ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Revisiting Mixture Design Experiment from a Compositional Point of View

12 September 2016, 12:10 – 12:30

Abstract

Submitted by
Marina Vives-Mestres
Authors
Marina Vives-Mestres (Universitat de Girona), Josep Antoni Martín-Fernández (Universitat de Girona)
Abstract
The aim of this talk is to share with researchers and applied scientists the questions that arise when revisiting the fundamentals of mixture design experiment from a compositional point of view. Mixture design deal with experiments with factors that are ingredients in a mixture. Compositional Data (CoDa) analysis has been proved to be useful when dealing with data living in a restricted space, as the proportions of ingredients are. Methods such as principal component analysis, cluster analysis, linear discriminant analysis and linear regression models have been developed for CoDa based on the principle of working on log-ratio coordinates (log ratios of components). Those techniques are plenty consistent with the characteristics of CoDa.
J. Aitchison in 1984 introduced the log contrast models for experiments with mixtures, which are linear models in the log proportions. We revisit the proposed model and update its results with the latest advances in the CoDa field, mainly regarding regression models and differential calculus on the simplex. We follow the tracks of that publication with some results on optimal log contrast designs. We finally analyze the difficulties when traditional methods are used with mixtures and point out the solutions proposed by the log ratio approach.

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