Thanks for help in advance!!

My experimental design involves using DESeqs to look at the impact of three diets (diet1, diet2, and diet3) on gene expression at  three sites of animal's gut  (colon, cecum and rectum) .  Each diet was fed to three animals.  All animals were sacrificed at the end of trial and three sections  of the intestine (colon, cecum and rectum) was sampled and gene expression was analyzed.

diet                       animal                   site                        var1                       var2

diet1                      a1                          site1

diet1                      a2                        site1

diet1                      a3                        site1

diet1                      a1                          site2

diet1                      a2                        site2

diet1                      a3                        site2

diet1                      a1                          site3

diet1                      a2                        site3

diet1                      a3                        site3

diet2                    a4                        site1

diet2                    a5                        site1

diet2                    a6                        site1

diet2                    a4                        site2

diet2                    a5                        site2

diet2                    a6                        site2

diet2                    a4                        site3

diet2                    a5                        site3

diet2                    a6                        site3

diet3                    a7                         site1

diet3                    a8                        site1

diet3                    a9                         site1

diet3                    a7                         site2

diet3                    a8                        site2

diet3                    a9                         site2

diet3                    a7                         site3

diet3                    a8                        site3

diet3                    a9                         site3

I tried    " design(dds) <- ~  diet + site:animal + site"

I got the following information

______________

Error in DESeqDataSet(se, design = design, ignoreRank) :

  the model matrix is not full rank, so the model cannot be fit as specified.

  one or more variables or interaction terms in the design formula

  are linear combinations of the others and must be removed

_________________

> sessionInfo()

R version 3.1.3 (2015-03-09)

Platform: x86_64-apple-darwin13.4.0 (64-bit)

Running under: OS X 10.9.5 (Mavericks)

locale:

[1] en_CA.UTF-8/en_CA.UTF-8/en_CA.UTF-8/C/en_CA.UTF-8/en_CA.UTF-8

attached base packages:

 [1] stats4    parallel  grid      splines   stats     graphics  grDevices utils     datasets  methods   base

other attached packages:

 [1] ecodist_1.2.9            Biostrings_2.34.1        doParallel_1.0.8         foreach_1.4.3

 [5] iterators_1.0.7          metagenomeSeq_1.8.3      interactiveDisplay_1.4.1 limma_3.22.7

 [9] Biobase_2.26.0           DESeq2_1.6.3             GenomicRanges_1.18.4     GenomeInfoDb_1.2.5

[13] RcppArmadillo_0.5.000.0  Rcpp_0.12.3              XVector_0.6.0            IRanges_2.0.1

[17] S4Vectors_0.4.0          BiocGenerics_0.12.1      locfit_1.5-9.1           phangorn_2.0.2

[21] genefilter_1.48.1        adephylo_1.1-6           scatterplot3d_0.3-35     analogue_0.16-0

[25] rgl_0.93.1098            princurve_1.1-12         labdsv_1.6-1             mgcv_1.8-6

[29] indicspecies_1.7.5       biom_0.4.0               ggplot2_1.0.1            reshape2_1.4.1

[33] plyr_1.8.3               phyloseq_1.10.0          pamr_1.55                cluster_2.0.1

[37] survival_2.38-1          vegan_2.2-1              lattice_0.20-31          permute_0.8-3

[41] RColorBrewer_1.1-2       matrixStats_0.14.0       MASS_7.3-40              ape_3.4

[45] ade4_1.7-2               nlme_3.1-120

If you want to control for the pairing of animals within each diet, you can do the nesting suggestion from the vignette. Code animal as a1, a2, a3 for all diets (so a4 => a1, etc.). Then use a design of ~ diet:animal.nested + diet + site. Or you can also add an interaction term site:diet on the end of the formula if you want to investigate if the diet differences change across site.

Thanks for your quick reply.  For each animal, there were three sites sampled and tested.  Should I concern about the association among these three sites?