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, [EMAIL PROTECTED] 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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