Since you are using a loop design, you should have 2 replicates per 
factor combination.  In that case, you should be able to fit up to 
4-way interactions.

--Naomi

At 01:59 PM 1/19/2009, Wei Xu wrote:
>Thanks, Gordon and Naomi.
>One of the examples in limma manual talks about 2x2 factorial 
>experiments of a two-channel array. It estimates the interaction in 
>the makeContrasts.
> > cont.matrix <- makeContrasts(
>+ WT11.MT11=P11mt-P11wt,
>+ WT21.MT21=P21mt-P21wt,
>+ WT11.WT21=P21wt-P11wt,
>+ MT11.MT21=P21mt-P11mt,
>+ Int=(P21mt-P11mt)-(P21wt-P11wt),
>+ levels=design)
>Since I got more factors (2x2x2x2), can I make the interactions with 
>more factors (i.e. two-way, three-way, and four-way interactions)?
>
>Wei
>
>On Fri, Jan 16, 2009 at 11:10 PM, Naomi Altman 
><<mailto:naomi@stat.psu.edu>naomi@stat.psu.edu> wrote:
>I think that Wei Xu is referring to the fact that one ANOVA is not 
>an identifiable model without a constraint - hence one either has to 
>construct the model matrix with an indicator variable, or with the 
>factor effects.
>
>In limma, this does not matter, because limma does the overall 
>F-test and then allows you to construct as many contrasts as are reasonable.
>
>I always use single channel analysis for loop designs, which makes 
>it easier to set up the main effects and interactions.
>
>This was a kind of "statsy" comment on my part, but I hope that 
>those who have taken a course including factorial designs can follow.
>
>--Naomi
>
>
>
>At 10:33 PM 1/16/2009, Gordon K Smyth wrote:
>
>Date: Thu, 15 Jan 2009 16:12:08 -0500
>From: Wei Xu <<mailto:xuwei3@msu.edu>xuwei3@msu.edu>
>Subject: [BioC] reference argument in limma factorial design
>To: <mailto:bioconductor@stat.math.ethz.ch>bioconductor@stat.math.ethz.ch
>Content-Type: text/plain
>
>Hi, everyone,
>
>I am working on a dual-channel cDNA microarray project which includes 32
>slides as a loop design. It is a 2x2x2x2 factorial experimental design that
>combines 16 treatments. When I was trying to use modelMatrix to design the
>matrix, it always asked me to input a reference. However, in my experiment,
>I don't really have one as a reference. I tried to assign a random treatment
>as reference but that way I couldn't make contrasts of the reference with
>the other treatments.
>
>
>Yes, you can make contrasts between the reference and other 
>treatments, in fact that is what the coefficients now mean.  Please 
>refer to the examples on common reference designs in the limma 
>User's Guide (for example Section 7.3), or past advice given on this list.
>
>Best wisehs
>Gordon
>
>How should I set this argument? Is there a different
>way that allows me not to assign a reference? Thanks.
>
>Wei
>
>--
>Wei Xu
>Aquatic Animal Health Laboratory
>Pathobiology and Diagnostic Investigation
>College of Veterinary Medicine
>Michigan State University
>East Lansing, MI, 48824
>Tel: 1-517-432-8258
>
>
>_______________________________________________
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>
>
>Naomi S. Altman                                814-865-3791 (voice)
>Associate Professor
>Dept. of Statistics                              814-863-7114 (fax)
>Penn State University                         814-865-1348 (Statistics)
>University Park, PA 16802-2111
>
>
>
>
>
>--
>Wei Xu
>Aquatic Animal Health Laboratory
>Pathobiology and Diagnostic Investigation
>College of Veterinary Medicine
>Michigan State University
>East Lansing, MI, 48824
>Tel: 1-517-432-8258

Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
University Park, PA 16802-2111

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