Skip to main content

A Review of Compositional Data Analysis

  • Chapter
  • First Online:
Geostatistics for Compositional Data with R

Part of the book series: Use R! ((USE R))

Abstract

This chapter provides the concepts from compositional data analysis required to prepare compositional data for geostatistical treatment. Specifically we define the term closure, its rationale and caveats, and the various ways of escaping from its curse, i.e. the various forms of log-ratio transformation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    There is an incompatible function called select in package “MASS”. To ensure using the right function in such cases, the syntax package::command is useful.

  2. 2.

    Note the use of the pipe %>% from package “magrittr”, where X %>% fun is equivalent to fun(X). Piping is a comfortable way of nesting functions in R, easy to write and to read: from the data set australia, select some variables, do absolute values, compute the row sums and return their summaries.

  3. 3.

    Gangue: part of a mineral deposit considered as not valuable.

References

  • Aitchison, J. (1986). The statistical analysis of compositional data (416 pp.). Monographs on Statistics and Applied Probability. London, UK: Chapman & Hall Ltd. (Reprinted in 2003 with additional material by The Blackburn Press).

    Google Scholar 

  • Aitchison, J. (1997). The one-hour course in compositional data analysis or compositional data analysis is simple. In V. Pawlowsky-Glahn (Ed.), Proceedings of IAMG’97 - The III Annual Conference of the Int. Association for Mathematical Geology, Volume I, II and addendum, Barcelona (E) (pp. 3–35, 1100 pp.). International Center for Numerical Methods in Engineering (CIMNE), Barcelona (E).

    Google Scholar 

  • Barceló-Vidal, C. (2000). Fundamentación matemática del análisis de datos composicionales (77 pp.). Number IMA 00-02-RR.

    Google Scholar 

  • Barceló-Vidal, C., Martín-Fernández, J. A., & Pawlowsky-Glahn, V. (2001). Mathematical foundations of compositional data analysis. In G. Ross (Ed.), Proceedings of IAMG’01 – The VII Annual Conference of the Int. Association for Mathematical Geology, Cancun (Mex), 20 p.

    Google Scholar 

  • Billheimer, D., Guttorp, P., & Fagan, W. (2001). Statistical interpretation of species composition. Journal of the American Statistical Association, 96(456), 1205–1214.

    Article  MathSciNet  Google Scholar 

  • Boogaart, K. G. v. d., & Tolosana-Delgado, R. (2008). “compositions”: a unified R package to analyze compositional data. Computers and Geosciences, 34(4), 320–338.

    Google Scholar 

  • Boogaart, K. G. v. d., & Tolosana-Delgado, R. (2013). Analysing compositional data with R (280 pp.). Heidelberg: Springer.

    Google Scholar 

  • Boogaart, K. G. v. d., Tolosana-Delgado, R., & Bren, M. (2011). The compositional meaning of a detection limit. In J. J. Egozcue, R. Tolosana-Delgado, M. I. Ortego (Eds.), Proceedings of the 4th International Workshop on Compositional Data Analysis (2011). CIMNE, Barcelona, Spain. ISBN:978-84-87867-76-7.

    Google Scholar 

  • Buccianti, A., Mateu-Figueras, G., & Pawlowsky-Glahn, V. E. (2006). Compositional data analysis in the geosciences: From theory to practice. Special publications (Vol. 264, 212 pp.). London: Geological Society.

    Google Scholar 

  • Butler, J. C. (1978). Visual bias in R-mode dendrograms due to the effect of closure. Mathematical Geology, 10(2), 243–252.

    Article  Google Scholar 

  • Butler, J. C. (1979). The effects of closure on the moments of a distribution. Mathematical Geology, 11(1), 75–84.

    Article  Google Scholar 

  • Chayes, F. (1960). On correlation between variables of constant sum. Journal of Geophysical Research, 65(12), 4185–4193.

    Article  Google Scholar 

  • Chayes, F., & Trochimczyk, J. (1978). An effect of closure on the structure of principal components. Mathematical Geology, 10(4), 323–333.

    Article  Google Scholar 

  • Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3), 279–300.

    Article  MathSciNet  Google Scholar 

  • Martín-Fernández, J. A., Palarea-Albadalejo, J., & Gómez-García, J. (2003). Markov chain Montecarlo method applied to rounding zeros of compositional data: first approach. In S. Thió-Henestrosa, J. A. Martín-Fernández (Eds.), Proceedings of CoDaWork’03, The 1st Compositional Data Analysis Workshop, Girona (E). Universitat de Girona. ISBN:84-8458-111-X. http://ima.udg.edu/Activitats/CoDaWork2003/.

    Google Scholar 

  • Palarea-Albaladejo, J., & Martín-Fernández, J. A. (2008). A modified EM alr-algorithm for replacing rounded zeros in compositional data sets. Computers and Geosciences, 34(8), 2233–2251.

    Article  Google Scholar 

  • Pawlowsky, V. (1984). On spurious spatial covariance between variables of constant sum. Science de la Terre, Sér. Informatique, 21, 107–113.

    Google Scholar 

  • Pawlowsky, V. (1989). Cokriging of regionalised compositions. Mathematical Geology, 21(5), 513–521.

    Article  Google Scholar 

  • Pawlowsky-Glahn, V., & Egozcue, J. J. (2001). Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment (SERRA), 15(5), 384–398.

    Article  Google Scholar 

  • Pawlowsky-Glahn, V., Egozcue, J. J., & Lovell, D. (2015). Tools for compositional data with a total. Statistical Modelling, 15(2), 175–190.

    Article  MathSciNet  Google Scholar 

  • Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R. (2015). Modeling and analysis of compositional data (272 pp.). Chichester, UK: John Wiley & Sons.

    Google Scholar 

  • Pearson, K. (1897). Mathematical contributions to the theory of evolution. On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the Royal Society of London, LX, 489–502.

    Google Scholar 

  • Shurtz, R. F. (2003). Compositional geometry and mass conservation. Mathematical Geology, 35(8), 927–937.

    Article  Google Scholar 

  • Tjelmeland, H., & Lund, K. V. (2003). Bayesian modelling of spatial compositional data. Journal of Applied Statistics, 30(1), 87–100.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tolosana-Delgado, R., Mueller, U. (2021). A Review of Compositional Data Analysis. In: Geostatistics for Compositional Data with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-030-82568-3_2

Download citation

Publish with us

Policies and ethics