1. A Short History of Compositional Data Analysis

  1. Vera Pawlowsky-Glahn2 and
  2. Antonella Buccianti3
  1. John Bacon-Shone

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch1

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Bacon-Shone, J. (2011) A Short History of Compositional Data Analysis, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch1

Editor Information

  1. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 3

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. Social Sciences Research Centre, The University of Hong Kong, Hong Kong

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462

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Keywords:

  • compositional data analysis - elements of composition, non-negative and sum to unity;
  • compositional data analysis - and problem of ‘spurious correlation’ between ratios of variables;
  • Chayes (1960), and explicit connection - Pearson's work and compositional data;
  • log and log-ratio transforms - and McAlister of log-normal distributions to model data;
  • public introduction of properties of logistic-normal distribution - in Aitchison and Shen (1980);
  • Dirichlet distribution, restrictive properties - as complete subcompositional independence;
  • generalization of logistic-normal distribution - to additive logistic skew-normal distribution on the simplex;
  • subcompositional dependence - logistic-normal distribution, modelling useful dependence structures;
  • key question for using log-ratio transformations - choosing the divisor;
  • mixtures, important application - of compositional data, covariate determining a mixture

Summary

This chapter contains sections titled:

  • Introduction

  • Spurious Correlation

  • Log and Log-Ratio Transforms

  • Subcompositional Dependence

  • alr, clr, ilr: Which Transformation to Choose?

  • Principles, Perturbations and Back to the Simplex

  • Biplots and Singular Value Decompositions

  • Mixtures

  • Discrete Compositions

  • Compositional Processes

  • Structural, Counting and Rounded Zeros

  • Conclusion

  • Acknowledgement

  • References