Re: st: 3-way continuous interaction - comparing simple slopes

[Roman Wörner <h0953997@wu.ac.at>]

Dear David,

what I actually do is to regress two performance measures (return on 
assets and relative patent performance) on two strategies (strategy A 
and strategy B), their interaction and an additional moderator (vertical 
integration). Return on assets is negative for the bigger part of the 
sample - so, log or sqrt won't work. Relative patent performance (#of 
patents per employee) is null for the bigger part of the sample - again, 
log is not an option.

I argue, that the relationship of the two strategies changes with the 
vertical integration of the firm. Based on the regression results I plot 
simple slope diagramms (high/low levels of strategy A/B @low levels of 
vertical scope and of high/low levels of strategy A/B @high levels of 
vertical scope). I then want to test if the slopes @high levels of 
vertical scope are significantly lower than the slopes @low levels of 
vertical scope.

What the procedure described down below - lincom ($HzHw)-($HzLw) - does 
is to test whether the two slopes are different ("plain different") 
without considering the direction ("is one steeper than the other").

To get rid of the 3-way interaction I initially considered dichotomizing 
the vertical scope variable into two groups (high/low) and split the 
sample. But I think that would make the situation even worse --> two 
samples and two models would require out of sample tests to compare the 
slopes...

Kind regards,

Roman

Am 21.05.2013 23:59, schrieb David Hoaglin:
> Dear Roman,
>
> Is the nature of your y such that you could transform it (e.g., by
> taking the logarithm or the square root) and have an analysis that has
> fewer or even no interactions?
>
> David Hoaglin
>
> On Tue, May 21, 2013 at 2:58 PM, Roman Wörner <h0953997@wu.ac.at> wrote:
> > Dear Statalister,
> >
> > I am a student and in my current research project I have to deal with a
> > three-way continuous interaction. I found some material on the website of
> > UCLA (http://www.ats.ucla.edu/stat/stata/faq/con3wayb.htm) where they
> > explain how to use the -lincom- command to calculate simple slopes.
> > Furthermore, they show how to use -lincom- to compare two simple slopes (I
> > attached the code at the end of the message). This material was extremely
> > helpful to me (how to put Aiken/West 1991 and Cohen et al. 2003 into
> > practice).
> >
> >
> > My question is as follows: to my understanding
> >
> > *lincom ($HzHw)-($HzLw)*
> >
> > tests whether the two slopes are different. What I actually want to test is
> > not whether the two slopes are different but whether one slope is "steeper"
> > than the other (my hypothesis is that two variables complement each other;
> > with an increase in the third variable the complementarity effect becomes
> > weaker). I would be very grateful for any advice on how to adapt the
> > procedure as described down below or any other technique which does the
> > trick.
> >
> > I am fairly new to STATA and statistics in general - so my appologies if
> > this question sounds very basic to most of you.
> >
> > Thanks in advance and kind regards,
> >
> > Roman
> >
> > --
> >
> > use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear
> >
> > rename write y
> > rename read x
> > rename math w
> > rename science z
> > rename socst v1
> > rename ses v2
> >
> > generate xz  = x*z
> > generate xw  = x*w
> > generate zw  = z*w
> > generate xzw = x*z*w
> >
> > regress y x z w xz xw zw xzw v1 v2
> >
> > quietly sum x
> > global hi=r(max)
> > global lo=r(min)
> > quietly sum w
> > global Hw=r(mean)+r(sd)
> > global Lw=r(mean)-r(sd)
> > quietly sum z
> > global Hz=r(mean)+r(sd)
> > global Lz=r(mean)-r(sd)
> > quietly sum v1
> > global m1=r(mean)
> > quietly sum v2
> > global m2=r(mean)
> >
> > global HzHw "x + ($Hz)*xz + ($Hw)*xw + ($Hz)*($Hw)*xzw"
> > global HzLw "x + ($Hz)*xz + ($Lw)*xw + ($Hz)*($Lw)*xzw"
> > global LzHw "x + ($Lz)*xz + ($Hw)*xw + ($Lz)*($Hw)*xzw"
> > global LzLw "x + ($Lz)*xz + ($Lw)*xw + ($Lz)*($Lw)*xzw"
> >
> > /* simple slopes */
> > lincom $HzHw /* slope 1 */
> > global b1 = r(estimate)
> > lincom $HzLw /* slope 2 */
> > global b2 = r(estimate)
> > lincom $LzHw /* slope 3 */
> > global b3 = r(estimate)
> > lincom $LzLw /* slope 4 */
> > global b4 = r(estimate)
> >
> > /* differences in simple slopes */
> > lincom ($HzHw)-($HzLw)  /* a) HzHw vs HzLw */
> > lincom ($HzHw)-($LzHw)  /* b) HzHw vs LzHw */
> > lincom ($HzLw)-($LzLw)  /* c) HzLw vs LzLw */
> > lincom ($LzHw)-($LzLw)  /* d) LzHw vs LzLw */
> > lincom ($HzHw)-($LzLw)  /* e) HzHw vs LzLw */
> > lincom ($HzLw)-($LzHw)  /* f) HzLw vs LzHw */*
> *
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