[R-sig-ME] Interaction with quadratic variable

Elizabeth Crone ecrone at fas.harvard.edu
Sat Apr 16 13:10:49 CEST 2011

I'm not sure why this query was posted to a _mixed_ models list, but
the answer to all your questions is that you need to become familiar
with plotting the back-transformed function, i.e., if you are using a
logit link function, exp(b0 + b1*N^2 + b2*N^2)/[1+exp(b0 + b1*N^2 +
b2*N^2)].  For interactions of N with categorical variables, my
approach would be to ask whether the entire function differs between
treatments, e.g., by comparing a full model with b0, b1 and b2
interacting with the categorical variable to one with constant values
for these variables.  For interactions among continuous variables, go
back to plotting the function you have fit to your data.

Good luck,
Elizabeth Crone

> Message: 2
> Date: Wed, 13 Apr 2011 11:18:24 -0400
> From: <Solene.Tremblay-Gendron at UQAR.QC.CA>
> To: <r-sig-mixed-models at r-project.org>
> Subject: [R-sig-ME] Interaction with quadratic variable
> Message-ID:
>        <1AFF299063CAB341B3C55EA50E451DD487B8B0 at owadepot.bureautique.uqar.qc.ca>
> Content-Type: text/plain
> Hi,
> I got some questions about assumption and interpretation of conditional logistic regression. It seems that two of my variables (let says N and O) have non-linear effects. In fact, their effects look parabolic, so I transform O and N into quadratics variables (now N+N2 and O+O^2) in my model. The variable O (now became O+O^2) is the most interesting variable in my model and I want to look for interaction of this variable with some others including variable N (now became N+N^2).
> The questions are:
> 1. Is the transformation necessary (what does the transformation do to the variable/model) for the assumption and how do I interpret quadratics terms after (O+O^2)?
> 2. How do I put interaction between a quadratic and a simple variable (O^2:O:X, O^2:X + O:X, etc.)?
> 3. How do I put interaction between two quadratics variables in the model (O^2:N^2:O:N, O:N+ O^2:N + O:N^2: O^2:N^2, etc.)
> 4. How do I interpret these quadratics interactions?
> Thanks,
> Solčne Tremblay-Gendron
Elizabeth E. Crone
Senior Ecologist, Harvard Forest
Harvard University
Petersham MA 01366
phone: (978)724-3302
FAX: (978)724-3595
email: ecrone at fas.harvard.edu

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