I am a bit confused on how to use normalizationFactors in DESeq2.

In the manual it says that "Normalization factors should include library size normalization".

Does that mean that I should divide each column of the normalization matrix by the 

corresponding sizeFactor, or it will be done automatically?

Additionally, should I use the size of the feature for normalization, or it's inverse:

i.e. if I want to compare reads that fall withing 5'UTRs and 3'UTRs of the same gene, I have

to normalize by the feature length, should I use width(5'UTR), width(3'UTR) or 1/width(5'UTR), 1/width(3'UTR)

Best,

Vedran 

"Does that mean that I should divide each column of the normalization matrix by the corresponding sizeFactor, or it will be done automatically?"

It is not done automatically by normalizationFactors(dds)<-, but see the normMatrix argument of estimateSizeFactors(). This will correct for library size given a matrix of normalization factors which do not yet correct for library size. Note that the rows of normMatrix should be roughly centered on 1 (you can accomplish this by dividing out the geometric mean for each row).

"should I use the size of the feature for normalization, or it's inverse"

It helps to go to the formula in the paper. We have:

K ~ NB(mu_ij, alpha_i)

mu_ij = s_ij q_ij 

where q_ij is the quantity we are interested in, and s_ij is the normalization factor. So we want s_ij to help remove changes in the expected value of K due to technical factors, e.g. library size or differences in feature length across samples. So s_ij should be correlated with feature length.

Can you explain more what you are trying to do?