V-optimal mixture designs for the qth degree model

This paper revisits the problem of finding continuous V-optimal mixture designs for the qth degree model. For this problem, Liu and Neudecker [10] present general analytical expressions for the weights of the points of the simplex-centroid design and claim that the resulting designs are V-optimal. F...

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Bibliographic Details
Published in:Chemometrics and intelligent laboratory systems 2014-08, Vol.136, p.173-178
Main Authors: Goos, Peter, Syafitri, Utami
Format: Article
Language:English
Subjects:
I-optimality
IV-optimality
Q-optimality
Simplex-centroid design
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Summary:This paper revisits the problem of finding continuous V-optimal mixture designs for the qth degree model. For this problem, Liu and Neudecker [10] present general analytical expressions for the weights of the points of the simplex-centroid design and claim that the resulting designs are V-optimal. For a problem involving three mixture ingredients, Liu and Neudecker's results are in conflict with those of Laake [6]. We find that Laake's design for three ingredients is superior to that of Liu and Neudecker, and we establish the V-optimality of Laake's design and report V-optimal weights for the points of the simplex-centroid design for cases involving more than three ingredients. All newly proposed designs are superior to those of Liu and Neudecker. •This paper discusses V-optimal designs for mixture experiments.•The focus is on the qth degree model.•The paper identifies some conflicting results in the literature.•V-optimal designs are presented and verified using the general equivalence theorem.
ISSN:0169-7439
1873-3239
DOI:10.1016/j.chemolab.2014.04.019