[BioC] question: fit2$F.p.value

[Gordon Smyth]

Hi James,

Thanks for handingly this query. In the limma documentation, the term 
"coefficient" is consistently used to refer to the coefficients 
multiplying the columns of the design matrix, whereas "contrast" is 
consistently used to refer to the columns specified by 
contrasts.fit(). In other words, the coefficients are the columns in 
the lmFit() fit while the contrasts are the columns given to 
eBayes(). When the documentation says that the F-test corresponds to 
"all contrasts", it means all the contrasts in the above sense. In 
other words, the F-test always corresponds to the columns in the same 
fitted model object. It is an overall test statistic computed from 
the set of t-statistics in the same object. This has to be so, 
because there is no other way in limma to extract F-tests for 
particular subjects of contrasts.

If someone as familiar with limma as you found this unclear, then it 
must be unclear, so I've revised the help for ?eBayes to try to make 
it more transparent. The description of the output component F now reads

"numeric vector of moderated F-statistics for testing all contrasts 
defined by the columns of \code{fit} simultaneously equal to zero"

The details section says

"The empirical Bayes moderated t-statistics test each individual 
contrast equal to zero. The moderated F-statistics test whether all 
the contrasts are zero for each probe (row). For each probe, the 
F-statistic is an overall test computed from the set of t-statistics 
for that probe. This is exactly analogous the relationship between 
t-tests and F-statistics in conventional anova, except that the 
residual mean squares and residual degrees of freedom have been 
moderated between probes."

Best wishes
Gordon

>Date: Wed, 09 Aug 2006 15:49:37 -0400
>From: "James W. MacDonald" <jmacdon at med.umich.edu>
>Subject: Re: [BioC] question: fit2$F.p.value
>To: "Mistretta, Toni-Ann" <toniannm at bcm.tmc.edu>
>Cc: bioconductor at stat.math.ethz.ch
>Message-ID: <44DA3C51.7030407 at med.umich.edu>
>Content-Type: text/plain;  charset="utf-8";  format=flowed
>
>Hi Scott,
>
>Mistretta, Toni-Ann wrote:
> >
> >
> > Hello,
> >
> >
> > I have fit a group means parameterization to my three samples: A, B,
> > C (fit1).  I used contrasts.fit to fit my contrasts of interest: B-A,
> > and C-A (fit2).  My question: does fit2$F.p.value apply to the
> > differences between the three samples A, B, and C (similar to a
> > one-way ANOVA) or does it apply to the differences between the two
> > contrasts B-A and C-A?  I really need someone to clarify this point
> > for me before I go on and select differentially expressed genes.  In
> > my case treatments B and C are very similar so this point is almost
> > mute.  However, I will be analyzing data sets in the future where
> > treatments B and C are very different making my question very
> > important.
>
>Well, I was working under the assumption that the F-statistic was the
>'usual' F-stat (MSR/MSE), but apparently I was mistaken. The help page
>for the MArrayLM class states:
>
>'F.stat': 'numeric' vector giving moderated F-statistics for
>            testing all contrasts equal to zero
>
>'F.p.value': 'numeric' vector giving p-value corresponding to
>            'F.stat'
>
>That's not perfectly clear (all contrasts could be 'all possible
>contrasts', yes?). So a test:
>
>  > library(fibroEset)
>  > data(fibroEset)
>  > library(limma)
>  > design <- model.matrix(~0+pData(fibroEset)[,2])
>  > contrast <- matrix(c(-1,1,0))
>  > fit <- lmFit(log2(exprs(fibroEset)), design)
>  > fit2 <- contrasts.fit(fit, contrast)
>  > fit2 <- eBayes(fit2)
>  > contrast <- matrix(c(-1,1,0,-1,0,1,0,-1,1), nc=3)
>  > fit3 <- contrasts.fit(fit, contrast)
>  > fit3 <- eBayes(fit3)
>  > cbind(fit2$F,fit3$F)[1:10,]
>                [,1]       [,2]
>   [1,] 15.118961041  7.7401961
>   [2,] 11.105009661 19.8022284
>   [3,]  0.007904608  1.4477756
>   [4,]  1.748568559  1.3576871
>   [5,]  0.187640831  4.1238891
>   [6,]  1.633728790  0.8174006
>   [7,]  2.116625209  1.7426943
>   [8,]  0.208801377  0.5223336
>   [9,]  9.813763553 10.9888647
>[10,]  0.010995645  0.8344381
>
>Looks like 'all contrasts' means 'all specified contrasts'.
>
>HTH,
>
>Jim
>
>
>
> >
> > Scott Ochsner Baylor College of Medicine One Baylor Plaza Houston,
> > TX. 77030
> >
> >
> > thanks,
> >
> > S
> >
> >
> > Sent for S. Ochsner by TAM
> >
> > [[alternative HTML version deleted]]
> >
> > _______________________________________________ Bioconductor mailing
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>
>
>--
>James W. MacDonald, M.S.
>Biostatistician
>Affymetrix and cDNA Microarray Core
>University of Michigan Cancer Center
>1500 E. Medical Center Drive
>7410 CCGC
>Ann Arbor MI 48109
>734-647-5623