An integrated development of correspondence analysis with applications to environmental data.

Abstract

Correspondence Analysis (CA) is a multivariate method that has been developed from different perspectives, for a variety of purposes. There have been reservations on the use of CA for data measured on a ratio scale, which is the usual type of data encountered in the earth and environmental sciences. These reservations have to do to with the usual approaches to CA, which are restricted to count type data, and with the actual nature of CA, as being either an exploratory or an inferential method. We present CA as an exploratory technique that provides an algebraic model for data matrices with non negative entries. This model can be used for dimension reduction or for pattern recognition purposes. As with any other exploratory technique, the use of CA has to be supplemented with diagnostics and post-analysis, if we are to have some measure of confidence in the results. We provide a set of diagnostics and a methodology for post-analysis, and we test its use on three example data sets from the earth and environmental sciences.