I tried crossprod(S) but the results were identical. The term -0.5*log(det(S)) is a complexity penalty meant to make it unattractive to include too many components in a finite mixture model. This case was for a 9-component mixture. At least up to 6 components the determinant behaved as expected and increased with the number of components.
Thanks for your comments. > Hmm, S'S is numerically singular. crossprod(S) would be a better way to > compute it than crossprod(S,S) (it does use a different algorithm), but > look at the singular values of S, which I suspect will show that S is > numerically singular. > > Looks like the answer is 0. > > > On Sun, 9 Dec 2007, [EMAIL PROTECTED] wrote: > >> I thought I would have another try at explaining my problem. I think >> that >> last time I may have buried it in irrelevant detail. >> >> This output should explain my dilemma: >> >>> dim(S) >> [1] 1455 269 >>> summary(as.vector(S)) >> Min. 1st Qu. Median Mean 3rd Qu. Max. >> -1.160e+04 0.000e+00 0.000e+00 -4.132e-08 0.000e+00 8.636e+03 >>> sum(as.vector(S)==0)/(1455*269) >> [1] 0.8451794 >> # S is a large moderately sparse matrix with some large elements >>> SS <- crossprod(S,S) >>> (eigen(SS,only.values = TRUE)$values)[250:269] >> [1] 9.264883e+04 5.819672e+04 5.695073e+04 1.948626e+04 >> 1.500891e+04 >> [6] 1.177034e+04 9.696327e+03 8.037049e+03 7.134058e+03 >> 1.316449e-07 >> [11] 9.077244e-08 6.417276e-08 5.046411e-08 1.998775e-08 >> -1.268081e-09 >> [16] -3.140881e-08 -4.478184e-08 -5.370730e-08 -8.507492e-08 >> -9.496699e-08 >> # S'S fails to be non-negative definite. >> >> I can't show you how to produce S easily but below I attempt at a >> reproducible version of the problem: >> >>> set.seed(091207) >>> X <- runif(1455*269,-1e4,1e4) >>> p <- rbinom(1455*269,1,0.845) >>> Y <- p*X >>> dim(Y) <- c(1455,269) >>> YY <- crossprod(Y,Y) >>> (eigen(YY,only.values = TRUE)$values)[250:269] >> [1] 17951634238 17928076223 17725528630 17647734206 17218470634 >> 16947982383 >> [7] 16728385887 16569501198 16498812174 16211312750 16127786747 >> 16006841514 >> [13] 15641955527 15472400630 15433931889 15083894866 14794357643 >> 14586969350 >> [19] 14297854542 13986819627 >> # No sign of negative eigenvalues; phenomenon must be due >> # to special structure of S. >> # S is a matrix of empirical parameter scores at an approximate >> # mle for a model with 269 paramters fitted to 1455 observations. >> # Thus, for example, its column sums are approximately zero: >>> summary(apply(S,2,sum)) >> Min. 1st Qu. Median Mean 3rd Qu. Max. >> -1.148e-03 -2.227e-04 -7.496e-06 -6.011e-05 7.967e-05 8.254e-04 >> >> I'm starting to think that it may not be a good idea to attempt to >> compute >> large information matrices and their determinants! >> >> 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. >> > > -- > Brian D. Ripley, [EMAIL PROTECTED] > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > University of Oxford, Tel: +44 1865 272861 (self) > 1 South Parks Road, +44 1865 272866 (PA) > Oxford OX1 3TG, UK Fax: +44 1865 272595 > > ______________________________________________ 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.
