Inner workings of REML [General Sta­tis­tics]

posted by ElMaestro  – Belgium?, 2019-10-31 19:48 (335 d 06:47 ago) – Posting: # 20740
Views: 2,445

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?

I could be wrong, but...

Best regards,
ElMaestro

R's base package has 274 reserved words and operators, along with 1761 functions. I can use 18 of them (about 14 of them properly). I believe this makes me the Donald Trump of programming.

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