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

[Julien Beguin]

I think that the reviewer's comment saying that you need to "qualify the
type of interaction in order to decide whether or not the main effects
can be interpreted" means that you need to establish that you have interval or ratio data because 
an apparent interaction could be an artifact of ordinal scale measurement. 

Have a look at this link:
http://www.markwebtest.netfirms.com/Appendix/WebAppOrdinalInteraction/WebAppOrdinalInteractions.htm

Julien Beguin 
________________________________________
De : r-sig-mixed-models-bounces at r-project.org [r-sig-mixed-models-bounces at r-project.org] de la part de J.A. Etzel [J.A.Etzel at med.umcg.nl]
Date d'envoi : 17 mai 2010 09:50
À : r-sig-mixed-models at r-project.org
Objet : [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

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