[R-sig-ME] Simple explanation of the lme Algorithms?

[Douglas Bates]

On 3/25/07, Andrew Robinson <A.Robinson at ms.unimelb.edu.au> wrote:
> Hi everyone,
>
> I'm trying to figure out how the loops work together in lme().  I
> understand that we start with some EM iterations to get close to the
> optimum, and then switch to Newton-Raphson (eg Pinheiro and Bates
> 2000, p. 80).  However, I can't reconcile that understanding with my
> reading of the lmeControl switches.  There, I see
>
> maxIter: maximum number of iterations for the 'lme' optimization
>           algorithm. Default is 50.
>
> msMaxIter: maximum number of iterations for the 'nlm' optimization
>           step inside the 'lme' optimization. Default is 50.
>
> niterEM: number of iterations for the EM algorithm used to refine the
>           initial estimates of the random effects variance-covariance
>           coefficients. Default is 25.
>
> Clearly, niterEM covers the initial EM portion, and I guess that
> msMaxIter refers to the invocation of nlm, which performs the Newton
> Raphson optimization, but then what role does maxIter play, and what
> is 'lme' optimization

IIRC the maxiter setting is for cases where there is a variance
function or a correlation function in the model specification.
Conditional on parameters for the variance function or the correlation
function or both, the parameters in the mixed-effects specification
are optimized, then the parameters in the variance or correlation
function are updated then ...

> If I've missed the obvious page in P&B 2000, or the obvious paper,
> then I apologize: please let me know!  I tried to find a copy of
>
> Bates, D.M. and Pinheiro, J.C. (1998) "Computational methods for
> multilevel models" available in PostScript or PDF formats at
> http://franz.stat.wisc.edu/pub/NLME/
>
> but franz appears to be down.
>
> Cheers,
>
> Andrew
> --
> Andrew Robinson
> Department of Mathematics and Statistics            Tel: +61-3-8344-9763
> University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
> http://www.ms.unimelb.edu.au/~andrewpr
> http://blogs.mbs.edu/fishing-in-the-bay/
>