R help - Feb 2013 - Negative Binomial Regression - glm.nb

Dear all,

I would like to ask, if there is a way to make the variance / dispersion
parameter $\theta$ (referring to MASS, 4th edition, p. 206) in the function
glm.nb dependent on the data, e.g. $1/ \theta = exp(x \beta)$ and to estimate
the parameter vector $\beta$ additionally.

If this is not possible with glm.nb, is there another function / package which
might do that?

Thank you very much for your answer in advance!

Best,

Martin

On 28/02/2013 07:27, Martin Spindler wrote:
> Dear all,
>
> I would like to ask, if there is a way to make the variance / dispersion
parameter $\theta$ (referring to MASS, 4th edition, p. 206) in the function
glm.nb dependent on the data, e.g. $1/ \theta = exp(x \beta)$ and to estimate
the parameter vector $\beta$ additionally.
That is no longer a glm, so no.
> If this is not possible with glm.nb, is there another function / package
which might do that?
You can maximize the likelihood directly.  How to do that is exemplified 
in the optimization chapter of MASS.
> Thank you very much for your answer in advance!
>
> Best,
>
> Martin

-- 
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

Martin Spindler <Martin.Spindler <at> gmx.de> writes:
> 
> Dear all,
> 
> I would like to ask, if there is a way to make the
> variance / dispersion parameter $\theta$ (referring to
> MASS, 4th edition, p. 206) in the function glm.nb dependent on the 
> data, e.g. $1/ \theta = exp(x \beta)$ and
> to estimate the parameter vector $\beta$ additionally.
> 
> If this is not possible with glm.nb, is there another 
> function / package which might do that?
> 
  As Brian Ripley says, that's outside the scope of glm.nb(),
and a later chapter in MASS tells you how to do it.

  The mle2 function in the bbmle package offers a possibly
convenient shortcut.  Something like

  mle2(response~dnbinom(mu=exp(logmu),size=exp(logtheta)),
     parameters=list(logmu~[formula for linear predictor of log(mu)],
                     logtheta~[formula for linear predictor of log(beta)]),
     start=list(logmu=[starting value for logmu intercept],
                logbeta=[starting value for logbeta intercept]),
     data=...)

should work ...

 Ben Bolker

On 02/28/2013 08:27 PM, Martin Spindler wrote:
> Dear all,
>
> I would like to ask, if there is a way to make the variance / dispersion
parameter $\theta$ (referring to MASS, 4th edition, p. 206) in the function
glm.nb dependent on the data, e.g. $1/ \theta = exp(x \beta)$ and to estimate
the parameter vector $\beta$ additionally.
>
> If this is not possible with glm.nb, is there another function / package
which might do that?
I believe that the VGAM package is designed precisely to do this sort of 
thing.

     cheers,

         Rolf Turner