Showing papers on "Mixture model published in 1974"
TL;DR: In this article, an algorithm was proposed for selecting a subset of extreme vertices when the number of candidate vertices is large, and the algorithm was found to produce designs which generally have small trace (X'X)−1, indicating the average variance of the estimated coefficients in the linear model will be small.
Abstract: Extreme vertices designs are useful in experimentation with mixtures, particularly when the response can be described by a linear model. An algorithm is proposed for selecting a subset of extreme vertices when the number of candidate vertices is large. This algorithm has been found to produce designs which generally have small trace (X'X)−1, indicating the average variance of the estimated coefficients in the linear model will be small.
108 citations
TL;DR: In this article, the authors show that the common practice produces misleading reslllts for mixtures, and that the correct mixture statistics correspond to a physically consistent null hypothesis and are also consistent with the expression of the mixture model in the older “slack-variable” form.
Abstract: Regression models of the forms proposed by Scheffe and by Becker have been widely and usefully applied to describe the response surfaces of mixture systems. These models do not contain a constant term. It has been common practice to test the statistical significance of these mixture models by the same statistical procedures used for other regression models whose constant term is absent (e.g., because the regression must pass through the origin). In this paper we show that the common practice produces misleading reslllts for mixtures. The mixture models require a different set of F, R 2, and R A 2 statistics. The correct mixture statistics correspond to a physically consistent null hypothesis and are also consistent with the expression of the mixture model in the older “slack-variable” form. An illustrative example is included.
81 citations