[R-sig-ME] lmer probit fit

[Ken Knoblauch]

> I have a question concerning lme4 library and 
probit function fitting:
> 
> Would it be possible to write custom-defined sigmoid 
link functions to use in combination with lmer?
> Specifically, is it possbile to
> write a sigmoid function (probit, for instance) that has 
2 more parameters that control the lower and the
> upper asymptote?
> 
> Attached below is an example that generates a 
synthetic dataset and approaches the problem from the glm
> standpoint. I wonder whether
> it is possible to do the same thing within the 
framework of lmer.
> 
> The question refers to the fact that in cognitive 
sciences we are often interest in modeling binary
> outcomes (for instance: YES/NO in
> a computerized task); however, in many experimental 
designs, the observer's response at chance will not
> asymptote at 0. Similarly
> the maximal performance is occasionally contaminated 
by errors (will not asymptote at 1). Therefore, it
> is necessary to model the
> asymptotes along with the other parameters.
> 
> Thank you very much
> best ragards
> Giovanni Mancuso
> 
> # The function 'psyfun.2asym', wrote by Dr Kenneth Knoblauch, 
estimates a best ?t to the data by
> alternating between calls to 'glm' for current best estimates 
of arguments to the link function and calls
> to optim to
> # estimate the values of the lower and upper asymptote.
> # 'psyfun.2asym' takes as a link function a user defined 
probit function with 4 free parameters (center and
> scale, and the upper and lower asymptote)
> 
> 	[[alternative HTML version deleted]]
> 
> 

Hi Giovanni,

 I would add that IMHO
the psyfun.2asym function is a bit of a kludge.  At some point,
I have a project to clean it up and have it estimate all parameters
by directly maximizing the likelihood.  I wrote psyfun.2asym in
order to take advantage of the fitting by glm and in order to
be able to take advantage with little extra programming of
using formula objects.  My goal, when I have more time,
is to write a more robust version that allows a lot more
flexibility in modeling the different parameters, a bit along
the lines of some of things that we did in the Yssaad & Knoblauch paper,
if you have seen that, but without resorting to Lindsey's packages.

( http://www.sbri.fr/files/publications/yssad%2006%20instrcomp.pdf )

THat doesn't answer your questions about lme4 and link functions.
As I said, I think that custom links will work (they used to) in
the development version, which means that they will at some future
time when the development version becomes the real one.  
I'm, of course, interested to know where the developers are
with that, though I understand perfectly that these things
do take time.  I don't think that you will be able to use glmer 
to estimate the asymptote parameters,
however, as these are outside the linear predictor.

best,

Ken

-- 
Kenneth Knoblauch
Inserm U846
Stem-cell and Brain Research Institute
Department of Integrative Neurosciences
18 avenue du Doyen Lépine
69500 Bron
France
tel: +33 (0)4 72 91 34 77
fax: +33 (0)4 72 91 34 61
portable: +33 (0)6 84 10 64 10
http://www.sbri.fr/members/kenneth-knoblauch.html