[R] Do Users of Nonlinear Mixed Effects Models Know Whether Their Software Really Works?

[Hans Julius Skaug]

Dear Andrew and R-list,

I guess Fournier is addressing the properties of the numerical routines
underlying the various packages, not the statistical properties of the MLE itself.
For this purpose using a small tricky dataset makes sense. Clearly,
a true unique MLE exists (except in pathological cases), defined
as the maximizer of the marginal likelihood, evaluated using perfect precision numerical integration.
Since all the packages are aiming at calculating the MLE, it makes sense to compare them 
on this ground. I think the point in Lesaffre et al is that the default settings of many packages may 
give you something very different from the true MLE.


best regards,

hans


> 1) If I understand correctly, you're trying to estimate parameters
>    from a real dataset.  Why not try a simulated dataset, where you
>    know exactly what the true values (and parameter distributions)
>    are?
> 
> 2) Furthermore, an argument from one dataset isn't very
>    convincing. The sample size for inference is too small.  Why not
>    repeat this procedure many times, sampling from the same base
>    model? 
> 
> 3) Then, you could also vary the structure of the underlying model
>    systematically, and assess the comparison of fits as a function of
>    the underlying model/dataset nexus.
> 
> 4) Next, a problem with the example (as I understand it) is that
>    although you've computed what you call exact MLE's, I think that
>    they're exact when conditioned on the model.  Are they very robust
>    to model misspecification?  (I mean beyond large-sample theory).
> 
> 5) Finally, of course, then making the scripts available for forsenic
>    investigations.
> 
> Cheers,
> 
> Andrew

_____________________________
Hans Julius Skaug

Department of Mathematics
University of Bergen
Johannes Brunsgate 12
5008 Bergen
Norway
ph. (+47) 55 58 48 61