Experiments with Mixtures: Estimated Regression Function of the Multiple-Lattice Design

Summary Lambrakis (1968) introduced the multiple-lattice design for experiments with mixtures as a generalization of the simplex-lattice design introduced by Scheffé (1958), and derived the estimating regression function of the double-lattice design. In this paper an expression due to Savage (see Kiefer, 1961, footnote 6), which generates orthogonal polynomials on the points of a simplex-lattice, is used to derive the estimated regression function of any multiple-lattice design.