Correspondence analysis of raw data

Correspondence analysis has found extensive use in ecology, archaeology, linguistics, and the social sciences as a method for visualizing the patterns of association in a table of frequencies or nonnegative ratio-scale data. Inherent to the method is the expression of the data in each row or each column relative to their respective totals, and it is these sets of relative values (called profiles) that are visualized. This "relativization" of the data makes perfect sense when the margins of the table represent samples from subpopulations of inherently different sizes. But in some ecological applications sampling is performed on equal areas or equal volumes so that the absolute levels of the observed occurrences may be of relevance, in which case relativization may not be required. In this paper, I define the correspondence analysis of the raw "unrelativized" data and discuss its properties, comparing this new method to regular correspondence analysis and to a related variant of nonsymmetric correspondence analysis.