[BioC] F-tests for factorial effects - limma

Gordon K Smyth smyth at wehi.EDU.AU
Wed Dec 22 14:23:02 CET 2004

> Date: Tue, 21 Dec 2004 17:21:19 -0500
> From: Naomi Altman <naomi at stat.psu.edu>
> Subject: [BioC] F-tests for factorial effects - limma
> To: bioconductor at stat.math.ethz.ch
>
> I am analyzing a 2-factor factorial Affy experiment, with 3 d.f. for each
> factor.
>
> I would like to get the F-tests for the main effects and interactions using
> limma.
>
> I have computed all the contrasts, and got the t-tests (both unadjusted and
> eBayes).  I do know how to combine these into F-tests "by hand" but I could
> not figure out if there was a simple way to do this using limma.

limma doesn't have any easy way to deal with main effects and interactions, at least not with main
effects, interactions are actually simpler.  I haven't implemented this because I've never been
able to figure out what one would do with these things in a microarray context.

To compute F-tests for main effects and interaction, the easiest way would probably be to compute
the SS for main effects and interactions by non-limma means, then use shrinkVar() to adjust the
residual mean squares, i.e., the F-statistic denominators.

If you only want F-tests for interactions, the following code would work:

X <- model.matrix(~a*b)
fit <- lmFit(eset, X)
p <- ncol(X)
cont.ia <- diag(p)[,attr(X,"assign")==3]
fit.ia <- eBayes(contrasts.fit(fit, cont.ia))

Now fit.ia contains the F-statistic and p-values for the interaction in fit.ia\$F and
fit.ia\$F.p.value.

> I had a look at FStat (classifyTestsF).  There seems to be a problem, in
> that the matrix tstat is not premultiplied by the contrast matrix when the
> F-statistics are computed.  So, if the contrasts are not full-rank, an
> error is generated (instead of the F-statistics) because nrow(Q) !=
> ncol(tstat)..  (See the lines below).

No, the code is correct.  FStat is quite happy with non full rank contrasts but the contrast
matrix must be applied using contrasts.fit() before entering FStat().  You should not expect to
see a contrast matrix inside the classifyTestsF() code.

Gordon

> if (fstat.only) {
>          fstat <- drop((tstat%*% Q)^2 %*% array(1, c(r, 1)))
>          attr(fstat, "df1") <- r
>          attr(fstat, "df2") <- df
>          return(fstat)
>      }
>
> I figured that before I fiddled with the code, I would check to make sure
> that I didn't miss an existing routine to do this.
>