[R] generalized negative binomial

[Spencer Graves]

      I whole-heartedly endorse Prof. Ripley's suggestion to write down 
the log(likelihood) and use optim;  I've done that many times with 
seemingly good results.  For confidence intervals, the best procedure is 
to use 2*log(likelihood ratio) being approximately chi-square.  If you 
are estimating two parameters, you can easily compute log(likelihood) 
for a grid of points about the maximum likelihood estimates (MLEs) and 
use "contour" to draw lines at the difference confidence levels.  You 
can also use the argument "hessian = TRUE" to get the observed 
information matrix and therefore also the covariance matrix of the 
standard asymptotic normal approximation to the distribution of the 
MLEs;  I've done both. 

      hope this helps.  spencer graves

Prof Brian Ripley wrote:

> 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.
>