Ratio Maps and Correspondence Analysis

UPF, Economics and Business Working Paper No. 598

Posted: 4 Sep 2002

See all articles by Michael Greenacre

Michael Greenacre

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional coherence, which assures that results are invariant to considering subsets of the composition. The second approach, correspondence analysis, is based on the chi-square approach to contingency table analysis. A cornerstone of correspondence analysis is the principle of distributional equivalence, which assures invariance in the results when rows or columns with identical conditional proportions are merged. Both methods may be described as singular value decompositions of appropriately transformed matrices. Correspondence analysis includes a weighting of the rows and columns proportional to the margins of the table. If this idea of row and column weights is introduced into the logratio biplot, we obtain a method which obeys both principles of subcompositional coherence and distributional equivalence.

Keywords: Biplot, compositional data, contingency tables, distributional equivalence, logratio transformation, singular value decomposition, subcompositional coherence

JEL Classification: C19, C88

Suggested Citation

Greenacre, Michael John, Ratio Maps and Correspondence Analysis. UPF, Economics and Business Working Paper No. 598, Available at SSRN: https://ssrn.com/abstract=311556

Michael John Greenacre (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
34 93 542 25 51 (Phone)
34 93 542 17 46 (Fax)

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