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.