[Rd] Parametric links for glm?

From: roger koenker <roger_at_ysidro.econ.uiuc.edu>
Date: Sun 30 Jul 2006 - 15:29:37 GMT

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$double.eps,nu)
             eta <- pmin(thresh, pmax(eta, -thresh))
         mu.eta <- function(eta) pmax(dt(eta,nu), .Machine$double.eps)
         valideta <- function(eta) TRUE


Just prior to the useR meeting, there were some changes in R-devel to 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

url:    www.econ.uiuc.edu/~roger                Roger Koenker
email   rkoenker@uiuc.edu                       Department of Economics
vox:    217-333-4558                            University of Illinois
fax:    217-244-6678                            Champaign, IL 61820

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