[BioC] limma's eBayes error: No residual degrees of freedom in linear model

[Gordon Smyth]

 >[BioC] limma's eBayes error: No residual degrees of freedom in linear
 >model
 >Li,Qinghong,ST.LOUIS,Molecular Biology Qinghong.Li at rdmo.nestle.com
 >Thu Nov 17 21:40:38 CET 2005
 >
 >Dear Gordon,
 >
 >I would like to thank you for pointing out the problem. This is the
 >first time I tried to use Limma. The main reference materials I used
 >is the Ch. 23 of Book Bioinformatics and Comp. Biol. solutions Using R
 >and BioC. and the lab notes from microarray short course @ IBC 2004.
 >In particular, the example I was following was the 23.10 in the book,
 >factorial designs where we have five chips, 2 for WT and 3 for
 >Mutants. In each genotype, there are unstimulated and stimulated. I
 >thought that resembled the experimental designs in my case (target
 >file):
 >
 >FileName Sib Sex Treatment
 >anim1     1   M         C
 >anim2     2   F         C
 >anim3     3   M         C
 >anim4     3   F         C
 >anim5     1   M         R
 >anim6     2   F         R
 >anim7     3   M         R
 >anim8     3   F         R
 >
 >Where Sib indicates sibling pairs: anim1 and anim5 are siblings and so
 >forth. My question is quite simple: I would like to know if there is
 >any difference between C and R in treatment for now. Although I might
 >be interested in the gender effect (and/or gender*treatment) in a
 >later time.
 >
 >First, I read in all CEL files and normalized the chips using Limma
 >package and it looked quite good in diagnostic plots. Say I called
 >that file "eset", which is an exprSet file. I used the following
 >scripts to create the design matrix:
 >
 >> TBS<-paste(target$Treatment, target$Sex, target$Sib, sep=".")
 >> TBS<-factor(TBS, levels=unique(TBS))
 >> design<-model.matrix(~0+TBS)
 >> colnames(design)<-levels(TBS)
 >
 >>cont.matrix<-makeContrasts(diff=
 >(C.M.1+C.F.2+C.M.3+C.F.3)-(R.M.1+R.F.2+R.M.3+R.F.3))
 >
 >model fitting:
 >>fit1<-lmFit(eset,design)
 >>fit2<-contrasts.fit(fit1, cont.matrix)
 >>fit3<-eBayes(fit2) (this is where I got the error message)
 >
 >Best wishes,
 >Johnny

Thanks for your detailed explanation here which makes what you're doing far 
clearer. I've just realised what the reasoning was behind your analysis, so 
I'll add a few more comments to my previous email.

I see that you're trying to extend the two-factor example in the book 
chapter to three factors. You can't do this because you don't have enough 
data. Your 3-way factorial model would generate 3 x 2 x 2 = 12 factor 
combinations, so you would need at least 13 arrays whereas you only have 8.

There actually is no need to fit a 3-way factorial model. Sib pairs are not 
a factor but rather a blocking variable. You do not need to allow for 
interactions between Sib pairs and the other two factors.

Best wishes
Gordon