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Re: st: positive interaction - negative covariance


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: positive interaction - negative covariance
Date   Sat, 23 Feb 2013 17:02:07 +0100

>>>>>>> Also, both b1 and the combined coefficient (b1+b3) are positive, but
>>>>>>> the covariance between b1 and b3 is negative. It sounds strange to
>>>>>>> me...

Remember, the covariance refers to the sampling distribution not the
data. So, you would expect that covariance to be negative. Think about
a simpler problem: a linear regression with one covariate. You have a
constant and a slope. The covariance refers to the sampling
distribution, so to what happens when you would draw a different
dataset from the same population. Your curve will remain in roughly
the same area. So if you happen to draw a dataset with a slope that is
a bit steeper than the constant will have to be a bit lower to remain
in the same area. If you draw a dataset with a constant that is a bit
higher, than the slope has to be a bit shallower in order for the
curve to remain in the same general area. So the covariance of the
sampling distribution of the constant and the slope will be negative.
A similar argument holds for the covariance of the sampling
distribution of a main effect and an interaction term.

Hope this helps,
Maarten

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

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