[R-sig-ME] strategy for interpreting significant interactions

[J.A. Etzel]

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