# [R] Proby densities from the GLM object

Bill Venables William.Venables at cmis.CSIRO.AU
Thu Oct 14 11:02:57 CEST 1999

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To: R.E.Darnell at newcastle.ac.uk (R. E. Darnell)
Subject: Re: [R] Proby densities from the GLM object
In-Reply-To: Your message of "14 Oct 1999 09:44:15 +0100."
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Date: Thu, 14 Oct 1999 19:02:57 +1000
From: Bill Venables <venables at acland.nsw.cmis.csiro.au>

> Is it possible to generate the probability densities for a GLM family
> member from the glm object? Prior.weights, y's, parameters, scale
> parameters are there but what about the \tau function (using V&R's notation).

In practice I'd say no but it's an intriguing problem.

The characteristic function of the distribution only depends on the \theta and
\gamma functions, A and \phi.  Given that there is a distribution (and this is not always true) the \tau is implied by all the others.

But even to re-construct the characteristic function you would need the
functional forms for \theta and \gamma, at least.  \theta can be ignored if you
can assume the natural link, say, but \gamma is not available directly, as far
as I can see, and even if it were do you really want to go into numerical
inversion of the characteristic function?

Your troubles really start if you are dealing with one of the quasi-likelihood
models for which there is no distribution, of course!

Bill.

- --
- -----------------------------------------------------------------
Bill Venables, Statistician, CMIS Environmetrics Project.

CSIRO Marine Laboratories,                   PO Box 120,
233 Middle St, Cleveland, Queensland         Cleveland, Qld, 4163
AUSTRALIA                                    AUSTRALIA

Telephone: +61 7 3826 7251     Email: Bill.Venables at cmis.csiro.au
Fax: +61 7 3826 7304

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