[R-sig-ME] lmer probit fit

[Ben Bolker]

Ken Knoblauch <ken.knoblauch at ...> writes:

> 
  [snip snip]

> 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.

 As I answered off-list, the development version does still allow
custom link functions (and should continue to).  I have an example
posted at http://rpubs.com/bbolker/4082 that uses a custom link function
to fit a model with a link function of the form

μ=(plogis(η)^e,

where e is an exposure time.

As Ken says, you would have to fit the asymptote parameters by setting up
an "outer loop" that fits a glmer model for specified values of the
asymptote parameters and does optimization over that space.  With the
development version, it *might* be possible (I'm not sure) to extract
a deviance function and optimize over the variance-covariance and
link-function parameters in one go, although now that I think about it
I'm not sure whether that will really work ....