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Re: st: indicator variable and interaction term different signs but both significant


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: indicator variable and interaction term different signs but both significant
Date   Mon, 8 Apr 2013 10:46:27 -0400

As Richard has explained in his comments and instructional materials,
the presence of an interaction makes results more difficult to
interpret.

When the interaction is between a continuous variable and an indicator
for a group, the result is that the group has a different slope for
the continuous variable.  In that situation, the indicator for the
group simply provides the difference in intercept implied by the
different slope; it is usually not of separate interest.

Richard also mentioned models that include X and X^2.  Here also the
linear term is secondary.  It may be helpful to look at X^2 as a
mathematical function.  Y = X^2 is symmetric about the Y axis, and Y =
0 when X = 0.  If X^2 should be located elsewhere, to fit the data,
shifting it horizontally requires the X term.  For example, Y = X^2 -
4X  equals 0 when X = 0 and when X = 4 (and is symmetric about the
vertical line at X = 2).  Then shifting the quadratic vertically is
handled by the constant term.  For example, adding 4 shifts the
quadratic up so that Y = X^2 - 4X + 4 equals 0 when X = 2 (a double
root).  In a model, the coefficient of X^2 is the main focus, and the
linear and constant terms fill in what is needed.

David Hoaglin

On Sun, Apr 7, 2013 at 6:21 AM, Nahla Betelmal <nahlaib@gmail.com> wrote:
> Thank you all for your valuable comments. It was very interesting to
> interact with you guys.
>
> I think my case is shown in this useful file
> http://www.sagepub.com/upm-data/21120_Chapter_7.pdf . Figure 7.9, page
> 134.
>
> Many thanks again
>
> Nahla
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