[R] Estimation of Dispersion parameter in GLM for Gamma Dist.

Prof Brian Ripley ripley at stats.ox.ac.uk
Sat May 26 06:58:21 CEST 2007

This is discussed in the book the MASS package (sic) supports, and/or its 
online material (depending on the edition).

On Fri, 25 May 2007, fredrik odegaard wrote:

> Hi All,
> could someone shed some light on what the difference between the
> estimated dispersion parameter that is supplied with the GLM function
> and the one that the 'gamma.dispersion( )' function in the MASS
> library gives? And is there consensus for which estimated value to
> use?
> It seems that the dispersion parameter that comes with the summary
> command for a GLM with a Gamma dist. is close to (but not exactly):
> Pearson Chi-Sq./d.f.

Sometimes close to, but by no means always.  Again, discussed in MASS.

> While the dispersion parameter from the MASS library
> ('gamma.dispersion ( )' ) is close to the approximation given in
> McCullagh&Nelder (p.291):
> Res.Dev./n*(6+Res.Dev./n) / (6 + 2*Res.Dev./n)
> (Since it is only an approximation it seems reasonable that they are
> not exactly alike.)
> Many thanks,
> Fredrik
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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

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