[R] Calculating large determinants

From: <maj_at_stats.waikato.ac.nz>
Date: Wed, 5 Dec 2007 14:18:23 +1300 (NZDT)

I apologise for not including a reproducible example with this query but I hope that I can make things clear without one.

I am fitting some finite mixture models to data. Each mixture component has p parameters (p=29 in my application) and there are q components to the mixture. The number of data points is n ~ 1500.

I need to select a good q and I have been considering model selection methods suggested in Chapter 6 of

  author    = {McLachlan, G. J. and Peel, D.},
  title     = {Finite Mixture Models},
  publisher = {Wiley},
  address   = {New York},
  year      = {2001}


One of these methods involves an "empirical information matrix" which is the matrix of products of parameter scores at the observation level evaluated at the MLE and summed over all observations. For example a six-component mixture will have 6 - 1 + 29*6 = 179 parameters. So for observation i I form the 179 by 179 matrix of products of scores and sum these up over all 1500-odd observations.

Actually it is the log of the determinant of the resultant matrix that I really need rather than the matrix itself. I am seeking advice on what may be the best way to evaluate this log(det()). I have been encountering problems using

and eigen(SS,only.values = TRUE)$values

shows some negative eigenvalues.

Advice will be gratefully received!

Murray Jorgensen

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