[BioC] limma - interpreting factorial design

[john seers (IFR)]

Hello All

Can someone help me with unravelling a bit of confusion I have about the
limma factorial design?

8.7 Factor Designs (Page 47 approx)  in the user guide has three
approaches that are basically equivalent. I am comparing the "sum to
zero" and the "treatment contrast" approaches. In the sum to zero
approach the comparisons are divided by 4 and this is where my
misunderstanding lies.

Just looking at the first gene as an example. I have put the expression
values below to give an idea of the magnitudes. 

With the treatment contrast just extracting the coefficients straight I
get the following (code below):

eb$coef[1,]
#  Intercept          dp         TNF Interaction 
# 4.84942088  0.05031631 -0.36610669  0.15883329

With the sum to zero the comparisons are divided by 4. So one way to
extract the coefficients is below in the code. Using this way (in effect
multiplying by 4) I get the following:

eb$coef[1,]
#         gm          dp         TNF Interaction 
# 18.9249361  -0.2594659   0.5733801   0.1588333

So here is my problem. The grand mean looks 4 times too large but the
interaction matches the interaction from the treatments contrast
approach. So I can have one "looking" right but not both. i.e. To
multiply by 4 or not to multiply by 4, that is the question. How do I
interpret this? What am I missing in my understanding?

Thanks for any help


Regards

John


# Sum to zero code

fit<-lmFit(eset, design)
contrast.matrix<-cbind(gm=c(4,0,0,0), dp=c(0,4,0,0), TNF=c(0,0,4,0),
Interaction=c(0,0,0,4)) 
#contrast.matrix<-cbind(Interaction=c(0,0,-2,-2)) 
fit2<-contrasts.fit(fit, contrast.matrix)
eb<-eBayes(fit2)


# Treatment contrasts code
design<-model.matrix(~dp*TNF) 
fit<-lmFit(eset, design)
contrast.matrix<-cbind(Intercept=c(1, 0, 0, 0), dp=c(0,1,0,0),
TNF=c(0,0,1,0), Interaction=c(0,0,0,1))


# Gene 1 expression level

exprs1<-exprs[1,]
#     4.865401      5.114202      4.719609      4.882969      4.857923 
#     4.807370      4.538509      4.759865      4.779017      4.430844 
#     4.519123      4.499975