[BioC] something wrong with my design matrix in edgeR

[Wang, Li]

Dear List members

My targets include 31 samples representing  two groups (south and north) and also four populations (FBK, NWL, SOU, CAR). 

> targets <- read.delim(file = "Targets.txt", stringsAsFactors = FALSE)
> targets
       files group pop
1  FBK01.txt     N FBK
2  FBK04.txt     N FBK
3  FBK05.txt     N FBK
4  FBK08.txt     N FBK
5  FBK09.txt     N FBK
6  FBK10.txt     N FBK
7  FBK13.txt     N FBK
8  NWL02.txt     N NWL
9  NWL04.txt     N NWL
10 NWL06.txt     N NWL
11 NWL08.txt     N NWL
12 NWL09.txt     N NWL
13 NWL10.txt     N NWL
14 NWL11.txt     N NWL
15 NWL14.txt     N NWL
16 SOU01.txt     S SOU
17 SOU02.txt     S SOU
18 SOU03.txt     S SOU
19 SOU04.txt     S SOU
20 SOU07.txt     S SOU
21 SOU09.txt     S SOU
22 SOU11.txt     S SOU
23 SOU15.txt     S SOU
24 CAR01.txt     S CAR
25 CAR02.txt     S CAR
26 CAR03.txt     S CAR
27 CAR04.txt     S CAR
28 CAR05.txt     S CAR
29 CAR11.txt     S CAR
30 CAR12.txt     S CAR
31 CAR14.txt     S CAR

We are interested with the differential expression between north and south group by adjusting for differences between populations. 

> latitude <- factor(targets$group)
> latitude <- relevel(latitude, ref="N")
> pop <- factor(targets$pop)
> design <- model.matrix(~pop+latitude)
> rownames(design) <- rownames(d$samples)
> design
   (Intercept) popFBK popNWL popSOU latitudeS
1            1      1      0      0         0
2            1      1      0      0         0
3            1      1      0      0         0
4            1      1      0      0         0
5            1      1      0      0         0
6            1      1      0      0         0
7            1      1      0      0         0
8            1      0      1      0         0
9            1      0      1      0         0
10           1      0      1      0         0
11           1      0      1      0         0
12           1      0      1      0         0
13           1      0      1      0         0
14           1      0      1      0         0
15           1      0      1      0         0
16           1      0      0      1         1
17           1      0      0      1         1
18           1      0      0      1         1
19           1      0      0      1         1
20           1      0      0      1         1
21           1      0      0      1         1
22           1      0      0      1         1
23           1      0      0      1         1
24           1      0      0      0         1
25           1      0      0      0         1
26           1      0      0      0         1
27           1      0      0      0         1
28           1      0      0      0         1
29           1      0      0      0         1
30           1      0      0      0         1
31           1      0      0      0         1
attr(,"assign")
[1] 0 1 1 1 2
attr(,"contrasts")
attr(,"contrasts")$pop
[1] "contr.treatment"

attr(,"contrasts")$latitude
[1] "contr.treatment"

I am wondering maybe there is something wrong with my design matrix. So, when I tried to estimate the dispersions, I got the following errors. 

> d <- estimateGLMCommonDisp(d, design)
Error in solve.default(R, t(beta)) : 
  system is computationally singular: reciprocal condition number = 5.16368e-17

The following is session information. Any comments are very appreciated.

> sessionInfo()
R version 2.15.0 (2012-03-30)
Platform: x86_64-unknown-linux-gnu (64-bit)

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=C                 LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] qvalue_1.30.0 edgeR_2.6.0   limma_3.12.0 

loaded via a namespace (and not attached):
[1] tcltk_2.15.0 tools_2.15.0

Thanks in advance!

Best wishes
Li