Advertisement

Measurement error in compositional data

  • J. Aitchison
  • S. M. Shen
Article

Abstract

Compositional data, consisting of vectors of proportions summing to unity such as the geochemical compositions of rocks, have proved difficult to analyze. Recently, the introduction of logistic and logratio transformations between the d-dimensional simplex and Euclidean space has allowed the use of familiar multivariate methods. The problem of how to model and analyze measurement errors in such data is approached through the concept of a perturbation of a composition. Such modeling allows investigation of the role of “rescaling,” quantification of measurement error, analysis of observor error, and assessment of the effect of measurement error on inferences.

Key words

compositional data logistic-normal distribution measurement error perturbation testing hypotheses of independence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchison, J., 1981, A new approach to null correlations of proportions: Jour. Internat. Assoc. Math. Geol., v. 13, p. 175–189.Google Scholar
  2. Aitchison, J., 1982, The statistical analysis of compositional data: Jour. Roy. Stat. Soc. Ser. B, v. 44, p. 139–177.Google Scholar
  3. Aitchison, J. and Lauder, I. J., 1979, Statistical diagnosis from imprecise data: Biometrika, v. 66, p. 475–483.Google Scholar
  4. Aitchison, J. and Shen, S. M., 1980, Logistic-normal distributions: Some properties and uses: Biometrika, v. 67, p. 261–272.Google Scholar
  5. Chayes, F., 1956, Petrographic modal analysis: John Wiley & Sons, Inc., New York.Google Scholar
  6. Chayes, F., 1971, Ratio correlation: University of Chicago Press, Chicago.Google Scholar
  7. Chayes, F. and Fairbairn, H. W., 1951. A test of the precision of thin-section analysis by point counter: Amer. Min., v. 36, p. 707–712.Google Scholar
  8. Chayes, F. and Kruskal, W., 1966. An approximate statistical test for correlations between proportions: Jour. Geol., v. 74, p. 692–702.Google Scholar
  9. Krumbein, W. C. and Tukey, J. W., 1956, Multivariate analysis of mineralogic, lithologic, and chemical composition of rock bodies: Jour. Sed. Pet., v. 26, p. 322–337.Google Scholar
  10. Morrison, D. F., 1976, Multivariate statistical methods: McGraw-Hill, New York.Google Scholar
  11. Thompson, R. N., Esson, J., and Duncan, A. C., 1972, Major element chemical variation in the Eocene lavas of the Isle of Skye, Scotland: Jour. Pet., v. 13, p. 219–253.Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • J. Aitchison
  • S. M. Shen
    • 1
  1. 1.Department of StatisticsUniversity of Hong KongHong Kong

Personalised recommendations