Bioequivalence and Bioavailability Forum

Dear all,

based on this previous thread I'd like to start a discussion about V matrices in mixed models.

There seems to be some principles about those matrices that I don't understand .
In particular, please see this post where I laid out my immature understanding of V matrices. d_labes has been fighting a tough game here to make me understand and I still don't. I thought I would continue the discussion in a new thread as it goes off the original thread's topic. It all evolves around the fact that people seem to operate with V's where the s_WR's and s_WT's are present only on the diagonal of V. Elmaestro no get it.
So to get towards an understanding my issues are:

1. I don't understand why the sigma that goes into the V where a treatment is replicated within a patient (VT and VR in my previous post) is not a within-sigma but a between-sigma. I have searched the internet a lot and there are webpages out there that discuss covariances matrices but I have not found one that addresses this in a way that eases my understanding.

2. Let's take the case of a 3-per, 3-seq, 2-trt study. What do you think the V matrix should look like? Assuming the first patient is RTR I -having a walnut-sized brain- want it to be something like this for the first 3x3:
V0+VR 0 VR
0 V0 0
VR 0 v0+VR
where I would call the VR's withins. Of course, given a good answer to the previous quesiton this may change into betweens. But I'd like to know why.

3. In relation to question 2, I'd like to hear your opinions of which sigma goes into the diagonal where the treatment is T for a 3-seq, 3-per, 2-trt study. If you say s_WT which to me is incomprehensible then please provide a statistical basis for it (We put a s_WT in there because we have to write something and then we overfit the model... that's not a real explanation ).
Can we at least agree that whatever it is, it isn't a zero?


I am afraid in this case it isn't enough to throw references at me.
Many thanks for any input you can provide.