[R] glm
Jim Lindsey
jlindsey at alpha.luc.ac.be
Wed Feb 2 08:49:50 CET 2000
>
> On Tue, 1 Feb 2000, Jim Lindsey wrote:
>
> > > 4. I don't think AIC is stricly correct. My understanding of AIC is that
> > > it is the log likelihood maximised over all the parameters, including
> > > the dispersion parameter. Now the problem is that the mle of the
> > > dispersion parameter for the gamma family (and the exponential family in
> > > general) is really awkward - I think it has to be found by interative
> > > methods, using the derivative of the gamma function - I see from a print
> > > of Gamma that you are using dev/n, but I don't think this is the mle....
> >
> > Yes you are right. I chose this only as a reasonable approximation for the
> > gamma and inverse Gaussian distributions. If you want the exact AIC,
> > you can get it from the gnlr function in my gnlm library.
>
> Another way to get the MLE of the dispersion parameter from the glm output
> is to use the function gamma.shape.glm (by Bill Venables) in the MASS
> package. Its help says
>
> Details:
>
> A glm fit for a Gamma family correctly calculates the maximum
> likelihood estimate of the mean parameters but provides only a
> crude estimate of the dispersion parameter. This function takes
> the results of the glm fit and solves the maximum likelihood
> equation for the reciprocal of the dispersion parameter, which is
> usually called the shape (or exponent) parameter.
>
> and yes it is optimized over an expression using the digamma and trigamma
> functions, but the code is about 30 lines only including all the warnings
> and housekeeping. (Such things show the power of S over GLIM: it would be
> `really awkward' in GLIM.)
>
> Note, though, that McCullagh and Nelder argue hard against the MLE of
> dispersion in the gamma family.
That argument can be made when a precision interval is required for
the dispersion parameter (conditional or REML estimate). I do not
believe that it can be made for substituting the estimate into the
likelihood or AIC for comparing different models which is the case in
question here. Jim
>
> Brian
>
> --
> 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 272860 (secr)
> Oxford OX1 3TG, UK Fax: +44 1865 272595
>
>
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