-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] Namens J.A. Etzel
Verzonden: maandag 17 mei 2010 15:51
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] strategy for interpreting significant
interactions
Good afternoon,
I think of myself as knowing enough about mixed models "to be
dangerous", but certainly not an expert. In a recent
manuscript I used mixed models, and a reviewer's comment has
me confused; I hope that someone on this list may be able to
point me in the right direction. My understanding is that it
is not proper to interpret main effects that are present in a
significant interaction, but rather that elements of the
interaction should be held constant so the others can be
examined in a sensible manner:
my text:
As expected, many significant interactions are present in the
data. The five-way interaction was not significant, nor were
any of the four-way interactions. All five factors (tc, d,
ds, p, s) are involved in at least one three-way interaction:
tc interacts with d and ds, p, and s; s and d also interact
with ds. In these [linear mixed] models it is not possible to
interpret main effects or lower-order interactions when
higher-order interactions are present, so no attempt will be
made to do so here. Instead, additional models with certain
factors held constant were constructed to characterize the
interactions and allow interpretation of the effects.
reviewer's comment:
The authors argue that "interpretation of main effects is not
possible in the presence of significant interactions". This
statement is only one-third true. Indeed, main effects must
not be interpreted in the presence of disordinal
interactions. However, in the case of semi-disordinal
interactions one main effect can be interpreted and in the
case of ordinal interactions even both main effects can be
interpreted. Thus, for every interaction the authors have to
qualify the type of interaction in order to decide whether or
not the main effects can be interpreted.
Is my text/the strategy I followed correct? If so, do you
have any suggestions for references to use in the response to
reviewers on this point? I have had a surprising (to me!)
amount of difficulty finding references detailing what should
be done in the face of significant interactions.
Thanks for your help!
Jo Etzel