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

[ONKELINX, Thierry]

Dear Jo,

In case that at most one variable in an interaction is continuous, you
can give *some* interpretation on the main effects and lower order
interactions. But you have to be very carefull on the interpretation.
Suppose you have two factors: Var1 with levels A, B and C. Var2 with
levels x, y and z. Then below you have the interpretation of the
parameters from the model Var1*Var2

Intercept = level Ax
Var1:B = level Bx
Var1:C = level Cx
Var2:y = level Ay
Var2:z = level Az
Var1:Var2:B:y = level By
Var1:Var2:C:y = level Cy
...

Note that the 'main effects' does not yield the marginal effect of a
level, but the effect conditional on the reference level of the other
variables.

HTH,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics & Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
  

> -----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
> 
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 

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