[R] generalized linear mixed models - how to compare?

[Peter Spreeuwenberg]

  Liset

 Dat moet lukken en hoe sneller je het anlevert hoe eerder je resultaten terug ziet.
Dus, Ik wacht af.


groet Peter S



Date sent:      	Sun, 17 Apr 2005 18:07:28 +0100 (BST)
From:           	Prof Brian Ripley <ripley at stats.ox.ac.uk>
To:             	Deepayan Sarkar <deepayan at stat.wisc.edu>
Subject:        	Re: [R] generalized linear mixed models - how to compare?
Copies to:      	r-help at stat.math.ethz.ch,
	Nestor Fernandez <nestor.fernandez at ufz.de>

> On Sun, 17 Apr 2005, Deepayan Sarkar wrote:
> 
> > On Sunday 17 April 2005 08:39, Nestor Fernandez wrote:
> 
> >> I want to evaluate several generalized linear mixed models, including
> >> the null model, and select the best approximating one. I have tried
> >> glmmPQL (MASS library) and GLMM (lme4) to fit the models. Both result
> >> in similar parameter estimates but fairly different likelihood
> >> estimates.
> >> My questions:
> >> 1- Is it correct to calculate AIC for comparing my models, given that
> >> they use quasi-likelihood estimates? If not, how can I compare them?
> >> 2- Why the large differences in likelihood estimates between the two
> >> procedures?
> >
> > The likelihood reported by glmmPQL is wrong, as it's the likelihood of
> > an incorrect model (namely, an lme model that approximates the correct
> > glmm model).
> 
> Actually glmmPQL does not report a likelihood.  It returns an object of 
> class "lme", but you need to refer to the reference for how to interpret 
> that.  It *is* support software for a book.
> 
> > GLMM uses (mostly) the same procedure to get parameter estimates, but as 
> > a final step calculates the likelihood for the correct model for those 
> > estimates (so the likelihood reported by it should be fairly reliable).
> 
> Well, perhaps but I need more convincing.  The likelihood involves many 
> high-dimensional non-analytic integrations, so I do not see how GLMM can 
> do those integrals -- it might approximate them, but that would not be 
> `calculates the likelihood for the correct model'.  It would be helpful to 
> have a clarification of this claim.  (Our experiments show that finding an 
> accurate value of the log-likelihood is difficult and many available 
> pieces of software differ in their values by large amounts.)
> 
> Further, since neither procedure does ML fitting, this is not a maximized 
> likelihood as required to calculate an AIC value.  And even if it were, 
> you need to be careful as often one GLMM is a boundary value for another, 
> in which case the theory behind AIC needs adjustment.
> 
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
> 
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