Towards standard errors for biplots via bootstrapping: dealing with re-ordering of eigen-values and switching of the signs of loadings in bootstrapped samples.
by
Maaike Bendall
Crop and Food Research

The bootstrapped estimate of the variation in a principal component's loadings may be artificially inflated when the signs of all the loadings are reversed, and when the eigen-value for a particular principal component is not the 'nth' largest in all the bootstrapped samples. Because it is too time-consuming to inspect all the bootstrapped samples, a general and automatic method for dealing with these problems is needed. The inflation of the estimate of variation in loadings can be corrected within a computer program by inspecting the correlations between bootstrapped principal components. However, if the principal components are very unstable, the corrections become unreliable and the user is directed to a diagnostic graph, which shows the distribution of the correlations between bootstrapped principal components for a particular principal component. Departures in the shape of the distribution from the ideal reveal the likely cause for, and the degree of, instability in the principal component.

Date received: August 29, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajn-17.