[R] variance specification using glm and quasi
Prof Brian Ripley
ripley at stats.ox.ac.uk
Mon Jun 12 14:06:32 CEST 2006
On Mon, 12 Jun 2006, Jeff Miller wrote:
> Cameron and Trivedi in their 1998 Regression Analysis of Count Data refer to
> NB1 and NB2
>
> NB1 is the negative binomial model with variance = mu + (alpha * mu^1)
> yielding (1+alpha)*mu
>
> NB2 sets the power to 2; hence, variance = mu + (alpha*mu^2)
>
> I think that NB2 can be requested via
>
> negbin2<-glm(hhm~sex+age,family=quasi(var="mu^2",link="log"))
>
> Is that right?
No. That is variance = phi*mu^2, not mu + (alpha*mu^2).
> If so, how I can get NB1? The quasi family appears to be very
> limited in variance specification options.
[Not so in the R-devel version of R: you can supply any variance
function.]
You can use your own family in any version of R. Package MASS has for
many years supplied negative.binomial, which has mu + mu^2/theta, a
parametrization of `NB2'. It even provides glm.nb to estimate theta.
Note that (and this is explicitly in your reference) (1+alpha)*mu = phi*mu
so that NB1 can be fitted as a quasipoisson GLM, although the
quasilikelihood used is the *not* the likelihood of the model (which is
not a GLM). You could easily fit this model by maximum likelihood by
direct maximization: p.445 of MASS provides a suitable template.
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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