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Re: st: high correlation interaction & main effect


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: high correlation interaction & main effect
Date   Tue, 5 Mar 2013 10:32:57 +0100

On Tue, Mar 5, 2013 at 6:12 AM, Caroline Wilson wrote:
> I'm using Stata to run a multilevel model. I have a few interaction variables in my model, which are the product of a continuous variable (time) and a categorical variable. My variable for time was defined as years from the start of the study, to the nearest day, and was defined this way because it makes sense in the context of my study. The interaction variables are in some cases highly correlated (0.8) with the main effects.
> A couple of questions:
> 1. How much should I worry about the high correlation?
> 2. What, practically speaking, can I do about the high correlation? I'd like to keep the interaction terms in the model since they represent my key research question.

You should know about it, and know about the consequences: low power,
i.e. you are less likely to find a effect when you should. This is not
nice but it is an accurate representation of the amount of information
available in the data. One way you can see this is by looking at the
minumum number of observations necessary to estimate an effect. The
larger that minimum, the less information is present in each
individual observation.

Consider a main effect. The absolute minimum number of observations
necesary for estimating it is 2: one observation in group 1, the other
in group 2 and the difference in response is your effect.

For an interaction effect the absolute minimum number of observation
necessary is 4: You need 2 observations in group a, one each in group
1 and 2, in order to compute the effect of group 1 versus 2 in group
a. You need another 2 observations in group b, one each in group 1 and
2, in order to compute the effect of group 1 versus 2 in group b. The
difference in these effects is your interaction effect.

So striclty speaking there is nothing you can and should do about this
high correlation.

-- Maarten

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

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

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