Hello Paul and Emmanuel,

Thank you so much for your feedback. I'm sorry if I was confusing, but I am indeed also modeling the main effects. The model I specified in the email would automatically compute them. Again, apologies for any confusion. Given that, do you, or anyone, know of a straightforward way to tease apart the interaction? In standard multiple regression, you would compute simple slopes, and test, them using the regression equation computed by the model. Is the same method recommended for mixed effect models, and if so, does anyone have recommendations on how to assess the significance of simple slopes in mixed effect models? Or perhaps there is another recommended method?

Sincerely,
Chris


Christopher A. Kurby
Assistant Professor of Psychology
Grand Valley State University
Allendale, MI 49401
phone: 616-331-2418
email: kurbyc@gvsu.edu<mailto:kurbyc@gvsu.edu>



On Jan 30, 2013, at 9:36 AM, "Thompson,Paul" <Paul.Thompson@SanfordHealth.org<mailto:Paul.Thompson@SanfordHealth.org>>
 wrote:

Definitely agree. The full model with interaction is

X1 X2 x1*X2 x1*x1 x2*x2

The model as specified in the post has X1*X2.

The use of the interaction term without the main effects ends up sweeping variance which should be attributed to the X1 and X2 terms into the interaction, producing an artifactual inflated significance.

-----Original Message-----
From: r-sig-mixed-models-bounces@r-project.org<mailto:r-sig-mixed-models-bounces@r-project.org> [mailto:r-sig-mixed-models-bounces@r-project.org<mailto:sig-mixed-models-bounces@r-project.org>] On Behalf Of Emmanuel Curis
Sent: Wednesday, January 30, 2013 3:02 AM
To: Christopher Kurby
Cc: r-sig-mixed-models@r-project.org<mailto:r-sig-mixed-models@r-project.org>
Subject: Re: [R-sig-ME] follow up test on interaction from mixed effect model

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@gvsu.edu<mailto:kurbyc@gvsu.edu>
<
<
<
<
< [[alternative HTML version deleted]]
<
< _______________________________________________
< R-sig-mixed-models@r-project.org mailing list < https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

--
                               Emmanuel CURIS
                               emmanuel.curis@univ-paris5.fr

Page WWW: http://emmanuel.curis.online.fr/index.html

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