[R-sig-ME] Using Observations as Random Effect in GLMM?

[Ben Bolker]

John Maindonald <john.maindonald at ...> writes:

> 
> I've been looking recently at animal count data that I've modeled
> as Poisson with an observation level random effect, and have
> worried a bit about such issues.
> 
> The observation level random effects model and the over-dispersion 
> model add variances on different scales -- for the observation level
> random effects random effects model the added variance is 
> proportional to the square of the Poisson mean, whereas for the
> over-dispersion model it is proportional to the mean. (These 
> comments assume small additional error; but they do delineate
> the broad ballparks in which the two models operate.   The glmer() 
> function is making its own very specific assumptions about the 
> scale on which to add the additional normal error.
> 
> The models are thus pretty much equivalent only if the range of 
> expected values is small.  It would be useful to have more flexibility,
> at the observation level at least, in the modelling of the extra-Poisson
> error.  Among the various packages that handle GLMMs, do any of
> them offer such flexibility, maybe allowing e.g. a quasi-Poisson error? 

  Recent versions of the glmmADMB package offer two flavors of negative
binomial model, either with variance = mu*(1+mu/k) (the classic
'quadratic' (almost) parameterization, which Hardin and Hilbe call
NB2) or with variance = phi*mu (which Hardin and Hilbe call
NB1; I believe this is what you are calling "quasi-Poisson" above).
The variance-mean relationship of NB2 and of the lognormal-Poisson
model are the same, although the details do differ ...

> (Sure, there are issues about how legit quasi-Poisson errors are.  
> I expect however someone will sometime work out how to give them 
> full theoretical respectability, and they will duly be admitted to the part 
> of the statistical pantheon allocated to those models that are thus 
> theoretically respectable.)

  I haven't tried it yet, but my response to the original poster
would have been to try a well-behaved simulation and see whether
the same phenomenon occurred ...