IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i8p3145-3158.html
   My bibliography  Save this article

Better biplots

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00317-4
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. 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.
    4. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.
    2. Bruno Ricca & Massimiliano Ferrara & Salvatore Loprevite, 2023. "Searching for an effective accounting-based score of firm performance: a comparative study between different synthesis techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3575-3602, August.
    3. Bastiaan Bruinsma & Marlene Mußotter, 2023. "A Move Forward: Exploring National Identity Through Non-linear Principal Component Analysis in Germany," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(1), pages 885-903, February.
    4. Svetlana Zhuchkova & Aleksei Rotmistrov, 2022. "How to choose an approach to handling missing categorical data: (un)expected findings from a simulated statistical experiment," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(1), pages 1-22, February.
    5. Takane, Yoshio & Jung, Sunho, 2009. "Regularized nonsymmetric correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3159-3170, June.
    6. Wenmei Yang & Adriano S. Koshiyama, 2019. "Assessing qualitative similarities between financial reporting frameworks using visualization and rules: COREP vs. pillar 3," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 26(1), pages 16-31, January.
    7. Michael Greenacre & Paul Lewi, 2009. "Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 29-54, April.
    8. Josse, Julie & Husson, François, 2016. "missMDA: A Package for Handling Missing Values in Multivariate Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i01).
    9. Menconi, M.E. & Tasso, S. & Santinelli, M. & Grohmann, D., 2020. "A card game to renew urban parks: Face-to-face and online approach for the inclusive involvement of local community," Evaluation and Program Planning, Elsevier, vol. 79(C).
    10. Ganiere, Pierre & Chern, Wen S. & Hahn, David E. & Chiang, Fu-Sung, 2004. "Consumer Attitudes towards Genetically Modified Foods in Emerging Markets: The Impact of Labeling in Taiwan," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association, vol. 7(3), pages 1-20.
    11. Julie Josse & Marie Chavent & Benot Liquet & François Husson, 2012. "Handling Missing Values with Regularized Iterative Multiple Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 29(1), pages 91-116, April.
    12. Michael Greenacre & Patrick J. F Groenen & Trevor Hastie & Alfonso Iodice d’Enza & Angelos Markos & Elena Tuzhilina, 2023. "Principal component analysis," Economics Working Papers 1856, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Tor Korneliussen & Michael Greenacre, 2016. "Information sources used by European tourists: A cross-cultural study," Economics Working Papers 1527, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Ganiere, Pierre & Chern, Wen S. & Hahn, David E., 2004. "Who Are Proponents And Opponents Of Genetically Modified Foods In The United States?," Working Papers 28315, Ohio State University, Department of Agricultural, Environmental and Development Economics.
    15. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3145-3158. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.