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Re: st: positive interaction - negative covariance


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: positive interaction - negative covariance
Date   Fri, 22 Feb 2013 17:47:32 +0000

Why not draw a graph of your two curves? There are various ways to do
it, but here is one

local b1 = .0021067
local b2 = -.3692713
local b3 = -.0010758

twoway function `b0' + `b1' * x, ra(0 100) || ///
       function `b0' + (`b1' + `b3')*x + `b2', ra(0 100)

Naturally, I don't know your -b0- or the range of -x- to use.

You should plot your data too.

As the second two terms seem less important, it's possible that they
are secondary corrections at best and hardly worth interpreting.

On Fri, Feb 22, 2013 at 5:32 PM, andrea pedrazzani
<andrea.pedrazzani.piter@gmail.com> wrote:

> I have a simple regression model with an interaction: Y = b0 + (b1)X +
> (b2)Z + (b3)XZ.
> Z is a dummy (0 or 1).
>
> b1 = .0021067  (SE= .0008513 and p=0.013)
> b2 = -.3692713  (SE= .2329837 and p=0.113)
> b3 = -.0010758  (SE= .000926 and p=0.245)
>
> Hence, the combined coefficient (i.e., the coefficient on X when Z=1)
> is positive:
> b1+b3 =  .0021067 + -.0010758 = .0010309
>
> with SE = sqrt( var(b1) + var(b3)*(Z^2) + 2Z*cov(b1,b3)  )
>             = sqrt( .0000007246 + .0000008574*1 + -.0000007079*2 )
>             = .00040768
>
> To get the p-value for the combinet coefficient, I did
> .0010309/.00040768 = 2.528699.  The corresponding p = 0.0114.
>
> Summing up, X has a positive impact on Y when the condition Z is
> present (.0010309), and a positive impact also when the condition Z is
> not present (.0021067).
> So, what can I say about the interaction? What kind of interaction is
> it when the impact of X is positive both when the condition is present
> and when it is absent? Moreover, the coefficients b1 and (b1+b3) are
> very similar to each other.
> 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...
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