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Abstract
In multivariate graphics, correlations between variables are often approximated by the cosines of the angles between vectors. In practice, it is difficult to reliably estimate correlations from such displays by eye. In this article, we therefore develop new graphs, called linear-angle correlation plots, that have a linear relationship between correlation and angle, and from which correlation coefficients are read off more easily. Several multivariate datasets are used to illustrate the proposed graphs. The goodness-of-fit properties of the new graphs are compared with standard multivariate methods such as principal component analysis and principal factor analysis. Cosine-based plots typically gave the poorest approximation to the correlation matrix. A linear interpretation rule for the angle often improved the fit. The best fit was generally obtained by principal factor analysis using scalar products to approximate correlations.
ACKNOWLEDGMENTS
This study was supported by grants ECO2011-28875 and CODARSS MTM2009-13272 of the Spanish Ministry of Education and Science. The author thanks two anonymous referees for their comments on the article.
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Jan Graffelman
Jan Graffelman, Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, Barcelona 08028, Spain (E-mail: [email protected]).