Mixture Experiments and Their applications in Agricultural Research

Statistical techniques used to analyze data from Mixture Experiments involve fitting Multiple Regression models with the intercept set to zero, Canonical Analysis to determine the shape of the fitted response, and the Response Surface System. One can use Mixture Design Macros (e.g., ADXMIX File) in SAS or the point-and-click ADX Interface of SAS to analyze data and obtain graphs. Contour plot, the residual plot showing the deviations of the observed values from their predictions, and Box-Cox transform plot, etc. would also be provided by the ADX Interface of SAS. Two experiments with 3-component (X1, X2, and X3) Mixture Design consisting of equally spaced proportions of 0, 0.5, and 1 (designated as {3, 2} Design) and 0, 1/3, 2/3, and 1 (designated as {3, 3} Design), and a 4-component mixture design (X1, X2, X3, and X4) will be considered to show analyses and interpretations of the results. The Simplex Lattice Design using all possible blends of these 3 components will create 6 different mixtures for {3, 2} Design and 10 different mixtures for {3, 3} Design. These design points are the blending coordinates arranged such that all combinations of factor levels are tested. The Simplex-Centroid Design will be applied to the 4-component design and to the augmented 3-component design. One purpose of statistical modeling in a Mixture Experiment is to model the blending surface such that predictions of the response for any mixture component, singly or in combination, can be made empirically. Testing of the model adequacy will also be an important part of the statistical procedure in a Mixture Experiment.