[R-sig-ME] Fixed effects structure

Douglas Bates bates at stat.wisc.edu
Thu Dec 2 23:37:06 CET 2010

On Thu, Dec 2, 2010 at 3:45 PM, Ned Dochtermann
<ned.dochtermann at gmail.com> wrote:
> List members,
> I have a question regarding the structure of fixed effects and I was hoping
> to get a bit of feedback and hopefully direction to a few references. I
> figured this topic should be okay here since "mixed" necessarily includes
> "fixed".
> A colleague of mine is working on a project where she is primarily
> interested in the effects of an experimental treatment and the interaction
> of the experimental treatment with another fixed factor. She is not,
> however, interested in the main effect of this additional factor.
> I know that the conventional wisdom has been that you shouldn't include a
> term in an interaction if it isn't also included as a main effect (based on
> undergraduate stats mantra). My comment was that since the statistical
> hypothesis is meant to represent the biological hypothesis, not including
> the main effect *might* be okay. She has some power concerns and would
> prefer to maximize her denominator degrees of freedom (yes it is actually a
> mixed model; yes I'm aware of the problems with calculating the dfs).

Having a term in the model and performing significance tests on that
term are different.  For example, a blocking factor would typically be
included in the model, even if it was not contributing substantially
to the model.

There is one occasion where it makes sense to include an interaction
but not one of the corresponding main effects.  I refer to this as the
"zero dose" or "zero time on treatment" situation.  If you randomly
allocate subjects to a control and one or more treatment groups and
follow them over time, you might expect different slopes with respect
to time in the different groups but you would not expect a difference
in response between groups at time zero.  Thus you would end up
specifying a model with

resp ~ time + time:trt

but no treatment.
> Are there compelling statistical reasons against not including the main
> effect? Are there good references discussing this (I know she's gone through
> Sokal & Rohlf and a few other books) that would support either argument?
> Cliff notes:
> is: ~ trt + trt:grp
> versus: ~ trt + grp + trt:grp
> okay?
> Thanks for any feed back,
> Ned
> --
> Ned Dochtermann
> Department of Biology
> University of Nevada, Reno
> ned.dochtermann at gmail.com
> http://wolfweb.unr.edu/homepage/mpeacock/Ned.Dochtermann/
> http://www.researcherid.com/rid/A-7146-2010
> --
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