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A parametric approach to correspondence analysis. (English) Zbl 1096.62061

Summary: We compare correspondence analysis (CA) and an alternative approach using the Hellinger distance (HD), for representing categorical data in a contingency table. As both methods may be appropriate, we introduce a parameter and define a generalized version of correspondence analysis (GCA) which contains CA and HD as particular cases. Comparison with alternative approaches are performed. We propose a coefficient which globally measures the similarity between CA and GCA, which can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions on the difference between both representations. Two criteria for choosing the best value of the parameter are proposed.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62H17 Contingency tables
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