Date: Thu, 16 Sep 2010 08:30:42 -0500
Reply-To: "Steve Simon, P.Mean Consulting" <firstname.lastname@example.org>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: "Steve Simon, P.Mean Consulting" <email@example.com>
Subject: Re: Pesky Statistical Interactions
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On 9/16/2010 8:03 AM, Gerónimo Maldonado wrote:
> I've constructed a binary regressional model (interactions included) and
> regretfully found 2 significant (p<0.05) interactions among my
> predictors. Question is... How to deal with these interactions??, I
> mean, should I leave them in my model???, should I leave them in my
> model and included them in my results??, is it bad to have them in my
> model???. I know how to interpret them, my question is really some
> technical stuff.
What did you write in your protocol. If your protocol is vague on this
point, then you can do whatever you please. But if the protocol spelled
out a certain approach, then you need to follow that approach or report
the alternative approach in your paper as a protocol deviation.
Even if you have latitude to do what you want, you still may be at a
loss as to what to do. An interaction in many situations is effectively
the same as finding a different effect in a subgroup. So you may want to
look at some of the literature on subgroup analysis. In particular, you
need to think about the scientific plausibility of the findings. It's
plausible to believe that men have a different response to some
medications than women if the medication is sensitive to various
hormones. But it is not plausible to believe that left-handed patients
have a different response to most medications that right-handed patients.
You also did not specify how you fit the model. Did you use a stepwise
approach or something similar where you compared multiple models with
different variables and added/removed variables based on their p-values?
In this case, the interaction might be spurious. Stepwise approaches
tend to inflate p-values, and this is especially true when there are a
large number of models being considered, as is the case with
interactions. There are far more potential interactions than there are
potential main effects.
Also, look at the type of interaction you have. Is it a quantitative
interaction (the effect of A is present for one level of B and absent or
the opposite direction for another level of B)? Is it a qualitative
interaction (the effect of A is in the same direction for all levels of
B, but for some levels it is somewhat stronger and for other levels it
is somewhat weaker). Ignoring a qualitative interaction is less serious
than ignoring a quantitative interaction.
If the goal of the model is prediction rather than inference about
individual predictors, AND if you have lots of data, put in every
interaction and compare its predictive power to a model that has no
interactions (don't look at anything in between). Hold out a portion of
your sample from the model fitting and see how the predictions work on
the hold-out portion compared to the portion that was used to fit the
data. If the predictions are great for the interactions model in the
portion used in estimation, but lousy in the portion held back, that is
very good evidence that the interactions are spurious.
I had a weird interaction in one of my studies and I reported it, but
with a rather skeptical tone. It did not re-occur in a replicated study,
so if I were doing it now, I would not report it at all.
For future studies, if interactions are troublesome, don't look for
them, especially not with stepwise approaches. There's nothing wrong
with saying that you will limit your attention to a certain class of
models if previous work in the area only considered models in that same
class. One such class of models is models with no interactions. Only
look for interactions if there is a scientific reason to believe that
they may be out there. If you do look for interactions when there is no
a priori reason to believe they exist, make sure you bill by the hour
and not by the project.
Steve Simon, Standard Disclaimer
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