
are specifying three predictors: an indicator variable whose value is
1 when Dummy == 1, a continuous variable whose value equals that of
Continuous when Dummy == 0, and a continuous variable whose value
equals that of Continuous when Dummy == 1.  The coefficient for Dummy
in your output is the effect of Dummy == 1 (the coefficient of _const
applies when Dummy == 0).  The two coefficients under
Dummy#c.Continuous are, respectively, the slope of DV against
Continuous when Dummy == 0 and the slope of DV against Continuous when
Dummy == 1.  Each of these coefficients summarizes the contribution of
its predictor after adjusting for simultaneous linear change in the
other predictors in the model (Including the "other control
variables").

If you used the predictors Dummy, Continuous, and Dummy*Continuous,
you would have an equivalent model (i.e., it would produce the same
predicted values of DV), but one of the coefficients would be
different: the coefficient of Continuous would be the slope of DV
against Continuous when Dummy == 0 (as before), but the coefficient of
Dummy*Continuous would be the additional slope of DV against
Continuous when Dummy == 1 (from your output, 37.70141 - 31.54672 =
6.15469).

David Hoaglin

On Thu, Jul 11, 2013 at 7:00 AM, Yu Chen, PhD <profyuchen@gmail.com> wrote:
> Dear Statalist,
> I have a dummy variable that takes values of one or zero, and a
> continuous variable. I ran the following regression.
> Dependent Variable (DV) = Dummy + Dummy*Continuous + other control
> variables. I used factor variables (i.e., i.Dummy +
> i.Dummy#c.Continuous )
> I got results as below. My question is how should I interpret the two
> lines below Dummy#c.Continuous? The first line shows a 0. I interpret
> it as Dummy takes 0 for this line. However, if Dummy takes 0, the
> whole term should be zero and should be eliminated from the results.
> But Stata still gave me a Coef. What is going on?
> Thank you in advance for your help.
>
>
> ------------------------------------------------------------------------------
>         DV |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> Dummy#c.Continuous |
>           0  |   31.54672   9.438251     3.34   0.001     13.04526    50.04818
>           1  |   37.70141   7.609734     4.95   0.000     22.78433     52.6185
>              |
> Dummy |   .1026062   .1648457     0.62   0.534    -.2205349    .4257472
>
>
> Yu Chen
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