[R] binomial(link="inverse")

[Ben Bolker]

Prof Brian Ripley wrote:
> This isn't accurate. You are talking about link functions *known by name*.
> 
>     link: a specification for the model link function.  This can be a
>           name/expression, a literal character string, a length-one
>           character vector or an object of class '"link-glm"' (provided
>           it is not specified via one of the standard names given
>           next).
> 
> Nothing is stopping you giving the link as an object, and there is an
> example on the help page.  We made this easily user-extensible quite a
> while back.

  Thanks, I had overlooked this.  So the short answer to my question is
really

  glm(...,family=binomial(link=make.link("inverse"))

> As to why the list of links known by name is as it is, that seems
> history. in part the White Book history of S.  I've always thought it an
> error that 'log' was a standard link for binomial, as the range does not
> match the specification of probabilities (and S did not do so, MASS
> Table 7.1 ). For each of log and inverse you have a valid model only for
> some values of the data, and can easily ask for predictions that give an
> out-of-range error.

  True, but there are some ecological examples where log(mu)=a+b*x
or 1/mu=a+b*x are very natural models for the data: e.g.

Strong, D. R., A. V. Whipple, A. L. Child, and B. Dennis. 1999. Model
selection for a subterranean trophic cascade: root-feeding caterpillars
and entomopathogenic nematodes. Ecology 80: 2750-2761.

Tiwari, Manjula, Karen A Bjorndal, Alan B Bolten, and Benjamin M Bolker.
2006. Evaluation of density-dependent processes and green turtle \em
Chelonia mydas production at Tortuguero, Costa Rica. Marine Ecological
Progress Series 326: 283-293.

  Berwin Turlach also pointed out off-list that binomial GLMs with
identity links often have convergence and other fitting problems --
presumably this applies to inverse links as well.

  Ben Bolker




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