Hi Murray, A likely reason for the observed information matrix not to be positive definite is the inaccuracies in the numerical estimation of the scores. You might want to try more accurate methods (e.g. Richardson extrapolation) for approximating numerical derivatives, such as available in the package "numDeriv". This would likely alleviate your problem.
Please disregard my advice, if you are using analytical, closed-form expressions for the scores. In this case, you might try the approaches suggested by Martin. It is also likely that your likelihood is quite flat around the MLE, which, of course, means that you don't have enough information in your data to separate the mixtures and estimate 179 parameters. Have you tried estimating with fewer mixture components and then working your way up? Also, with this many parameters and relatively few data points, can you ensure that you have a "global" maximum? Ravi. ---------------------------------------------------------------------------- ------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Martin Maechler Sent: Wednesday, December 05, 2007 4:42 AM To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Subject: Re: [R] Calculating large determinants >>>>> "MJ" == maj <[EMAIL PROTECTED]> >>>>> on Wed, 5 Dec 2007 14:18:23 +1300 (NZDT) writes: MJ> I apologise for not including a reproducible example MJ> with this query but I hope that I can make things clear MJ> without one. MJ> I am fitting some finite mixture models to data. Each MJ> mixture component has p parameters (p=29 in my MJ> application) and there are q components to the MJ> mixture. The number of data points is n ~ 1500. MJ> I need to select a good q and I have been considering model selection MJ> methods suggested in Chapter 6 of MJ> @BOOK{mp01, MJ> author = {McLachlan, G. J. and Peel, D.}, MJ> title = {Finite Mixture Models}, MJ> publisher = {Wiley}, MJ> address = {New York}, MJ> year = {2001} MJ> } MJ> One of these methods involves an "empirical information MJ> matrix" which is the matrix of products of parameter MJ> scores at the observation level evaluated at the MLE and MJ> summed over all observations. For example a six-component MJ> mixture will have 6 - 1 + 29*6 = 179 parameters. So for MJ> observation i I form the 179 by 179 matrix of products of MJ> scores and sum these up over all 1500-odd observations. MJ> Actually it is the log of the determinant of the resultant matrix that I MJ> really need rather than the matrix itself. I am seeking advice on what may MJ> be the best way to evaluate this log(det()). I have been encountering MJ> problems using MJ> determinant(SS,logarithm=TRUE) MJ> and eigen(SS,only.values = TRUE)$values MJ> shows some negative eigenvalues. which is a problem? In that case I guess your problem is that you want to estimate a positive definite matrix S but your estimate S^ is not quite positive definite. Function posdefify() in CRAN package "sfsmisc" provides an old cheap solution to this problem, where nearPD() in package 'Matrix' (based on a donation from Jens Oehlschlaegel) provides a more sophisticated algorithm for this problem. If you really only need the eigenvalues of the "corrected" matrix, you might want to abbreviate the nearPD() function by just returning the final 'd' vector of eigenvalues. MJ> Advice will be gratefully received! I'll be glad to hear if and how you'd use one of these two functions. Martin Maechler, ETH Zurich MJ> Murray Jorgensen ______________________________________________ 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. ______________________________________________ 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.
