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| 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 --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/