Re: st: Question about interactions

[Maarten Buis <maartenlbuis@gmail.com>]

On Thu, Mar 7, 2013 at 12:03 PM, K Jensen wrote:
> Thanks for the replies I received on interactions. They were very
> helpful and I think that I understand the model now.
>
> Say we are looking at the interactions of two variables. A colleague
> wondered why we don't just fit the possible group combinations as
> indicator variables (i.e. 1-1 as a group (baseline), 1-2, 1-3, 1-4,
> 2-1, 2-2, 2-3, 2-4, etc) and get an OR (I am doing logisitic
> regression) for each group combination except 1-1 .
>
> What is the advantage of fitting the conventional model?

What your colleague proposes should be equivalent to what you called
the conventional model. So you will get the same predicted values and
there is no way to statistically choose between the two; they are just
two different ways of looking at the same object.

One of the advantages of the conventional model is that it is
conventional. This may seem trivial, but as you noticed interactions
are hard, so it can make a real difference if you stick to patterns
that your readers expect so they don't have to rethink the entire
model (basically recalculate everything in their mind to fit in their
usual pattern). However, this only applies when this pattern is indeed
the convention for the people with who you correspond.

Another is that in the conventional model you explicitly look at
differences (actually ratios) between effects, which is what you
typically (but not always) want when you include interaction terms.

If you change the setup you need to take care that it is indeed the
equivalent model as the conventional model (unless you explicitly want
a different model). It is very easy to get this wrong. One check you
could perform is predict probabilities for both models and check
whether they are the same.

If this is the way you want to go, than there are couple of tips in
this Stata tip that may help:
M.L. Buis (2012) "Stata tip 106: With or without reference", The Stata
Journal, 12(1), pp. 162-164.
<http://www.maartenbuis.nl/publications/ref_cat.html>

In essence, your collegues model was to remove one of the reference
categories but leave the other in.

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

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