[R-sig-ME] Quasilikelihood considered harmful? was: Examples of GLMM fits?

[Ben Bolker]

Murray Jorgensen wrote:
> Doug's response indicates a certain scepticism about quasilikelihood and 
> it's use in modelling. I am quite interested in this question and may 
> even get around to attempting some theoretical work about it. What I 
> would like to know about literature and discussions critical of QL and 
> its role in modelling. I think I am generally aware of pro-QL literature.
> 
> Cheers,  Murray Jorgensen
> 
> On 9/03/2010 3:50 a.m., Douglas Bates wrote:
> [...]
>> I will leave it to others more skilled than I to decide how to
>> formulate parameter estimates for fictitious distributions.  I have
>> enough trouble working in the non-fiction end of statistical theory.

  I am interested too.

  I suspect most of the criticism of QL has to do with its extension
beyond the GLM framework to other areas, such as quasi-AIC, or
application of QL ideas in frameworks such as GLMMs where the
fundamental theory hasn't really been worked out (that I know of).
These methods are used a lot by people in applied fields, *without*
worrying about those missing foundations ... for example, most of the
citations for QAIC in the ecological literature go back to Lebreton et
al 1992, who say:

(p. 85): In priniciple [sic], the LRTs should be modified, as should the
AIC criterion. These matters, which need further work, show up in our
last example (Greater Flamingo) ... (p. 107) Similarly, the AIC should
be modified as DEV/c-hat+2*n*p. ***We caution that these ideas are
exploratory and not yet confirmed by fundamental statistical theory, but
the ideas are consistent with quasi-likelihood theory*** [emphasis mine]

  Others (such as Shane Richards 2008) have tested these ideas *by
simulation*, and they seem to work out OK, but I would be curious to
know about work that establishes the theoretical foundations for these
approaches.

  A wild guess would be that generalized estimating equations are the
more respectable (theoretically grounded?) approach to this kind of
problem ... on the other hand, it would be nice to have a version of GEE
where one had something better than Wald tests to rely on for smaller
data sets ...

  One final remark (which may get me in trouble): ecologists (and
others) have to deal with overdispersion in small, discrete (i.e.
plausibly exponential family) data sets with blocking factors (i.e.
random effects) all the time.  The approaches that I know of for
statistical analysis in this case are
1. GEE (only Wald tests -- see above),
2. using an alternative distribution such as the negative binomial (not
currently possible in glmer -- arguably could be hacked similarly to the
way that MASS::glm.nb() extends glm(), if there were a slot in the data
structure that allowed the internal code to make use of an additional
parameter for the variance function)
3. allowing random effects at the individual level (equivalent to
assuming a marginal lognormal-Poisson distribution) -- not currently
possible in lme4 because of tests comparing the number of random effects
to the number of observations [but can be hacked by expeRts]
4. quasi-likelihood approaches

#1 is presumably possible in gee(), geepack()
#2 is possible in ADMB, glmmADMB
#3 is possible in MCMCglmm, R2WinBUGS ...
#4 is possible in glmmPQL (but PQL has its own problems)

  So it's understandable (to me) why people are still asking about
quasi- in lme4 , given that people take it as the standard for mixed
modeling in R and that it has broad applicability ...

  Disclaimer: I think I'm not talking nonsense, but I would be happy to
be corrected.

  Ben Bolker

============================
Lebreton, J. D., K. P. Burnham, J. Clobert, and D. R. Anderson. 1992.
Modeling Survival and Testing Biological Hypotheses Using Marked
Animals: A Unified Approach with Case Studies. Ecological Monographs
62:67-118. .

Richards, S. A. 2008. Dealing with overdispersed count data in applied
ecology. Journal of Applied Ecology 45:218-227. doi:
10.1111/j.1365-2664.2007.01377.x.



-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc