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

From: Andrew Robinson <A.Robinson_at_ms.unimelb.edu.au>
Date: Sat 15 Oct 2005 - 11:15:10 EST

Dear Hans,

these are interesting points. I guess that I'm approaching it from the point of view of a decision: I'd be more comfortable using a fitting routine that has stability under a wide range of identifiable circumstances. Obtaining the MLE exactly in any instance is a function of the data and the model. So, to me, obtaining it well in one instance is less interesting than obtaining it well in a wide array of instances.

In short, I guess that I'm connecting the numerical routines with the actual data, in the sense that that's what they operate on, and therefore the statistical properties of the overall approach. Perhaps I'm being naive!

Cheers,

Andrew

On Fri, Oct 14, 2005 at 02:55:59PM +0200, Hans Julius Skaug wrote:
>
> 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
>
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-- 
Andrew Robinson
Senior Lecturer in Statistics                       Tel: +61-3-8344-9763
Department of Mathematics and Statistics            Fax: +61-3-8344-4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson_at_ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au

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Received on Sat Oct 15 11:26:21 2005

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