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Re: AW: st: AW: beta coefficients for interaction terms

Subject   Re: AW: st: AW: beta coefficients for interaction terms
Date   Tue, 21 Apr 2009 18:17:59 +0200

Thank you very much Maarten.
So for the interpration of the beta coefficicients:
For example Y=5.09-2.30X+4.50Z+1.20XZ
The interpretion for my interaction term would be: the interaction lowers the negative effect of X and it increases the positiv effect of Z. Am I getting it right?


Zitat von Maarten buis <>:

--- On Tue, 21/4/09, wrote:
Without having iteraction terms, as far as I know you have
to coed -regress, beta- to get the standardised beta
coefficients, so you can  tell which variable has the
biggest effect.

With interactions you have to very precise about what you
exactly want. The whole point of an interaction is that
the effect of a variable is allowed to change when
another variable changes. So the question which variable
has the bigger effect now has multiple answers.

The way forward is to go back to your substantive problem
and try to figure out what it is exactly what you want to
know, and derive your interaction term and standardizations
from that.

One way that could make sense is to present the difference
between standardized effects for different values of both
variables in a graph like in the example below:

*------------------------ begin example -------------------
sysuse auto, clear
local vlist "price mpg rep78"
foreach var of varlist `vlist' {
	sum `var'
	qui gen double z_`var' = (`var' - r(mean))/r(sd)
gen z_mpgXz_rep78 = z_mpg*z_rep78

reg z_price z_mpg z_rep78 z_mpgXz_rep78

gen effdif0 = _b[z_mpg] + _b[z_mpgXz_rep78]* z_mpg - ///

gen effdif_2 = _b[z_mpg] + _b[z_mpgXz_rep78]* z_mpg - ///
              (_b[z_rep78] + _b[z_mpgXz_rep78]*-2)

gen effdif2 = _b[z_mpg] + _b[z_mpgXz_rep78]* z_mpg - ///
              (_b[z_rep78] + _b[z_mpgXz_rep78]*2)

twoway line effdif_2 effdif0 effdif2 mpg, sort ///
   ytitle("difference in standardized effects" ///
          "of mileage and repair status")      ///
   legend(order(1 "z_rep78 = -2"               ///
                2 "z_rep78 = 0"                ///
                3 "z_rep78 = 2"))              ///
*------------------- end example --------------------------

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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