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A comparison of different methods for representing categorical data. (English) Zbl 1093.62061

Summary: We first compare correspondence analysis, which uses chi-square distance, and an alternative approach using the 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 log-ratio approach based on compositional data. These three methods of representation can produce quite similar results. Two illustrative examples are given.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62H17 Contingency tables
62-07 Data analysis (statistics) (MSC2010)
65C60 Computational problems in statistics (MSC2010)
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