On Tue, 17 Dec 2013 15:21:57 +0000, Ravi Varadhan wrote: RV> The optimization algorithms did converge to a limit point. But, RV> not to a stationary point, i.e. a point in parameter space where RV> the first and second order KKT conditions are satisfied. If you RV> check the gradient at the solution, you will see that it is quite RV> large in magnitude relative to 0. So, why did the algorithms RV> declare convergence? Convergence is based on absolute change in RV> function value and/or relative change in parameter values between RV> consecutive iterations. This does not ensure that the KKT RV> conditions are satisfied.
This makes sense to me. Although I have indicated other possible explanations, the most plausable was that the selected point is not at a minimum, as you confirmed. As in many other cases, the stopping rule of an optimizer can be a delicate issue. However, since optim computes (on request) the Hessian matrix, a check on its positive-definiteness seems to me a reasonable check to be made by optim before declaring successful convergence. RV> RV> Now, to the real issue: your problem is ill-posed. As you can RV> tell from the eigenvalues of the hessian, they vary over 9 orders RV> of magnitude. This may indicate a problem with the data in that RV> the log-likelihood is over-parametrized relative to the information RV> in the data set. Get a better data set or formulate a simpler RV> model, and the problem will disappear. RV> I had noticed this aspect of the relative order of magnitudes of the eigenvalues. The model is not over-parameterized (in a formal sense), but in some cases maximization of the log-likelihood can be a delicate issue, yes. I am not specifically interested in fitting these data, nor any other data. I am working on an update of package 'sn'. Thanks for your informative reply. Adelchi -- Adelchi Azzalini <azzal...@stat.unipd.it> Dipart.Scienze Statistiche, Università di Padova, Italia tel. +39 049 8274147, http://azzalini.stat.unipd.it/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
