[BioC] limma: percent of variance explained

[Gordon K Smyth]

> Date: Wed, 21 May 2014 16:26:39 +0200
> From: Julien Roux <julien.roux at unil.ch>
> To: bioconductor at r-project.org
> Subject: [BioC] limma: percent of variance explained
>
> Dear all,
> I am analyzing an RNA-seq experiment with voom+limma.
> The design of the experiment had two fixed effect factors that I
> combined into one vector including all combinations of the levels of the
> 2 factors (as explained in the limma user guide, section 9.5), and a
> random effect that I model using the block and correlation arguments in
> lmFit.
> I am wondering if it would be possible to estimate, for each gene, what
> is the proportion of variance explained by each factor from the lmFit
> result?

Yes, but you have to determine in which order the factors are to be added 
to the model.  There are three terms: 1. First factor added, 2. Second 
factor adjusted for first, 3. Interaction adjusted for main effects.

Note that the proportion of variance explained is just a descriptive 
measure that is associated with any regression model.  It is not something 
that is "estimated", it is just an observed number.  You can't do any 
inference with it.  Also it doesn't take account of any empirical Bayes 
considerations.

> Is it possible to get ANOVA-like tables for all genes?

Yes, again you have to determine the order the factors are to be added.

I don't recommend anova-like tables.  The values for the main effects are 
pretty meaningless in the presence of an significant interaction.

> Is it also possible to get the proportion of variance explained by the 
> random effect factor?

No it isn't. The concept is undefined for random effects and REML.

Gordon

> I have seen this kind of analysis performed in published studies (e.g.,
> Figure 3c in t Hoen PA et al. 2013 Nat Biotechnol
> http://www.ncbi.nlm.nih.gov/pubmed/24037425), but the details are
> missing in the Materials & Methods.
> Thanks a lot for your help
> Julien
>
> -- 
> Julien Roux, PhD
> Gilad lab, Department of Human Genetics, University of Chicago
> http://giladlab.uchicago.edu/
> 920 East 58th Street, CLSC 317, Chicago, IL 60637, USA
> tel: +1-773-834-1984   fax: +1-773-834-8470

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