Taxicab Correspondence Analysis and Taxicab Logratio Analysis: A Comparison on Contingency Tables and Compositional Data

Abstract

In this paper, we attempt to see further by relating theory with practice: First, we review the principles on which three interrelated well developed methods for the analysis and visualization of contingency tables and compositional data are erected: Correspondence analysis based on Benzécri’s principle of distributional equivalence, Goodman’s RC association model based on Yule’s principle of scale invariance, and compositional data analysis based on Aitchison’s principle of subcompositional coherence. Second, we introduce a novel index named intrinsic measure of the quality of the signs of the residuals for the choice of the method. The criterion is based on taxicab singular value decomposition, on which the package TaxicabCA in R is developed. We present a minimal R script that
can be executed to obtain the numerical results and the maps in this paper. Third, we introduce a flexible method based on the novel index for the choice of the constant to be added to contingency tables with zero counts so that logratio methods can be applied.