[R-sig-ME] generalized linear mixed models: large differences when using glmmPQL or lmer with laplace approximation

[Ben Bolker]

Douglas Bates wrote:
  [snip]
> 
> It may be that the problem you are encountering has more to do with
> the use of the quasipoisson family than with the Laplace
> approximation.  I am not sure that the derivation of the standard
> errors in lmer when using the quasipoisson family is correct, in part
> because I don't really understand the quasipoisson and quasibinomial
> families.  As far as I know, they don't correspond to probability
> distributions so the theory is a bit iffy.
> 
> Do you need to use the quasipoisson family or could you use the
> poisson family?  Generally the motivation for the quasipoisson familiy
> is to accomodate overdispersion.  Often in a generalized linear mixed
> model the problem is underdispersion rather than overdispersion.

  In ecological data it's quite common to have dispersion remaining
in a GLMM even after accounting for known grouping factors.

> In one of Ben's replies in this thread he discusses the degrees of
> freedom attributed to certain t-statistics.  Regular readers of this
> list are aware that degrees of freedom is one of my least favorite
> topics.  If one has a reasonably large number of observations and a
> reasonably large number of groups then the issue is unimportant.
> (Uncertainty in degrees of freedom is important only when the value of
> the degrees of freedom is small.  In fact, when I first started
> studying statistics we used the standard normal in place of the
> t-distribution whenever the degrees of freedom exceeded 30).
> Considering that the quasi-Poisson doesn't correspond to a probability
> distribution in the first place, (readers should feel free to correct
> me if I am wrong about this) I find the issue of the number of degrees
> of freedom that should be attributed to a distribution of a quantity
> calculated from a non-existent distribution to be somewhat off the
> point.

  Fair enough, but backing up to wanting p-values associated with
(sensible???) hypothesis tests -- we don't have mcmcsamp for GLMMs,
so our options are (1) no p-values at all, (2) Z tests (i.e. don't
worry about uncertainty in the scale parameter estimate, (3) ??
simulation from the null hypothesis.  See

  http://www.zoo.ufl.edu/bolker/glmm/glmersim.pdf

> I think the problem is more likely that the standard errors are not
> being calculated correctly.  Is that what you concluded from your
> simulations, Ben?

  Yes.

  http://www.zoo.ufl.edu/bolker/glmm/quasitest.pdf

  By the way, I'd be more than happy for any input on the
above-referenced URLs -- if anyone thinks (and can argue
reasonably convincingly) that they're wrong and/or misguided
I'll take them down so as not to mislead the public.
The Sweave files are up in the same place (substitute .Rnw
for .pdf)

  cheers
    Ben