R help - Jun 2006 - variance specification using glm and quasi

Hi all,

 

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? If so, how I can get NB1? The quasi family appears to be very
limited in variance specification options.

 

Thanks,

Jeff

 

 


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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