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

[Spencer Graves]

No puedo entender.  Nicht versteh. Je ne comprend pas. 

Peter Spreeuwenberg wrote:

>  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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>>    
>>
>
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>Peter Spreeuwenberg
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