Prescott, Philip and Draper, Norman R.
Modeling in restricted mixture experiment spaces for three mixture components.
Quality Technology and Quantitative Management, 6, (3), .
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Quadratic models, fitted to data arising from mixture experiments with highly constrained ingredients proportions, often have large estimated coefficients that bear little resemblance to the size of the observations. Many practitioners find this disconcerting. Various transformations have been suggested to overcome this problem, although the predictions are unaffected by re-parameterizing the original terms in the model. We propose a new transformation of the coordinate system to the largest simplex that can be fitted inside the restricted region defined by the mixture constraints. In some cases the largest simplex will not be unique, in which case the one containing as many design points as possible is recommended. Then, the estimated coefficients will be much closer to the observations and thus more acceptable to the experimenter.
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