[R] Help with glmer {lme4) function: how to return F or t statistics instead of z statistics.

[Raldo Kruger]

Hi,

I'm new to R and GLMMs, and I've been unable to find the answers to my
questions by trawling through the R help archives. I'm hoping someone
here can help me.
I'm running an analysis on Seedling survival (count data=Poisson
distribution) on restoration sites, and my main interest is in
determining whether the Nutrients (N) and water absorbing polymer Gel
(G) additions to the soil substrate contribute positively to the
survival of the seedlings, over a 3 year time period (for simplicity
I'm just using 3 time periods, each in the same season for the 3
successive years).
Fixed factors: Nutrients (0 and 1), Gel (0 and 1)
Random factors: Site (4 non replicate sites), Year (3 time periods)
Response variable: Seedling numbers (counts) / 0.25m2 plot

According to the decision tree on page 131 in Bolker et al. (2008, in
TREE; thanks, very useful paper!), most of my data sets should be
analysed with Laplace or GHQ model with Wald t or F statistic (since
it is non-normal, can’t be transformed to normality, has a mean <  5,
has less than 3 random effects, and is overdispersed). I’m using the
glmer {lme4} function, since it allows for Laplace or GHQ, as well as
more than one random factor (glmmML {glmmML) and glmPQL {MASS}
apparently does not), as follows:
> m1<-glmer(Seedlings~N*G*(1|Year)*(1|Site), data=ex5m, family=poisson(link="log"))

My questions are:
1)	The model returns Z values, and I’m unable to find an argument in
the function where this can be changed to return a t or F value (as
Bolker et al. suggests I should use for my data).
2)	I’m unsure what the AIC or QAIC value means, other than knowing
that it should be as low as possible. Is there a rule of thumb of what
is a good AIC value? Mine are in the region of 2230.
3)	The default in glmer {lme4) for the argument  nAGQ = 1, which uses
the Laplace approximation. When nAGQ >1, it uses the GHQ method, but
I’m unsure how to determine the correct number of Gauss-Hermite points
to enter in the argument when using this method.  How is this
determined?
4)	Some of my data sets have means >5, and are also overdispersed, and
according to Bolker et al. should be analysed using a GLMM with PQL
and a Wald t or F. However, the glmmPQL {glmmPQL} does not accept more
than one random factor, and I have two, so how do I deal with that?
5) Lastly, what does the "1" imply in the random factor term, e.g.
(1|Site), and how does this affect the analysis?

Many thanks,
Raldo Kruger
MSc student
University of Cape Town
South Africa