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Re: st: positive interaction - negative covariance

From   David Hoaglin <>
Subject   Re: st: positive interaction - negative covariance
Date   Fri, 22 Feb 2013 19:36:18 -0500

Hi, Andrea.

In your initial model, b3 is the coefficient of the interaction term.
Thus, testing the significance of b3 (its difference from 0) directly
addresses the interaction.  It is not necessary, and not at all
appropriate, to compare the confidence interval for b1 and the
confidence interval for b1+b3.  (You did not mention the book that you
read, or the specific comparison that its authors made.  If their
comparison is literally the same as your comparison between the
confidence interval for b1 and the confidence interval for b1+b3, they
are making a beginner's mistake.)

I don't understand why the functions that you plotted are "really
jagged."  Both functions are straight lines.

David Hoaglin

On Fri, Feb 22, 2013 at 5:55 PM, andrea pedrazzani
<> wrote:
> Thank you very much Nick, Jay and David.
> My -x- is -dur-, whose range is from 1 to 1764.
> I plotted the two curves as you suggested me:
> local b0 = 1.663478
> local b1 = .0021067
> local b2 = -.3692713
> local b3 = -.0010758
> twoway function `b0' + `b1'*dur, ra(1 1764) || ///
>        function `b0' + (`b1' + `b3')*dur + `b2', ra(1 1764)
> The two functions have the same shape and are very close to each
> other. Both tend to slightly increase as -x- increases (the functions
> are really jagged, because -dur- has many values). The first one
> (where the condition Z is absent) is always a bit higher than the
> second (where the condition is present). If I am not wrong, this
> indicates that the impact of both on my dependent variable goes in the
> same (positive) direction.
> To Jay: actually my dependent variable is a proportion (I am using flogit)
> To David:
>> Thus, X has a positive impact on Y when Z is present and when Z is
>> absent, but those contributions are not significantly different.  That
>> is, the interaction is essentially absent.
> Thank you for clarifying the point. Indeed, if I compare the
> confidence interval of b1 to the confidence interval of (b1+b3), they
> are not statistically different. Is it the same? In a book I read, the
> authors make this comparison.
> Thanks again.
> Best,
> Andrea Pedrazzani
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