[R] problems with numerical optimisation

Spencer Graves spencer.graves at pdf.com
Wed Mar 12 16:45:56 CET 2003

Do you compute the singular value decomponsition of your gradients?

Unless you compute a marginal likelihood using Monte Carlo integration, 
I would expect convergence problems to be evident in the range of the 
absolute values of the singular values of the gradients:  If the 
smallest is less than, say, 1e-15 times the largest, you are chasing 
round-off, as discussed years ago by Box, Hunter, MacGregor, and Erjavec 
(1973) "Some problems associated with the analysis of multiresponse 
data", Technometrics, 15:  33-51.

(If you are using Monte Carlo integration, then I would ask if you've 
considered Markov Chain Monte Carlo?)

Hope this helps,
Spencer Graves

Ott Toomet wrote:
> Dear list,
> this is not a particular R question but perhaps someone can help.
> I am running a maximum likelihood estimation (competing risk duration
> model with unobserved heterogeneity) on 30 different datasets.  The
> problem is that on 2 datasets the model does not converge.  I am
> interested if there are any methods, based on the gradients or (an
> approximation of) the hessian which helps to determine what is the
> problem.  Can anybody recommend a good textbook about numerical
> optimisation?
> Currently I am using 100 BFGS iterations + 100 BHHH iterations and I
> have programmed analytic gradients.  The fool-proof method of
> excluding the variables one-by-one and simplifying the structure is
> quite a slow and not particularily insightsful.
> Thanks in advance
> Ott
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