Bioequivalence and Bioavailability Forum

Dear d_labes,

❝ My Power Beast told me (...)

❝ Seems the R matrix is sorted by R1, R2, T1, T2.

Thanks for all this.
I think I understand the R's, but I would like your help understanding how the G's from SAS can be read.

The reason why I am somewhat bewildered is as follows:
If you have say m observations on n subjects and subject is the only random effect*, then I would expect the Z matrix to have exactly m rows and n columns; can be parameterised by one column for per subject, i.e. no intercept, or can be specified with an intercept and same total number of cols. Same thing, just different parameterisation.
(I find it easier to grasp the former, where one column corresponds to one subject and hence no intercept).
Now, for ZGZ^t we know that "Multiplying an m×n matrix with an n×p matrix results in an m×p matrix", so as our Z is m×n, G must be n×n, Z^t is n×m and law an order is restored in V being m×m.
Am I mistaking something here?
If not, then G in your above post was 2×2, so obviously SAS expects the user to be able to figure out the rest. For matrix R, SAS spat out just a block, so the entire R can be constructed by just extending that diagonal down all subjects, but for G I am not sure how to expand the thing so that ZGZ^t comes into existence. Can you tell?

Is there a way you can ask the power to spit out V too for these models?

I have previous to this post looked at various webpages dealing with definitions of R and G's because getVarCov in the R software also spits out G in this odd fashion. The good places to start are in my opinion here and here. I also have the book by Pinheiro and Bates. unfortunately, in order to understand anything in that book you need an IQ of at least 200 and it does not cover this aspect at all.


Best regards
EM.

*: More random effects = ultimately more columns in Z.