[R-sig-ME] Help with glmer {lme4} function: how to return F or t statistics instead of z statistics?

[Ben Bolker]

Raldo Kruger wrote:
> 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).

   The "t statistic" and the "Z statistic" are the same (coefficient
divided by [the estimate of] its standard error) ... the difference is
whether you test the null hypothesis with dnorm or dt ...

> 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.

  see the other answer in this thread.

> 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?

   Try increasing it until the answers don't change much.  I have often
found that nAGQ=5 is sufficient, but if you've got noisy data and fairly
wide confidence intervals even the difference between Laplace and GHQ
may be swamped by the noise in your data.


> 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?

   Laplace/AGQ are probably *better* than GLMM/PQL in any case -- it's
just "acceptable" to use GLMM/PQL (and makes some things easier --
GLMM/PQL is much more flexible, faster, etc.) in the means>5 case.

> 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
> Unversity of Cape Town
> South Africa
> 
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-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / www.zoology.ufl.edu/bolker
GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc