2021/08/24 by Vartan Choulakian, Choulakian, Vartan
Agricultural and Biological Sciences · #62H25 #62H30 #FOS: Computer and information sciences #Methodology (stat.ME) #Sensory Analysis and Statistical Methods
paper · pdf · doi:10.48550/arxiv.2108.10685
openalex publication_date 2021/08/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Collins(2002, 2011) raised a number of issues with regards to correspondence\nanalysis (CA), such as: qualitative information in a CA map versus quantitative\ninformation in the relevant contingency table; the interpretation of a CA map\nis difficult and its relation with the % of inertia (variance) explained. We\ntackle these issues by considering CA and taxicab CA (TCA) as a stepwise\nHotelling/Tucker decomposition of the cross-covariance matrix of the row and\ncolumn categories into four quadrants. The contents of this essay are: First,\nwe review the notion of quality/quantity in multidimensional data analysis as\ndiscussed by Benz 'ecri, who based his reflections on Aristotle. Second, we\nshow the importance of unravelling the interrelated concepts of\ndependence/heterogeneity structure in a contingency table; and to picture them\ntwo maps are needed. Third, we distinguish between intrinsic and extrinsic\nquality of a principal dimension; the intrinsic quality is based on the signs\nof the residuals in the four quadrants, hence to the interpretability.\nFurthermore, we provide quantifications of the intrinsic quality and use them\nto uncover structure in particular in sparse contingency tables. Finally, we\nemphasize the importance of looking at the residual cross-covariance values at\neach iteration.\n