## Open issues [🇷 for BE/BA]

Hi PharmCat,

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).

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

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.

❝ 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

Pass or fail!

ElMaestro

### Complete thread:

- Semireplicated + REML in R ElMaestro 2020-07-10 13:19 [🇷 for BE/BA]
- Semireplicated + REML in R Helmut 2020-07-10 19:03
- Semireplicated + REML in R ElMaestro 2020-07-10 19:24
- Avoid partial replicate designs, pleeeze! Helmut 2020-07-11 11:57
- Avoid partial replicate designs, pleeeze! ElMaestro 2020-07-11 14:43
- Braveheart! Helmut 2020-07-11 15:38
- Who can help? ElMaestro 2020-07-12 12:28
- Who can help? ElMaestro 2020-07-12 13:26
- Update II ElMaestro 2020-07-12 21:36
- Update III ElMaestro 2020-07-12 21:46

- Final update today ElMaestro 2020-07-12 22:27
- Medium rare. Helmut 2020-07-13 13:52
- took just 52 hrs to do it :-) ElMaestro 2020-07-13 14:18
- Will take much more hours still… Helmut 2020-07-13 15:34

- Negative determinant ElMaestro 2020-07-14 03:22
- Are we loosers? Helmut 2020-07-14 13:58
- "we"? Loosers? ElMaestro 2020-07-14 15:07
- Misunderstanding? Helmut 2020-07-14 15:32

- "we"? Loosers? ElMaestro 2020-07-14 15:07

- Are we loosers? Helmut 2020-07-14 13:58

- took just 52 hrs to do it :-) ElMaestro 2020-07-13 14:18

- Medium rare. Helmut 2020-07-13 13:52

- Braveheart! ElMaestro 2020-07-13 10:13
- Braveheart! Helmut 2020-07-13 14:16
- Braveheart! PharmCat 2020-07-15 14:19
- Braveheart! ElMaestro 2020-08-02 17:39

- Who can help? ElMaestro 2020-07-12 12:28

- Braveheart! Helmut 2020-07-11 15:38

- Avoid partial replicate designs, pleeeze! ElMaestro 2020-07-11 14:43

- Avoid partial replicate designs, pleeeze! Helmut 2020-07-11 11:57

- Semireplicated + REML in R ElMaestro 2020-07-10 19:24
- We were all blind (except Detlew) Helmut 2020-07-15 14:27
- It is the opposite way around for me ElMaestro 2020-07-15 16:25
- Desultory thoughts Helmut 2020-07-15 17:33
- FDA RSABE is ISC d_labes 2020-07-15 18:13
- FDA RSABE is ISC Helmut 2020-07-16 11:11

- Desultory thoughts ElMaestro 2020-07-15 23:06
- Desultory thoughts Helmut 2020-07-16 10:59

- FDA RSABE is ISC d_labes 2020-07-15 18:13

- Desultory thoughts Helmut 2020-07-15 17:33
- Phoenix - which template? mittyri 2020-07-19 00:42
- FDA RSABE Project template_ v1.4.phxproj Helmut 2020-07-19 01:45

- It is the opposite way around for me ElMaestro 2020-07-15 16:25
- "By popular demand": likelihood ElMaestro 2020-07-24 10:07
- And by the way.... ElMaestro 2020-07-24 12:52
- And by the way.... PharmCat 2020-08-03 14:24
- Not understood ElMaestro 2020-08-03 22:55
- Not understood PharmCat 2020-08-05 01:41
- Not understood ElMaestro 2020-08-05 08:13
- Not understood PharmCat 2020-08-05 16:37
- Open issues ElMaestro 2020-08-06 21:11
- Open issues PharmCat 2020-08-07 00:02
- Open issuesElMaestro 2020-08-07 07:49
- Open issues PharmCat 2020-08-07 11:29
- Still can't make it work ElMaestro 2020-08-07 13:08
- Still can't make it work PharmCat 2020-08-07 15:42
- Still can't make it work ElMaestro 2020-08-07 16:44
- Still can't make it work PharmCat 2020-08-07 18:14
- Still can't make it work ElMaestro 2020-08-07 18:23
- And now it works ElMaestro 2020-08-07 21:31
- Still can't make it work PharmCat 2020-08-08 01:08
- Speed improvement ElMaestro 2020-08-08 12:25
- Speed improvement PharmCat 2020-08-08 17:27
- Speed improvement ElMaestro 2020-08-08 18:10
- Speed improvement PharmCat 2020-08-09 18:22
- Some tests... PharmCat 2020-08-10 11:48

- Speed improvement ElMaestro 2020-08-08 12:25

- Still can't make it work ElMaestro 2020-08-07 18:23

- Still can't make it work PharmCat 2020-08-07 18:14

- Still can't make it work ElMaestro 2020-08-07 16:44

- Still can't make it work PharmCat 2020-08-07 15:42

- Still can't make it work ElMaestro 2020-08-07 13:08

- Open issues PharmCat 2020-08-07 11:29

- Open issuesElMaestro 2020-08-07 07:49

- Open issues PharmCat 2020-08-07 00:02

- Open issues ElMaestro 2020-08-06 21:11

- Not understood PharmCat 2020-08-05 16:37

- Not understood ElMaestro 2020-08-05 08:13

- Not understood PharmCat 2020-08-05 01:41

- Not understood ElMaestro 2020-08-03 22:55

- And by the way.... PharmCat 2020-08-03 14:24

- And by the way.... ElMaestro 2020-07-24 12:52

- Semireplicated + REML in R Helmut 2020-07-10 19:03