st: 3-way continuous interaction - comparing simple slopes

[Roman Wörner <h0953997@wu.ac.at>]

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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