[R] glm gamma scale parameter

[Prof Brian Ripley]

On Tue, 6 Feb 2007, WILLIE, JILL wrote:

> Thank you.  You are correct, the shape parameter is what I need to
> change & I think I see how to use the MASS package to do it...or if not,
> at least I have enough now to figure it out.
>
> A question to reconcile terminology which will speed me up, if you have
> time to help me a bit more: phi = 'scale parameter' vs. 'dispersion
> parameter' vs. 'shape parameter'?  Excerpt below from the R intro.
> manual defining phi & the stats compliment discussion.

You need to compare the complement with MASS the book.  The dispersion is 
1/shape in the conventional parametrization of the gamma.  See 
?gamma.dispersion.

>
> R intro:
>
> distribution of y is of the form
> f_Y(y; mu, phi) =
> exp((A/phi) * (y lambda(mu) - gamma(lambda(mu))) + tau(y, phi))
>
> where phi is a scale parameter (possibly known), and is constant for all
> observations, A represents a prior weight, assumed known but possibly
> varying with the observations, and $\mu$ is the mean of y. So it is
> assumed that the distribution of y is determined by its mean and
> possibly a scale parameter as well.

Bill Venables wrote that and the equivalent part of MASS.  'dispersion' is 
a more common name for phi.

>
> Statistics Complements to Modern Applied Statistics with S, Fourth
> edition By W. N. Venables and B. D. Ripley Springer:
>
> 7.6 Gamma models
> The role of dispersion parameter for the Gamma family is rather
> different. This is a parametric family which can be fitted by maximum
> likelihood, including its shape parameter
>
>
> Jill Willie
> Open Seas
> Safeco Insurance
> jilwil at safeco.com
>
>
> -----Original Message-----
> From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk]
> Sent: Tuesday, February 06, 2007 12:25 PM
> To: WILLIE, JILL
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] glm gamma scale parameter
>
> On Tue, 6 Feb 2007, Prof Brian Ripley wrote:
>
>> I think you mean 'shape parameter'.  If so, see the MASS package and
>> ?gamma.shape.
>
> Also http://www.stats.ox.ac.uk/pub/MASS4/#Complements
> leads to several pages of discussion.
>
>>
>> glm() _is_ providing you with the MLE of the scale parameter, but
> really no
>> estimate of the shape (although summary.glm makes use of one).
>>
>>
>> On Tue, 6 Feb 2007, WILLIE, JILL wrote:
>>
>>> I would like the option to specify alternative scale parameters when
>>> using the gamma family, log link glm.  In particular I would like the
>>> option to specify any of the following:
>>>
>>> 1.  maximum likelihood estimate
>>> 2.  moment estimator/Pearson's
>>> 3.  total deviance estimator
>>>
>>> Is this easy?  Possible?
>>>
>>> In addition, I would like to know what estimation process (maximum
>>> likelihood?) R is using to estimate the parameter if somebody knows
> that
>>> off the top of their head or can point me to something to read?
>>>
>>> I did read the help & search the archives but I'm a bit confused
> trying
>>> to reconcile the terminology I'm used to w/R terminology as we're
>>> transitioning to R, so if I missed an obvious way to do this, or
> stated
>>> this question in a way that's incomprehensible, my apologies.
>>>
>>> Jill Willie
>>> Open Seas
>>> Safeco Insurance
>>> jilwil at safeco.com
>>>
>>> ______________________________________________
>>> R-help at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>
>

-- 
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