Possible extensions to the factorial ecology method: a note
The set of technical procedures commonly known as factorial ecology acts on a correlation matrix and so is based on variables standardised to the common base of zero mean and unit variance. This, according to the present note, is wasteful of the information on the data matrix being analysed. Alternative input matrices, to be treated as complementary to the correlation matrix, are suggested. These comprise firstly measures of variance - covariance, and secondly measures of the cross-products. Several examples of small data sets are used to illustrate the interpretative advantages of these matrices. No firm conclusions are offered, since further research is needed and unresolved problems still exist, but the possible extensions offered to the factorial ecology method seem worthy of serious consideration.
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