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Statistica Sinica 17(2007), 1417-1440





ON THE DESCRIPTION AND IDENTIFIABILITY ANALYSIS

OF EXPERIMENTS WITH MIXTURES


Hugo Maruri-Aguilar$^{1}$, Roberto Notari$^2$ and Eva Riccomagno$^{2,3}$


$^{1}$London School of Economics, $^{2}$Politecnico di Torino
and $^3$The University of Warwick


Abstract: In a mixture experiment the collinearity problems, implied by the sum to one functional relationship among the factors, have strong consequences on the identification and analysis of regression models for such designs. Here to address these problems, mixture designs are represented as sets of homogeneous polynomials. Techniques from computational commutative algebra are employed to deduce generalized confounding relationships on power products, and to determine families of identifiable models.



Key words and phrases: Algebraic statistics, cone of a mixture design, experiments with mixtures, fan of a design, regression analysis.

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