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

[Andrew Robinson]

On Sun, Mar 25, 2007 at 12:31:12PM -0500, Douglas Bates wrote:
> 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 ...

Thanks for your response, Doug.  So, if I may paraphrase, does maxIter
refer to the maximum number of Newton-Raphson steps allowed for the
updating (by which I guess that you mean estimation) of the parameters
in the variance or correlation function, having conditioned on the
other fixed and random effects?  If my interpretation is correct then
I'm afraid that I'm still confused.  For example, if I compare the
output of 

> fm1 <- lme(distance ~ age, data = Orthodont, random=~1|Subject, 
+ control=list(msVerbose=TRUE))
  0      320.256: -0.390137
  1      320.256: -0.390137

with 

> fm1 <- lme(distance ~ age, random=~1|Subject, data = Orthodont,
+ weights=varPower(), control=list(msVerbose=TRUE))
  0      320.256: -0.390137  0.00000
  1      320.254: -0.390137 0.00377348
  2      320.251: -0.402940 0.00405120
  3      320.109: -0.793763 0.127338
  4      319.381: -4.39127  1.26259
  5      319.359: -5.08632  1.48580
  6      319.359: -5.08547  1.48633
  7      319.359: -5.08607  1.48651
  0      319.985: -5.08607  1.48651
  1      319.984: -5.08517  1.48796
  2      319.984: -5.07930  1.48451
  3      319.966: -4.93970  1.43987
  4      319.874: -3.63622  1.02756
  5      319.872: -3.44497 0.967633
  6      319.872: -3.44235 0.966866
  7      319.872: -3.44233 0.966860
  0      319.721: -3.44233 0.966860
  1      319.721: -3.44261 0.966623
... etc


then I see that there are indeed an inner and outer loop with the
addition of the variance function, but both parameters appear to be
continuously updating.  So I guess that my interpretation is
incorrect.  Can you please help me clarify?

Andrew

 
> >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/
> >

-- 
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/