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

J.A. Etzel J.A.Etzel at med.umcg.nl
Tue May 18 09:46:11 CEST 2010

I received another reply, which I copy here since it wasn't sent to the 
I also just know enough to be dangerous, but here's a first 
approximation of the ultimate truth.

I think he is just arguing (rightly or wrongly) that some kinds of main 
effects in the presence of an interaction can indeed be safely 
interpreted. One example comes to mind: if the interaction only 
moderates the strength of a main effect and does not flip over its 
direction. If the variables are setup in some sensible way then the main 
effects will give a kind of average.

A more general approach would be somehow to make sense of the meaning of 
the interactions. Can they be given a theoretical interpretation, 
perhaps with the help of some graphing? This is where the theory comes 
in handy: to limit the space of statistical models you have to explain!

Andy Fugard

Thanks for the replies!

In this case, the data is on a ratio scale and floor/ceiling effects 
aren't a problem. This should have been obvious from the paper, but 
maybe wasn't. Thanks for the link; I wasn't familiar with this artifact.

Perhaps I should add plots of the interactions, demonstrating that they 
do cross ("disordinal interactions"). The approach I followed in the 
paper was to construct sensible (given the data) sub-analyses to 
describe the interactions, such as looking at the effect of p within 
each combination of d and tc (since p did not interact with ds or s).

thanks again,
Jo Etzel

Julien Beguin wrote:
> 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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