Hi,
I recently read a pdf by Ben Bolker, titled “Testing Quasi-likelihood
fitting with glmer.” (See below post).

##############
I spent a bit of time this weekend running simulations
of quasi-likelihood estimation in glmer. The results
are posted at

http://www.zoo.ufl.edu/bolker/glmm/quasitest.pdf
http://www.zoo.ufl.edu/bolker/glmm/quasitest.Rnw

 I confirmed my suspicion that glmer is scaling the
random-effects variance-covariance matrix by the
scale parameter when it shouldn't; I also discovered
that the quasi-likelihood fit to lognormal-Poisson-distributed
data is alarmingly (?) biased, although a lognormal-Poisson
fit with individual-level random effects works nicely.

 Any comments are welcome.

 cheers
  Ben Bolker

########################

I was wondering if this problem ever was fixed or dealt with, and if using
the quasi-Poisson distribution in glmer is ok.

I am currently working with an over-dispersed count data set, in which I
have counts of birds captured in nets over the course of two summers. Nets
and Site are random factors, with net nested within site. There are 10 nets
per site, and 3 sites. There is also a Habitat factor (upland vs. riparian),
an ordinal date continuous variable, a year factor (2 years), and an offset
variable for the number of hours a net was open on a given day. Here is the
script I used:

model1<-glmer(formula = freq ~   Habitat*date + offset(effortperhour) +
(1|Site/net) + Year, family = quasipoisson, data=juveniles)
summary(model1)

Before this, I took out date as a random effect (date|Site/net), because it
was not significant (when conducting an anova between models with and
without date as a random effect), and also because it did not explain much
variance as a random effect.

For the above model, the output is:

Generalized linear mixed model fit by the Laplace approximation
Formula: freq ~ Habitat * date + offset(effortperhour) + (1 | Site/net) +
   Year
  Data: juveniles
  AIC   BIC logLik deviance
445.7 474.8 -214.9    429.7
Random effects:
Groups   Name        Variance Std.Dev.
net:Site (Intercept) 0.147200 0.38367
Site     (Intercept) 0.025762 0.16050
Residual             0.276971 0.52628
Number of obs: 279, groups: net:Site, 30; Site, 3

Fixed effects:
                    Estimate Std. Error t value
(Intercept)        -12.354760   0.576725 -21.422
HabitatUpland        2.927038   1.237851   2.365
date                 0.037639   0.002718  13.847
Year2007            -1.087970   0.075414 -14.427
HabitatUpland:date  -0.023988   0.006096  -3.935

Correlation of Fixed Effects:
           (Intr) HbttUp date   Yr2007
HabittUplnd -0.439
date        -0.965  0.437
Year2007    -0.171 -0.002  0.151
HbttUplnd:d  0.417 -0.991 -0.435  0.001

Which seems to work ok. If there is a bias running glmer with a
quasi-Poisson, I could run a regular Poisson on the data, however I do not
think the data fits a regular Poisson as well, as the variance of the data
is about 5x greater than the mean. I also tried transforming the data into
binary and fitting it to a binomial distribution, which also worked well.
This latter option would be possible, however transforming the data
effectively changes the data from count into presence-absence.
Please let me know if anyone has any thoughts about this, it would be
greatly appreciated.

Thanks,

Mike Akresh
Dept. of Natural Resources Conservation
University of Massachusetts, Amherst

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