Perhaps I need to expand on the implications of what I said in my message. Because the Burnaby method removes dimensions from a matrix, the resulting matrix is supposed to be singular. That means that software that does not use some form of generalized inverse will complain about the covariance matrix being singular. In NTSYSpc I allow the user to specify a cutoff criterion. It should be small enough so that real dimensions are not discarded. Usually something like 1.0e-12 works well but that will depend on the variances of the variables you are using. Because of rounding error the last eigenvalue of the within covariance matrix will cannot be expected to be exactly zero.
An alternative strategy is to project the data onto its principal axes and discard axes corresponding to those with eigenvalues that are essentially zero. There should be as many of them as dimensions that were removed using the Burnaby method. Note that the Burnaby approach does not involve dividing by the geometric mean or adding a constant to the data. -------------------- F. James Rohlf - Dept. Ecology & Evolution SUNY, Stony Brook, NY 11794-5245 == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
