## Inner workings of REML [General Statistics]

Hi Jaimik,

» The change in the value of test product results in the change in LSM value in reference product!!

I think, without being absolutely certain....:

When a mixed model is fitted with ML, you have a straightforward way of estimating the fixed effects. You need only to iteratively estimate the variance components, and the fixed effects are simply estimated the same fashion as in a linear (non-mixed) model - deterministically.

When a model is fitted using REML, which is what happens when you do studies for FDA, then the likelihood depends both on the variance components and on the model effects, but what's worse, the model effects depend on the variance components, so you are not only iterating across the sigmas to find the likelihood optimum, but also need to optimise within the vector of fixed effects. So you can start out with estimates of both the variance components and the fixed effects. Then you first optimise the variance components "a little". Then you optimise the fixed effects "a little". And then you repeat the cycle. That is a safe way of arriving at the optimised REML solution, but I will not in any way say it is the only or the best - I simply do not know enough about matrix likelihood to state anything in this regard.

I imagine that you might not see this phenomenon if you pick ML in your mixmo (which is not what FDA want) in stead of REML. Can you try and test it?

» The change in the value of test product results in the change in LSM value in reference product!!

I think, without being absolutely certain....:

When a mixed model is fitted with ML, you have a straightforward way of estimating the fixed effects. You need only to iteratively estimate the variance components, and the fixed effects are simply estimated the same fashion as in a linear (non-mixed) model - deterministically.

When a model is fitted using REML, which is what happens when you do studies for FDA, then the likelihood depends both on the variance components and on the model effects, but what's worse, the model effects depend on the variance components, so you are not only iterating across the sigmas to find the likelihood optimum, but also need to optimise within the vector of fixed effects. So you can start out with estimates of both the variance components and the fixed effects. Then you first optimise the variance components "a little". Then you optimise the fixed effects "a little". And then you repeat the cycle. That is a safe way of arriving at the optimised REML solution, but I will not in any way say it is the only or the best - I simply do not know enough about matrix likelihood to state anything in this regard.

I imagine that you might not see this phenomenon if you pick ML in your mixmo (which is not what FDA want) in stead of REML. Can you try and test it?

—

I could be wrong, but...

Best regards,

ElMaestro

"Pass or fail" (D. Potvin et al., 2008)

I could be wrong, but...

Best regards,

ElMaestro

"Pass or fail" (D. Potvin et al., 2008)

### Complete thread:

- Least square mean calculation for the fully replicate design Jaimik Patel 2019-10-31 11:19
- Very, very strange! Helmut 2019-10-31 14:36
- Very, very strange! Shuanghe 2019-10-31 19:43
- Very, very strange! Helmut 2019-10-31 19:50

- Very, very strange! Jaimik Patel 2019-11-02 12:26
- G matrix mittyri 2019-11-03 01:38

- Very, very strange! Shuanghe 2019-10-31 19:43
- Inner workings of REMLElMaestro 2019-10-31 19:48
- Even in ANOVA… Helmut 2019-10-31 19:53
- Even in 2x2... zizou 2019-11-01 21:05
- trying to understand emmeans mittyri 2019-11-02 02:26

- Even in 2x2... zizou 2019-11-01 21:05

- Even in ANOVA… Helmut 2019-10-31 19:53
- Least square mean calculation for the fully replicate design PharmCat 2019-11-03 00:46

- Very, very strange! Helmut 2019-10-31 14:36