[R-sig-ME] follow up test on interaction from mixed effect model

[Emmanuel Curis]

Hi,

This is not really an answer, but I remember a text from Venables
about regression and interactions, and if I remember correctly, it was
said that for two continuous variables x & y (quantitative variables
in general I guess), using an interaction x*y without using x^2 and
y^2 was somehow meaningless.

http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf

The main idea was, IIRC, that the linear regression equation is a Taylor
expansion at first order, and for adding interactions one must
consider a second-order expansion, which gives the x*y term but also
the x^2 and y^2 terms... Which sounds quite sensible.

But with this idea in mind, I wonder how it would make sense to «
tease apart » the interaction for continuous variables. Instead,
presence and interaction would suggest that a linear relationship
between the dependant variable and the predictors is not suited, but
it gives another equation which may be useful by itself...

This is quite a different interpretation from the case of categorical
variables, in fact, even if the linear model formalism is the same...

Would be pleased to have comments on these ideas by more experimented
statisticians, by the way...

Best regards

On Wed, Jan 30, 2013 at 02:27:36AM +0000, Christopher Kurby wrote:
« Hello everyone,
« 
« I have a mixed effect model in which I am modeling an interaction between two continuous variables. The interaction between them is significant. Can anyone recommend a method to tease apart this interaction? For standard multiple regression, one would compute simple slopes from the regression equation. Is the same done for mixed effect models? Just for the sake of argument, let's say my model is below. In case it is important to know, I also have some covariates in the model, but I'm modeling only the main effect of the covariate. Again, I am interested in teasing apart the interaction between the two continuous predictors:
« 
« lmer(DV ~ var1 * var2 + cov1 + (1|Subject) + (1|item), data=dat)
« 
« Thank you in advance.
« 
« Chris
« 
« Christopher A. Kurby
« Assistant Professor of Psychology
« Grand Valley State University
« Allendale, MI 49401
« phone: 616-331-2418
« email: kurbyc at gvsu.edu<mailto:kurbyc at gvsu.edu>
« 
« 
« 
« 
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-- 
                                Emmanuel CURIS
                                emmanuel.curis at univ-paris5.fr

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