Re: st: 3-way interaction // interpretation

[Mario Jose <mariojose276@gmail.com>]

Dear Daniel Klein and David Hoaglin,

Many thanks for your helpful comments and explanations. I am going to
explore your suggestions. Also, I was wondering whether with the
purpose of interpret the coefficient it would help to use the
'margins', as follows:
margins, dydx(X) over (d1 d2) atmeans. Is there particular problems in
using margins with three way interaction?
Best regards,
Mario Jose

2013/11/4 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
> *
> *   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/
*
*   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/