From ripley@stats.ox.ac.uk  Wed Sep 22 11:38:29 1999
From: ripley@stats.ox.ac.uk (ripley@stats.ox.ac.uk)
Date: Wed, 22 Sep 1999 12:38:29 +0200 (MET DST)
Subject: quasi-likelihood in glm (PR#284)
Message-ID: <199909221038.MAA17899@pubhealth.ku.dk>

On Wed, 22 Sep 1999 plummer@iarc.fr wrote:

> I have been using quasi-likelihood to analyze some overdispersed lesion
> count data which requires the variance function "mu^2" (specifically,
> I am using glm with the family quasi(var="mu^2", link="log")). Some of
> the counts are zero which led to problems fitting the model in R.
> 
> 1) glm was unable to find starting values
> 2) after I supplied initial values from the fit of a Poisson
>    model, glm could not proceed because the deviance was infinite.
> 
> Splus 5.0 had no problems fitting the model.  I was able to
> reproduce the Splus results by editing the quasi() family
> generator and using the unnormalized quasi-likelihood
> 
> - log(mu) - y/mu                  (*)
> 
> in place of the normalized version
> 
> log(y/mu) - (y - mu)/mu            (**)
> 
> Further investigation of Splus shows how it overcomes these
> two problems
> 1) A fudge factor (in this case 0.167) is added to zero observations 
>    so that they can be used as starting values. 
> 2) The contribution to the deviance is (*) for zero observations
>    and (**) for the rest.
> 
> I suggest that R also uses this approach for quasi-likelihood
> models.

That is not quite what S-PLUS 5.1 and 2000 have: replace
(*) by

-log(mu) - (y - mu)/mu 

That is, the formula is

-log(mu) - (y - mu)/mu + log(y)I(y > 0)

Note that earlier versions of S-PLUS (e.g. 3.4) are plain wrong (and as
I found the bug I know what the replacment is).

Unless there are any objections I will put these fixes in.

-- 
Brian D. Ripley,                  ripley@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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quasi-likelihood in glm (PR#284)
ripley@stats.ox.ac.uk