## Open issues [🇷 for BE/BA]

Hi PharmCat,

❝ And if look generally - it really doesn't matter because -(N-p)*log(2π)/2 is a constant and it can be excluded from optimization. If you want find AIC ets - this will matter.

I am afraid you missed my point. The issue is not related to constants. As you say they are not of importance to find the maximum, which will just be vertically displaced.

Xi is the design matrix for fixed effects for the i'th subject.
Thus is has a rank of max 3 and never more. This means we can at most use it to work with three parameter estimates. For example an intercept, a treatment effect, a period effect (within any given subject).

Thus we cannot use Xi -if i is a single subject- during the optimization for the RTR/TRR/RRT design. Applying Gurkas equations will not work and I am looking for a way to work on derived versions of X (like for a few subjects at a time?) so that X retains in rank of 6 (in this design).

❝ So if you want find only θ, you can minimize REML without constants at all. And add constants when you need to have real value of REML or AIC, BIC, ets.

Don't worry, the constants are of no importance to find the variance components.

❝ Example N=3, n=9, p=6

These examples of X are possibly not very illustrative; as you can see column 2+3 add up to column 1, the intercept, column 4+5+6 add up to that as well, and so forth. X is column-wise not full rank.

Pass or fail!
ElMaestro