[R] how to adjust link function in logistic regression to predict the proportion of correct responses in 2AFC task?

[Prof Brian Ripley]

On Sat, 16 Dec 2006, baud-bovy.gabriel at hsr.it wrote:

> I have would like to use logistic regression to analyze the
> percentage of correct responses in a 2 alternative forced
> choice task. The question is whether one needs to take into
> account the fact expected probabilities for the percentage of
> correct responses ranges between 0.5 and 1 in this case.

Yes.

> Second, how can one implement a link function of the
> type f(x) = (1+exp(x)/(1+exp(x)))/2 in R?

Looking at make.link() should give you enough to go on.

> Third, can it be also done with gee and/or glmm?

For gee, you need to change the C-level internals. (I've done this in the 
far past for S-PLUS but not for R.)  It would be easier to use yags (but I 
think you still need to dive into the internals).

What 'glmm' did you have in mind?  Looks like e.g. glmmML and glmmPQL will 
work with the new link.

[...]

Someone may have been here already: e.g.
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1434755

-- 
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