[R-sig-ME] strategy for interpreting significant interactions
ONKELINX, Thierry
Thierry.ONKELINX at inbo.be
Tue May 18 10:54:26 CEST 2010
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
>
Druk dit bericht a.u.b. niet onnodig af.
Please do not print this message unnecessarily.
Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer
en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is
door een geldig ondertekend document. The views expressed in this message
and any annex are purely those of the writer and may not be regarded as stating
an official position of INBO, as long as the message is not confirmed by a duly
signed document.
More information about the R-sig-mixed-models
mailing list