A Comparison of Different Methods for Representing Categorical Data

Abstract

We first compare correspondence analysis, which uses chi-square distance, and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these two approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. We also make comparisons with the logratio approach based on compositional data. These three methods of representation can produce quite similar results. Two illustrative examples are given.

Keywords:

• Chi-square distance
• Correspondence analysis
• Compositional data
• Hellinger distance
• Multidimensional scaling

Mathematics Subject Classification:

• 62-09
• 62H17
• 62H25

Acknowledgments

Work supported in part by grants Ministerio de Educacion y Ciencia MTM 2004-00440 and Generalitat de Catalunya CUR 2001 SGR 00067 and CUR 2005 SGR 00871.