Re: [R] generalized negative binomial

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Mon 14 Mar 2005 - 03:40:08 EST

      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.
>



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