strategy for interpreting significant interactions
I received another reply, which I copy here since it wasn't sent to the
list:
-----
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 ? : 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 _______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models