[R] generalized negative binomial

[Prof Brian Ripley]

On Sat, 12 Mar 2005, Erin M Simpson wrote:

> I am looking for code that allows for a more flexible negative binomial
> model (similar to Stata's "gnbreg").

Your subject line is not clear to me: Stata appears to fit a negative 
binomial model, the point being that it is not a glm as fitted by glm.nb. 
(So when Stata says

      `gnbreg is a generalized negative binomial regression'

it is `regression' not `negative binomial' that is being generalized.)

> In particular, I am looking to be able to model the ancillary
> shape parameter in terms of a series of covariates.   So if,
>
> 	y[i] ~ poisson(mu[i])
>
> 	mu[i] = exp(x[i]beta + u[i])
>
> 	exp(u[i]) ~ Gamma(1/alpha, alpha)
>
> I am looking to parameterize alpha as exp(z[i]gamma).
>
> If you are familiar with a package that allows for this, I'd appreciate
> the heads up.  Similar information that allows for first differences with
> such a model is also appreciated.

Just write down the log-likelihood (I am not sure what the free parameters 
here are: are beta and gamma vectors?), and call optim() to maximize it.

-- 
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)
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