[R-sig-ME] Changes of estimate sign when interaction effects are highly significant

[Ben Bolker]

Adam Smith <raptorbio at ...> writes:

> 
> Teresa,
> 
> Correct, main effects cannot be interpreted in the 
> presence of an interaction, unless the main effect
> input variables are centered...

  More precisely, with R's default treatment contrasts,
the main effects parameters in a model with interactions
refer to the expected change when the other continuous
predictors in the interaction are at zero and the other
categorical predictors are at their baseline level.

  The best thing to do is often to draw a graph so
you can see visually what's going on.  For two continuous
covariates it may be a good idea to use cut() [or
cut_interval() or cut_number() from the ggplot2 package]
to subdivide one of the covariates into range.
 
> See, for example: Engqvist, L. (2005) The mistreatment of covariate
> interaction terms in linear model analyses of behavioural and
> evolutionary ecology studies. Animal Behaviour, 70, 967–971. 
 
> (free pdf here: http://pub.uni-bielefeld.de/download/2395676/2496935)
 
> Schielzeth H (2010) Simple means to improve the interpretability of
> regression coefficients. Methods in Ecology and Evolution, 1,
> 103–113. 

> (http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2010.00012.x/full)
> 
> Cheers,
> 
> Adam Smith
> 
> > Date: Tue, 5 Mar 2013 18:56:07 +0100
> > From: tmoranlopez at ...
> > To: r-sig-mixed-models at ...
> > 
> > Hi everyone,
> > I am trying to evaluate the effects of WUE and drought on trees 
> > growth. I am running a mixed model in which my dependent variable is 
> > growth and my fixed effects are WUE, drought and their interaction. My 
> > random variables treeID nested in year. When the interaction among the 
> > two variables is not included, the effects of WUE on growth is 
> > negative and the effects of drought negative which is very intuitive. 
> > However, the best model includes the interaction (which is highly 
> > significant), and then the sign of the main effects change, now both 
> > drought and WUE have a positive effect on growth! And the sign of the 
> > interaction is negative...
> > Does anyone know what could be happening? Does this mean that when we 
> > have a very significant interaction between two fixed effects they 
> > cannot be interpreted separately?
> > Thanks