[Rd] Parametric links for glm?

[Prof Brian Ripley]

There is no reason to add ...: you could have 
binomial(link = Gosset(nu=5)).

I really don't like the idea of changing system functions like make.link, 
and believe it is not necessary.

On Sun, 30 Jul 2006, roger koenker wrote:

> At useR 2006 I mentioned that it would be nice to have a way to  
> specify binomial links
> that involved free parameters  and described some experience with a  
> Gosset link involving
> a free degrees of freedom parameter, and a Tukey-lambda link with two  
> free parameters.
> My implementation of this involved some rather kludgey modifications  
> of binomial,
> make.link and glm that (essentially) added a "..." argument to  
> binomial permitting the
> parameters to be passed down to the fitting routines.  So, in the  
> Gosset case, for example,
> had the following passage in  make.link, involving a free degrees of  
> freedom parameter nu:
> 
> }, Gosset = {
>          linkfun <- function(mu) qt(mu,nu)
>          linkinv <- function(eta) {
>              thresh <- -qqt(.Machine$double.eps,nu)
>              eta <- pmin(thresh, pmax(eta, -thresh))
>              pt(eta,nu)
>          }
>          mu.eta <- function(eta) pmax(dt(eta,nu), .Machine$double.eps)
>          valideta <- function(eta) TRUE
> },
> 
> Just prior to the useR meeting, there were some changes in R-devel to  

Actually, it was a redesign of all the link functions to make them 
consistent: quasi was odd here.

> binomial that allow one to pass an object of class "link-glm" -- if I  
> understand properly, this allows one to more easily
> roll one's own links, but it leaves the question of passing  
> parameters on the table.  That is,
> presumably, I could pass a structure, like that above of class "link- 
> glm" and thereby avoid
> the Cerberus of  officially sanctioned links, but I still don't see  
> how to pass my parameters.
> Can someone enlighten me?  Or,  would it still be necessary to add  
> "..." to the binomial
> function?
> 
> url:    www.econ.uiuc.edu/~roger                Roger Koenker
> email   rkoenker at uiuc.edu                       Department of Economics
> vox:    217-333-4558                            University of Illinois
> fax:    217-244-6678                            Champaign, IL 61820
> 
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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