[R-sig-ME] single argument anova for GLMMs not yet implemented

[Murray Jorgensen]

The following is how I think about this at the moment:

The quasi-likelihood approach is an attempt at a model-free approach to 
the problem of overdispersion in non-Gaussian regression situations 
where standard distributional assumptions fail to provide the observed 
mean-variance relationship.

The glmm approach, on the other hand, does not abandon models and 
likelihood but seeks to account for the observed mean-variance 
relationship by adding unobserved latent variables (random effects) to 
the model.

Seeking to combine the two approaches by using both quasilikelihood 
*and* random effects would seem to be asking for trouble as being able 
to use two tools on one problem would give a lot of flexibility to the 
parameter estimation; probably leading to a very flat quasilikelihood 
surface and ill-determined optima.

But all of the above is only thoughts without the benefit of either 
serious attempts at fitting real data or doing serious theory so I will 
defer to anyone who has done either!

Philosophically, at least, there seems to be clash between the two 
approaches and I doubt that attempts to combine them will be successful.

Murray Jorgensen


Douglas Bates wrote:
> On Wed, Dec 10, 2008 at 9:56 AM, Ben Bolker <bolker at ufl.edu> wrote:
>> R.S. Cotter wrote:
>>> Dear all,
>>>
>>> Sorry if the question i stupid, I'm pretty new to this and have
>>> googled, and tried the help in R without finding a answer.
>>>
>>> I have sucsessfully used glmm, lmer {lme4}, family binomial. By using
>>> the summary (mod), I get the parameter estimates, but when using anova
>>> (mod) I get this error message: Error in anova(mod) :  single argument
>>> anova for GLMMs not yet implemented.
>>>
>>> I'm used to run lme {nlme} by using both summary () and anova (), is
>>> that impossible when running glmm, lmer {lme4}?
>>>
>>> Thanks for help
>>>
>>  Not stupid.  (The only stupid questions are not-doing-your-homework
>> ones.)
>>
>>  What information are you hoping to glean from anova(mod) ?
>> If it is p-values for individual predictors, or information
>> about "residual degrees of freedom", you're probably out of
>> luck: see the oft-repeated questions on this list and the FAQ entry
>> for why that's hard.
>>
>>  (Feel free to write back to clarify what you have in mind --
>> but be warned that the answer is probably something along the
>> lines of "lme4 doesn't work that way, you're still thinking
>> in the classical sums-of-squares paradigm" ...)
> 
> I certainly agree with Ben that new users, or any users for that
> matter, should feel free to ask questions about what does and doesn't
> seem to work in the lme4 package.  The many kind users of the package
> have been generous in allowing me to experiment in the code, sometimes
> breaking features that were formerly working, while I try to come to
> an understanding of mixed-effects models and computational methods for
> them.  The process has worked in that I feel that I understand them
> much better than I did in the past.  However, doing things the way I
> do - creating and maintaining a software package that will allow for
> fitting general versions of the model while I am still experimenting
> with the overall design - is an intensive and, regrettably, slow way
> of doing research.  My thanks to those who have had the tolerance to
> take this journey with me.
> 
> The particular issue of not providing sequential anova summary for a
> generalized linear mixed model is related to the "quasi" families of
> conditional distributions.  Families like "binomial" or "poisson" or
> "Gamma" or the default "gaussian" family (I find the capitalization of
> those names to be interesting - the two proper nouns, Poisson and
> Gaussian, are not capitalized and the common noun. gamma, is)
> represent a probability distribution from which a likelihood can be
> calculated.  The "quasi" families do not correspond to probability
> distributions so they produce a quasi-likelihood which is used in the
> GLM fitting.  I know how to add random effects to the linear predictor
> for a model with a likelihood.  I'm not sure how it should be done for
> the quasi families.  One can mimic the computations, but without a
> sound theoretical basis, it is possible that the results could be
> nonsense and I, at least, wouldn't know whether they were nonsense.
> 
> I may end up punting on the quasi families and simply provide some
> parameter estimates without estimates of precision or, perhaps more
> radically, not allow the quasi families to be used.  If you look at
> the families provided in R you will see that the misleadingly named
> "AIC" function in the family (it actually returns the deviance) is
> only defined for binomial, Poisson, Gaussian and gamma families.
> Those AIC functions evaluate probability densities or probability mass
> functions and I can work with that.  I'm afraid I don't know enough
> about the quasi families to make sense of them yet.
> 
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-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz    majorgensen at ihug.co.nz      Fax 7 838 4155
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