×

The role of perturbation in compositional data analysis. (English) Zbl 1069.62003

Summary: In standard multivariate statistical analysis, common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. Against the background of two motivating experimental studies in the food industry, involving the compositions of cow’s milk and chicken carcasses, this paper emphasizes the importance of recognizing this fundamental operation of change in the associated simplex sample space. Well-defined hypotheses about the nature of any compositional effect can be expressed, for example, in terms of perturbation values and subcompositional stability and testing procedures developed. These procedures are applied to lattices of such hypotheses in the two practical situations. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis.

MSC:

62-07 Data analysis (statistics) (MSC2010)
62J15 Paired and multiple comparisons; multiple testing
62P30 Applications of statistics in engineering and industry; control charts
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aitchison J, Journal of the Royal Statistical Society B 44 pp 139– (1982)
[2] Aitchison J, The statistical analysis of compositional data (1986) · Zbl 0688.62004
[3] Aitchison J, Proceedings of the Third Annual Conference of the International Association for Mathematical Geology pp 3–
[4] Aitchison J, Contemporary Mathematics Series 287. Providence, in: Algebraic methods in statistics and probability pp 1– (2001)
[5] Aitchison J, Terra Nostra, special issue: Eighth Annual Conference of the International Association for Mathematical Geology 3 pp 387– (2002)
[6] Aitchison J, Terra Nostra, special issue: Eighth Annual Conference of the International Association for Mathematical Geology 3 pp 381– (2002)
[7] Aitchison J, Biometrika 67 pp 261– (1980) · Zbl 0433.62012
[8] Aitchison J, Proceedings of IAMG’98 - The Fourth Annual Conference of the International Association for Mathematical Geology pp 499–
[9] Anderson TW, An introduction to multivariate statistical analysis (1958)
[10] Chang TC, Annals of Statistics 14 pp 907– (1988) · Zbl 0605.62079
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.