glmer , quasipoisson and standard errors of the coefficients

Hello,
I am trying to simplify backwards a mixed effects model, using lmer 
function from lme4 package. As my data are species numbers and there 
exists overdisperison, I think appropriate to use glmer function with 
error family quasipoisson. I compare one model with its simplification 
through log-likelihood ratio tests.
Nevertheless, once I have selected a simplified model, I find in the 
summary of this 'significant' model that estimated coefficients  are  
associated  to  very big  standard errors, to the point that no one of 
the coefficients seem to be significantly different from zero.

Here come my questions:
Can anybody explain this contradiction among standard errors of the 
estimated coefficients and the significance of the model?
Is unappropriated to use Log-likelihood backwards simplification with 
quasipoisson errors?

There are several issues here (and you should think about asking this 
question on r-sig-mixed-models , where there
is more expertise).

  1. glmer with a quasipoisson link does not provide a likelihood 
(rather, a quasilikelihood),
so you shouldn't necessarily assume that you can do *any* 
likelihood-based inference with
the results from this analysis.  The most conservative approach is to 
use only the estimated
standard errors or Z statistics on the parameters (this is a Wald test) 
for inference.

  2. if you _do_ want to use the likelihood for inference, you need to 
convert it to a "quasi-likelihood"
by dividing it by the estimated scale parameter (which you can extract 
via lme4:::sigma(model) ).
This is done (for example) when you state test="F" in anova() on 
generalized linear models --
also note that in this case you should technically do an F test rather 
than a chi-squared test,
with denominator df equal to the residual df (although it's hard to 
figure out what these should
be ...)

  3. it is generally advised *NOT* to use the likelihood ratio test for 
testing fixed effects
(see Pinheiro and Bates 2000).

  So ... bottom line ... for now, I would use the Z tests (labeled as t 
tests), i.e.
means / standard errors ...

  good luck,
   Ben Bolker