Correspondence analysis of raw data

Abstract

Correspondence analysis has found extensive use in the social and environmental sciences as a method for visualizing the patterns of association in a table of frequencies. Inherent to the method is the expression of the frequencies in each row or each column relative to their respective totals, and it is these sets of relative frequencies (called profiles) that are visualized. This "relativization" of the frequencies makes perfect sense in social science applications where sample sizes vary across different demographic groups, and so the frequencies need to be expressed relative to these different bases in order to make these groups comparable. But in ecological applications sampling is usually performed on equal areas or equal volumes so that the absolute abundances of the different species are of relevance, in which case relativization is optional. In this paper we define the correspondence analysis of raw abundance data and discuss its properties, comparing these with the regular correspondence analysis based on relative abundances.