IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/53068.html
   My bibliography  Save this paper

A data-based power transformation for compositional data

Author

Listed:
  • T. Tsagris, Michail
  • Preston, Simon
  • T.A. Wood, Andrew

Abstract

Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we examine a more general transformation which includes both approaches as special cases. It is a power transformation and involves a single parameter�. The transformation has two equivalent versions. The �first is the stay-in-the-simplex version. This expression is the power transformation as de�fined by Aitchison (1986). The second version, which is a linear transformation of the stay-in-the-simplex, is a Box-Cox type transformation. We call the second version the isometric �alpha-transformation because of the multiplication with the Helmert sub-matrix. We discuss a parametric way of estimating the value of alpha�, which is maximization of its pro�le like-lihood (assuming multivariate normality of the transformed data) and the equivalence between the two versions is exhibited. Other ways include maximization of the correct classi�cation probability in discriminant analysis and maximization of the pseudo-R2 in linear regression. We examine the relationship between the transformation, the raw data approach and the isometric log-ratio transformation. Furthermore, we also de�fine a suitable family of metrics corresponding to the family of �alpha-transformation and consider the corresponding family of Fr�echet means.

Suggested Citation

  • T. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2011. "A data-based power transformation for compositional data," MPRA Paper 53068, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:53068
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/53068/1/MPRA_paper_53068.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. J. Baxter, 1995. "Standardization and Transformation in Principal Component Analysis, with Applications to Archaeometry," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 513-527, December.
    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. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Improved classi cation for compositional data using the $\alpha$-transformation," MPRA Paper 67657, University Library of Munich, Germany.
    2. Michail Tsagris & Simon Preston & Andrew T. A. Wood, 2016. "Improved Classification for Compositional Data Using the α-transformation," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 243-261, July.
    3. Tsagris, Michail, 2015. "Regression analysis with compositional data containing zero values," MPRA Paper 67868, University Library of Munich, Germany.
    4. Yannis Pantazis & Michail Tsagris & Andrew T. A. Wood, 2019. "Gaussian Asymptotic Limits for the α-transformation in the Analysis of Compositional Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 63-82, February.
    5. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Nonparametric hypothesis testing for equality of means on the simplex," MPRA Paper 72771, University Library of Munich, Germany.

    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. Chrys Caroni & Nedret Billor, 2007. "Robust Detection of Multiple Outliers in Grouped Multivariate Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1241-1250.
    2. Chae, Seong S. & Warde, William D., 2006. "Effect of using principal coordinates and principal components on retrieval of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1407-1417, March.
    3. Yannis Pantazis & Michail Tsagris & Andrew T. A. Wood, 2019. "Gaussian Asymptotic Limits for the α-transformation in the Analysis of Compositional Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 63-82, February.
    4. Chong, Alain Yee-Loong & Ooi, Keng-Boon & Sohal, Amrik, 2009. "The relationship between supply chain factors and adoption of e-Collaboration tools: An empirical examination," International Journal of Production Economics, Elsevier, vol. 122(1), pages 150-160, November.
    5. Rajesh Barik & Sanjaya Kumar Lenka, 2023. "Does financial inclusion control corruption in upper-middle and lower-middle income countries?," Asia-Pacific Journal of Regional Science, Springer, vol. 7(1), pages 69-92, March.
    6. Ceyhun Elgin & Gökçer Özgür & Kerem Cantekin, 2023. "Measuring green technology adoption across countries," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(1), pages 1-11, February.

    More about this item

    Keywords

    Compositional data; power transformation; alpha; Frechet mean;
    All these keywords.

    JEL classification:

    • C89 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other

    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:pra:mprapa:53068. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.