generalized linear mixed models - how to compare?

Hello All:

Should I conclude from this discussion that there is no practical
means by which nested generalized mixed models can be compared from
output produced through glmmPQL or GLMM? What is one then to do???

Andrew

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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