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Better biplots

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  • Blasius, Jörg
  • Eilers, Paul H.C.
  • Gower, John

Abstract

The elements of a biplot are (i) a set of axes representing variables, usually concurrent at the centroid of (ii) a set of points representing samples or cases. The axes are (approximations to) conventional coordinate axes, and therefore may be labelled and calibrated. Especially when there are many points (perhaps several thousand) the whole effect can be very confusing but this may be mitigated by: 1. Giving a density representation of the points. 2. While respecting the calibrations, moving the axes to new positions more remote from the points, and possibly jointly rotating axes and points. 3. The use of colour -- when permissible. 4. Choosing more than one centre of concurrency. The principles are quite general but we illustrate them by examples of the Categorical Principal Component Analysis of the responses to questions concerning migration in Germany. This application introduces the additional interest of representing ordered categorical variables by irregularly calibrated axes.

Suggested Citation

  • Blasius, Jörg & Eilers, Paul H.C. & Gower, John, 2009. "Better biplots," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3145-3158, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3145-3158
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    References listed on IDEAS

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    1. Jörg Blasius & John Gower, 2005. "Multivariate Prediction with Nonlinear Principal Components Analysis: Application," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(4), pages 373-390, August.
    2. John Gower & Jörg Blasius, 2005. "Multivariate Prediction with Nonlinear Principal Components Analysis: Theory," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(4), pages 359-372, August.
    3. Michael Greenacre & Rafael Pardo, 2006. "Subset Correspondence Analysis," Sociological Methods & Research, , vol. 35(2), pages 193-218, November.
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    1. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    2. Vines, S.K., 2015. "Predictive nonlinear biplots: Maps and trajectories," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 47-59.
    3. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).
    4. Wieringa, Jaap & Dijksterhuis, Garmt & Gower, John & van Perlo, Frederieke, 2009. "Generalised Procrustes Analysis with optimal scaling: Exploring data from a power supplier," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4546-4554, October.

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