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

[baud-bovy.gabriel at hsr.it]

At 07:01 AM 12/16/2006, Prof Brian Ripley <ripley at stats.ox.ac.uk> wrote:

>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

Thank you for your reply and the above link. I am not sure yet which
function to use.  I am new at logistic regression for repeated-measure
designs and its various implementations in R.

glmmML seems to require changes at the C-level:
<http://www.stat.umu.se/forskning/reports/glmmML.pdf>http://www.stat.umu.se/forskning/reports/glmmML.pdf 


The new link might apparently be added to glmmPQL entirely at the
R-level.

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

If I understood your suggestion well, it is sufficient to add a new
link for the binomial family by extending the make.link function
and adding, say, a "half-logit" link (both for the glm and lme call in
glmPQL).

Then, the call to glmmPQL could be

glmmPQL(resp~shape*ecc*kappa,
         random=~1|subject,
         family=binomial("half-logit"),
         data,
         correlation=corCompSymm(form=~1|subject))

assuming that resp=1 if response is correct and 0 otherwise,
a random intercept (as in glmmML) and an "exchangeable" correlation structure.

Note that it might be better to specify a "random slope" in
this context (since proportions are expected to vary between 0.5 and 1
for all subjects, the main difference being that some subjects might
have a steeper S-shaped curve than others) but I am not sure how to do it.

Regards,

Gabriel Baud-Bovy
UHSR University, Milan, Italy