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