GLMM (lme4) vs. glmmPQL output
Although it has not been stated nor credited, this is very close to an example in MASS4 (there seems a difference in coding). Both the dataset and much of the alternative analyses are from the work of my student James McBroom (and other students have contributed). MASS4 does contain comparisons with other methods, including our implementation of the `gold standards', numerical ML and Bayes posterior densities with a vague prior. We have also run this example against several other implementations and simulated from the fitted (by numerical ML) model. All of our comparisons have suggested that glmmPQL is in the right ball park, so once I realised the origin of the example the GLMM results surprised me.
On Mon, 12 Jan 2004, Dieter Menne wrote:
Goran, from my reply to a message from Douglas Bates; ">" is quoted from a mail by DG.
I believe the distinction is explained in the lme4 documentation but, in any case, the standard errors and the approximate log-likelihood for glmmPQL are from the lme model that is the last step in the optimization. The corresponding quantities from GLMM are from another approximation that should be more reliable.
I have compared glmmPQL, glmmML, geese and GLMM, results and code see below. I am aware that glmmPQL uses another method to handle the problem, and geese (geepack) has considerable different assumptions, but the results are very similar. On the other hand, I had expected that glmmML results, if reasonable at all, should be close to GLMM. Yet they are not, but rather come close to the other three.
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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