Re: st: 3-way interaction // interpretation

[David Hoaglin <dchoaglin@gmail.com>]

Dear MJ,

You did not say what predictors you omitted from the output that you
quoted, so I will focus on X, d1, and d2 alone.  If the model contains
other predictors, then the main effects and interactions of X, d1, and
d2 incorporate adjustments for the contributions of those other
predictors (the model does not "control for" those predictors).

Since d1 and d2 are dummy variables, you are actually fitting four
lines for Y on X:
If d1 = 0 and d2 = 0, the line is _const - 3.56X
If d1 = 1 and d2 = 0, the line is (_const - 0.38) + (-3.56 + 1.14)X
If d1 = 0 and d2 = 1, the line is (_const - 0.16) + (-3.56 + 0.96)X
If d1 = 1 and d2 = 1, the line is (_const - 0.38 - 0.16 + 1.19) +
(-3.56 + 1.14 + 0.96 -0.60)X
This way of writing the model shows that the relation between Y and X
depends on d1 and d2 in a more-complicated way than if the
coefficients of d1#d2 and X#d1#d2 were both zero.  I hope this reduces
your struggle somewhat.

In some situations, transforming Y or X or both may allow you to use a
simpler model.  It may also be appropriate for you to consider a
generalized linear model.  Various plots of residuals and other
diagnostics should help you in learning what is going on in your data.

Regards,

David Hoaglin

On Mon, Nov 4, 2013 at 8:17 AM, Mario Jose <mariojose276@gmail.com> wrote:
> Dear Statalisters,
>
> I am working with a OLS fixed effects model which include a 3 way
> interaction variable between two dummies and a continuous variable x.
> I run the following model in Stata version12:
>
> regress Y c.x##d1 ##d2 ..., where d1 and d2 are dummy variables.
>
> I have obtained the following coefficient estimates:
>
> ***excerpt***
> Y                       Coef.              Std. Err.           t
> X                   -3.564897       .2696342       -13.22
> d1                  -.3814526      .0662797         -5.76
> X#d1            1.144184        .2277408           5.02
> d2                  -.1610461      .0704304         -2.29
> X#d2               .9596349      .234921            4.08
> d1#d2          1 .1886001     .078263             2.41
> x#d1#d2        -.601969       .2707492         -2.22
> .....
> .....
> ***end of excerpt ***
>
> I am strugling with the interpretation of the 3-way interaction:
> x#d1#d2, I would be really appreciate to receive references or help in
> the interpreation of this coefficient.
>
> Best regards,
> MJ
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