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st: Interpreting Nonlinear Interaction Terms Redux


From   Lloyd Dumont <lloyddumont@yahoo.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Interpreting Nonlinear Interaction Terms Redux
Date   Wed, 24 Jul 2013 08:44:50 -0700 (PDT)

Hello.  I am familiar with
the issue of interpreting interaction terms in nonlinear models that has been
written about by Maarten Buis in Stata tip 87 (2010) and by Ai and Norton (2003),
among others.
 
There are two issues that make it difficult for me to generalize
from the examples I have seen.  First, my
model is a Weibull proportional hazards model.  Second, both the variables I am interacting are continuous
 
So,
the estimation command looks something like…
-
streg c.VAR1##c.VAR2 VAR3 i.TIME i.ID, nohr d(weibull) cluster(TIMEID)
 
As
I hoped and hypothesized, the estimates for VAR1 and VAR2 are positive and the
estimate for their two-way, multiplicative interaction term is negative.
 
So,
I guess I am trying to figure out the best way to convince people that these
two variables interact negatively in their influence over the hazard.
 
At
present, the main way that I do this is by showing the fitted hazard function
using stcurve twice (i.e., two panels) —once for low values of VAR1 and then again
for high values of VAR1.
 
-
stcurve, hazard range(0 120) at1(VAR1=-2 VAR2=0 ) at2( VAR1=-2 VAR2=.5 ) at3(VAR1=-2
VAR2=1 ) 
-
stcurve, hazard range(0 120) at1(VAR1=2 VAR2=0 ) at2( VAR1=2 VAR2=.5 ) at3(VAR1=2
VAR2=1 ) 
 
Essentially,
this shows that the (stacking) order of the hazards reverses when VAR1 is low
relative to one it is high.
 
Is
there anything else I should/could be doing?  Ai and Norton’s (2003) -inteff- command does not work with streg.  Buis’s (2010) example uses a logit, not
streg, and does not work through an example in which VAR1 and VAR2 are both continuous.
 
Thank
you for your help.
 
Lloyd
Dumont

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