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

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