Fractional Simplex Designs for Interaction Screening in Complex Mixtures
Authors: McConkey, Brendan J.1; Mezey, Paul G.2; Dixon, D. George1; Greenberg, Bruce M.1
Source: Biometrics, Volume 56, Number 3, September 2000 , pp. 824-832(9)
Publisher: Blackwell Publishing
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Abstract:
Summary. In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of the design arrays is described, and designs for ≤31 factors are presented. Some of the proposed methodology is illustrated using generated data.Keywords: Binary interactions; Combinatoric designs; Complex mixtures; Environmental mixtures; Finite fields; Screening; Simplex centroid; Simplex lattice; Toxicity assessment
Document Type: Research article
DOI: 10.1111/j.0006-341X.2000.00824.x
Affiliations: 1: Department of Biology, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada 2: Mathematical Chemistry Research Unit, Department of Chemistry, University of Saskatchewan, 110 Science Place, Saskatoon, Saskatchewan S7N 5C9, Canada
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