[BioC] duplicateCorrelation and design matrix

[Carolyn Fitzsimmons]

Hi Gordon, thanks for your reply. I have a few more questions:

Quoting Gordon K Smyth <smyth at wehi.EDU.AU>:

> > Date: Thu, 30 Jun 2005 11:44:02 +0000
> > From: Carolyn Fitzsimmons <Carolyn.Fitzsimmons at imbim.uu.se>
> > Subject: [BioC] duplicateCorrelation and design matrix
> > To: Bioconductor list <bioconductor at stat.math.ethz.ch>
> >
> > Hello,
> >
> > I need an explanation of how the design matrix influences the consensus
> > correlation of the duplicateCorrelation function when accounting for
> technical
> > replicates.  Here is my specific example:
> >
> > Design matrix:
> >> design
> >    RJf RJm WLf WLm
> > 1    0   0   0   1
> > 2    0   0   0   1
> > 3    0   0   0   1
> > 4    0   0   0   1
> > 5    0   0   0   1
> > 6    0   0   0   1
> > 7    0   0   0   1
> > 8    0   0   0   1
> > 9    0   0   1   0
> > 10   0   0   1   0
> > 11   0   0   1   0
> > 12   0   0   1   0
> > 13   0   0   1   0
> > 14   0   0   1   0
> > 15   0   0   1   0
> > 16   0   0   1   0
> > 17   0   1   0   0
> > 18   0   1   0   0
> > 19   0   1   0   0
> > 20   0   1   0   0
> > 21   0   1   0   0
> > 22   0   1   0   0
> > 23   0   1   0   0
> > 24   0   1   0   0
> > 25   1   0   0   0
> > 26   1   0   0   0
> > 27   1   0   0   0
> > 28   1   0   0   0
> > 29   1   0   0   0
> > 30   1   0   0   0
> > 31   1   0   0   0
> > 32   1   0   0   0
> > #
> > each second slide is a replicate of the first (eg. 1 and 2 are replicates,
> then
> > 3 and 4,... etc.).  There are also 4 groups that I want to compare, with 4
> > individuals in each group (each duplicated).  So I continue with the
> > duplicateCorrelation:
> > #
> >> cor <- duplicateCorrelation(Mmatrix_ny, design=design,
> > +
> >
>
block=c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16))
> >> cor$cor
> > [1] -0.03060575
> > #
> > which is a pretty bad correlation so I probably should just use the
> technical
> > replicates as biological replicates (the limma user guide says).  But in
> > another comparison I want to put all the arrays in 2 groups, see design
> > matrix:
> >> designWLRJ
> >    RJ WL
> > 1   0  1
> > 2   0  1
> > 3   0  1
> > 4   0  1
> > 5   0  1
> > 6   0  1
> > 7   0  1
> > 8   0  1
> > 9   0  1
> > 10  0  1
> > 11  0  1
> > 12  0  1
> > 13  0  1
> > 14  0  1
> > 15  0  1
> > 16  0  1
> > 17  1  0
> > 18  1  0
> > 19  1  0
> > 20  1  0
> > 21  1  0
> > 22  1  0
> > 23  1  0
> > 24  1  0
> > 25  1  0
> > 26  1  0
> > 27  1  0
> > 28  1  0
> > 29  1  0
> > 30  1  0
> > 31  1  0
> > 32  1  0
> > #
> > and then do the duplicateCorrelation function and get a different
> correlation.
> > #
> >> corWLRJ <- duplicateCorrelation (Mmatrix_ny, design=designWLRJ,
> > +
> >
>
block=c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16))
> >> corWLRJ$cor
> > [1] 0.01745252
> > #
> > Moreover when I compute the consensus correlation without using a design
> matrix
> > I get 0.1073055.  I know from looking through previous posts and a lot of
> help
> > from Johan L. that the way the blocking is set up and using the design
> matrix
> > in these situations is correct.
> 
> You've used three different non-equivalent design matrices.  No more than one
> of these can be
> correct.

But if I need to group the individuals differently to test for differential
expression between different groupings of individuals (i.e. between
WLm/WLf/RJm/RJf and WL/RJ), the use of 2 different design matrixies in the
dupCorrelation function is warrented, yes?

> 
> > So how is the consensus correlation actually
> > being calculated in the above situations? (in loose mathamatical terms if
> > possible, as you can probably tell from my question).
> 
> In loose terms the correlation measures the variability between blocks
> relative to the variation
> within blocks.  Over-simplifying the design matrix will increase the
> between-blocks variation,
> because it will now reflect differences between your treatments as well as
> differences between
> biological replicates.  Hence the estimated correlation increases.
> 

Okay. Now I believe I understand how it is calculated. When you use a design
matrix here you create blocks, then the blocking argument creates blocks within
blocks. (Correct me if this is wrong).

Best Regards,  Carolyn