[R-sig-ME] single argument anova for GLMMs (really, glmer, or dispersion?)

Ben Bolker bolker at ufl.edu
Fri Dec 12 15:49:45 CET 2008

  Jumping in late here, generally agreeing with the pther ecologists
(who say that the data are often overdispersed even after
accounting for known grouping factors via random effects).
I also agree that negative binomial models would be a great
addition to lmer (? could perhaps do beta-binomial at the
same time, without much additional cost?). [glmmADMB will
also do these, it's not as widely used, but certainly worth
further testing]  Testing and strengthening lmer's ability
to handle individual-level variation (as in lognormal-Poisson
or logit-normal-binomial models) would provide another alternative
to quasi() ...

David Duffy's example (variation left over after random effects and
negative binomial model) makes me kind of nervous, I would hope that
such effects would be jumping out of exploratory graphics, or graphical
analyses of residuals ...

  My advice to students is usually "do whatever is most feasible,
you probably don't have enough data to distinguish between
Var = phi*mu (quasi-) and Var = mu*(1+phi*mu) (neg binom)
anyway" -- supported by Liang and McCullagh and Richards,
to some extent ... although recent simulation studies with
big data sets have told a somewhat different story ...

  Bottom line -- ecologists *will* often have overdispersion
that can't be explained by known grouping factors, but they
are pragmatists -- if you give them some way to handle that
overdispersion (parametric models or individual-level variation)
they probably won't complain about the lack of quasi- ...

   Ben Bolker

Liang, Kung-Yee, and Peter McCullagh. 1993. Case Studies in Binary
Dispersion. Biometrics 49, no. 2 (June): 623-630.

Richards, Shane A. 2008. Dealing with overdispersed count data in
applied ecology. Journal of Applied Ecology 45: 218-227.

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

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