Re: st: Modeling Interactions and Interpretation using ONLY factorial interactions (and having imputed data)

[Maarten Buis <maartenlbuis@gmail.com>]

On Thu, Oct 6, 2011 at 3:50 PM, Andrea Bennett <mac.stata@gmail.com> wrote:
> I'd like to know whether the following way of implementing and interpreting an interaction between say -female- (0 "Male" 1 "Female)
> and -treatment- ( 1 "Control" 2 "Treatment A" 3 "Treatment B") is correct.
>
> I've learned to model an interaction as: reg y i.female##i.treatment. However, is the following also correct?
> reg y i.female#i.treatment (using ONLY factorial interactions). The way I understand it, this generates 6 dummies for each
> combination of paired interactions whereas the dummy for male & control group is the base and hence omitted from the output. I therefore
> would prefer this approach over the more frequently applied.
>
> Output:
> female#treatment
> 0 2 | 3.85 (p=0.000)
> 0 3 | 2.87 (p=0.002)
> 1 1 | 1.97 (p=0.001)
> 1 2 | 4.39 (p=0.000)
> 1 3 | 5.622783 (p=0.000)

Notice that you get five coefficients not 6. In your case all
coefficients are comparisons with male controls. If you want 6
coefficients you have to add the -nocons- option. In that case you get
expected values of y within each gender-treatment combination (while
all other variables are equal to 0, so centering your other variables
is going to be useful).

> If I want to test whether females perform significantly better in treatment B compared to treatment A,
> I would have to run: mi estimate (diff: _b[1.female#2.treatment]-_b[1.female#3.treatment]): reg  y i.female#i.treatment + controls
>
> If I wanted to test whether females perform significantly better compared to males in treatment A,
> I would have to run: mi estimate (diff: _b[0.female#2.treatment]-_b[1.female#2.treatment]): reg  y i.female#i.treatment + controls

That will only work if you specified the -nocons- option.

> When I apply the standard procedure reg y i.female##i.treatment + controls the output is as follows:
>
> treatment
> 2 | 3.85 (p=0.000)
> 3 | 2.87 (p=0.002)
>
> female
> 1 | 1.97 (p=0.001)
>
> female#treatment
> 1 2 | -1.43 (p=0.127)
> 1 3 |.77 (p=0.403)
>
> The BIG question:
> What (always) confuses me is that the pure interaction term of 1 3 is highly insignificant. But we cannot conclude from this that the interaction between female and treatment B is indeed insignificant because we have to take into account 1) the treatment effect of 3, 2) the gender effect,
> and 3) the interaction term. Only if these three are jointly insignificant I cannot reject the hypothesis that females do not change behavior in
> treatment B.

That is not true, the interaction effect is insignificant, you just
not to be careful whether that means what you think it means. The
effect of treatment 3 is a comparison of treatment B with control. The
interaction effect says that this comparison is not significantly
different for men and women.

> how can I make sure that I do it right.

Basically I go to my whiteboard to keep track of which parameter
represent which comparison. Its a pain, but there is no real
alternative. Over time I have gotten better at it, that is, I can do
it more quickly, but I don't think I will ever be able to completely
avoid writing it down (I can of course, but than I will start making
errors again...).

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

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