[R-sig-ME] Dispersion parameter negbin1 in glmmADMB

[Ben Bolker]

Dean Castillo <dmcastil at ...> writes:

> 
> HI Hanna,
> 
> It may be very well that GLM and glmm ADMB calculate the
> overdispersion parameter in a different way, but the quasipoisson and
> negative binomial are not the same.
> Quasipoisson uses a mean regression function (like normal poisson) but
> leaves the overdispersion parameter unrestricted. Negative binomial
> can be represented as a gamma mixture of poisson distributions.

  Yes, but: the negative binomial 'type I', which is fitted here,
is parameterized so that it has the same expected mean-variance
relationship as the quasi-Poisson model, variance=phi*mean.

  Using GLM/quasi-Poisson fits the parameters by iteratively
reweighted least squares (IRLS), then calculates the dispersion
parameter according to

sum(residuals(g2,"pearson")^2)/df.residual(g2)

  Using glmmADMB with type="nbinom1" does a maximum-likelihood
fit to a full model using the aforementioned distribution.
I'm slightly but not terribly surprised that the results are
as different as they are.  I believe (but can't prove right now)
that the max. likelihood and IRLS estimates are the same as long
as you stay in the exponential family, but I think nbinom1 is
*not* in the exponential family.

  Also, when I run glmmADMB I get warning about 

Estimated covariance matrix may not be positive definite

which suggests the possibility that glmmADMB might have
gotten stuck at not-quite-the-optimum value.

> 
> The pscl package has some documentation explaining different types of
> count models. It is called: "Regression models for count data in R".
> It is useful to help understand count models.
> 
> Dean
> 
> On Tue, Mar 27, 2012 at 8:58 AM, Hanna ten Brink
> <hannatenbrink at ...> wrote:
> > Dear R users
> >
> > I am trying to understand how the dispersion parameter in the glmmADBM
> > package is calculated for the negbin1 family.
> > Is it correct that the negbin1 family is the same as the quasipoisson
> > family?
> > Because when I run a simple model in GLM(family=quasipoisson) or in
> > glmmADMB(family=negbin) for the Owls-dataset, it gives different dispersion
> > parameters.
> >
> > e.g.
> >
> > ADBM_binom1 <- glmmadmb(NCalls~(FoodTreatment+ArrivalTime)*SexParent+
> > offset(logBroodSize),
> > data=Owls,
> > zeroInflation=FALSE,
> > family="nbinom1")
> >
> > Dispersion parameter=8.2014
> >
> > GLM_quasipois <- glm(NCalls~(FoodTreatment+ArrivalTime)*SexParent+
> > offset(logBroodSize),
> > data=Owls,
> > family=quasipoisson)
> >
> > Dispersion parameter= 6.259856
> >
> > Does this mean that the negbin1 and quasipoisson family are not the same?
> > Or does the glmmADMB package calculates the dispersion parameter in a
> > different way?
> >