[R-sig-ME] glmer Z-test with individual random effects

[Jens Åström]

Dear list,

As I have read (Bolker et al. 2009 TREE), the Wald Z test is only
appropriate for GLMMs in cases without overdispersion.

Assuming we use family=poisson with lmer and tackle overdispersion by
incorporating an individual random effect AND this adequately "reduces"
the overdispersion, is it then OK to use the Wald z test as reported by
lmer?

In other words, are the p-values reported by lmer in those cases
useful/"correct"? Or do they suffer from the usual problems with
figuring out the number of parameters used by the random effects?

Secondly, is it good practice to judge lmer's capability of "reducing"
the overdispersion by summing the squared residuals (pearson) and
compare this to a chi square distribution (with N-1 degrees of freedom)?


Thankful for any comments or suggestions,

Jens Åström