Hi there,

I have a question on whether some of the contrasts I am making in a
multifactorial experiment should actually be made. I don't have a strong
grasp of GLMs, so I might be missing something conceptually, and am hoping
someone can advise.

I am basically looking for genes that are differentially expressed in a
certain phenotypic state (e.g. fluffy vs. smooth), but have set it up with
2 time-points (Day 2 and Day 5). I have trouble setting up the design using
an equation (columns seem to disappear) so have gone ahead and created the
design matrix using the method in 3.3.1 of the manual (pasting factors
together). The design looks like this (I have removed replicates and many
samples to simplify):

   Day2.Fluffy Day2.Smooth Day5.Fluffy Day5.Smooth
1            0           1           0           0
7            1           0           0           0
13           0           0           0           1
16           0           0           1           0
19           0           0           0           1
35           0           0           1           0
36           0           0           1           0

>From what I understand, the above design is set up for 2 main effects
(phenotype and time), and if I reduce it to 1 main effect (phenotype), I
get the design below.

   Fluffy Smooth
1       0      1
7       1      0
13      0      1
16      1      0
19      0      1
35      1      0
36      1      0

The contrast I make in the latter case is basically (Fluffy - Smooth). The
contrast that I did for the former case, and this is what I'm unsure of, is
((Day2.Fluffy - Day2.Smooth) + (Day5.Fluffy - Day5.Smooth)). These tests
are definitely not equivalent, and I get different number of sig. DE genes
for both (more for the 2 effect design). In my mind, it makes sense,
because the experiment *is *set up with 2 effects, and accounting for the
biological variation in your model should allow you to be more powered to
detect DE genes. However, I've never seen a contrast like that before. Does
it even make sense to have an addition sign in the equation? What does that
actually mean? Should I instead make contrasts of (Day2.Fluffy -
Day2.Smooth) and (Day5.Fluffy - Day5.Smooth) and get the union or intersect
of them?

Hope someone can help on this, and thanks in advance!

Regards,
Zhihao
Graduate Student
University of Washington

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