# [BioC] duplicateCorrelation and design matrix

Carolyn Fitzsimmons Carolyn.Fitzsimmons at imbim.uu.se
Thu Jun 30 13:44:02 CEST 2005

```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. 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).

Thanks a lot for your time,  Carolyn

--
Carolyn Fitzsimmons
Dept. Medical Biochemistry and Microbiology
Uppsala University
Box 597/BMC
SE-751 24
SWEDEN

E-mail: Carolyn.Fitzsimmons at imbim.uu.se
Tel: +46 (0)18 471 4593
Mobile: +46 (0)73 704 1248

```