[R-sig-ME] Quasipoisson: alternative implementation

[Gosselin Frederic]

Dear Colleague,

it seems that quasi-poisson interests more and more R members...

To your question 1:
> 1) Is it common knowledge that the quasipoisson family incorrectly weights things somewhere in glmer?  The example 
>below gives a demonstration.

I answer again (cf. https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q1/003348.html and https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q4/003059.html) that quasi-poisson implemented in glmer/lmer - as well as quasibinomial - has a very strange behaviour as the one you report in latter versions of R but not in older ones (let's say before version 2.5.1). I reproduced your test under R2.2.1: here is the result, much better - note the slight difference in the syntax:


>  lmer(x2 ~ 1+(1|z), family = "quasipoisson")
Generalized linear mixed model fit using PQL 
Formula: x2 ~ 1 + (1 | z) 
 Family: quasipoisson(log link)
      AIC      BIC    logLik deviance
 188.8215 194.0318 -92.41075 184.8215
Random effects:
 Groups   Name        Variance   Std.Dev.  
 z        (Intercept) 9.1691e-10 3.0280e-05
 Residual             1.8338e+00 1.3542e+00
number of obs: 100, groups: z, 2

Fixed effects:
            Estimate Std. Error t value
(Intercept) 4.621536   0.013432  344.08




Regarding your second suggestion, - including a innerlevel random effect - this is a different model, which is based on a "real" liklelihood, that might be worth considering, along e.g. negative binomial models in other R functions. Then, why not simply using:
	ind <- factor(1:100)
	glmer(x2 ~ (1|ind), family = poisson)

As you mention, you then cannot treat underdispersion, which might be a problem in some settings.

Sincerely,

Frédéric Gosselin 
Engineer & Researcher (PhD) in Forest Ecology 
Cemagref 
Domaine des Barres 
F-45290 Nogent sur Vernisson 
France 

http://www.cemagref.fr/les-contacts/les-pages-personnelles-professionnelles/gosselin-frederic/english-short-scientific-cv