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