[R-sig-ME] optimizers for mixed models

[Ross Boylan]

lme4 appears to use Nelder Mead for the final stage of its 
optimization.  The archives show various concerns about stability, but 
it looks as if even the prior optimizer was in the simplex class.

This surprised me, since I have found Nelder Mead to be relatively slow 
and imprecise, and in a more complex mixed model with sampling I've been 
using optim with L-BFGS-B, which is quasi-newton.  One of the parameter 
estimates kept creeping up over iterations; the bounds were necessary to 
cut it off.

If anyone can give me more insight into why Nelder Mead is in use, and 
perhaps whether I should be using it myself, I'd appreciate it.

The current behavior, in which about 10% of the simulated datasets have 
convergence problems, with one of the parameters heading toward an 
implausible value (a correlation of 1.0, where atanh(rho) is the actual 
parameter being estimated) is certainly not ideal.  I tried simulated 
annealing to see if the algorithm had wandered mistakenly toward a local 
rather than global optimum; there was no evidence that it had (the SA 
ended up in the same neighborhood as BFGS, and when that point was the 
starting value for BFGS it ended on essentially the same point as before).

Ross Boylan