Abstract
In mixture experiments, determination of the best model for modeling the mixture system is significant in both understanding and interpreting the system. For obtaining the best model in mixture experiments, different methods have been used. Most commonly used methods are the stepwise type methods. However, the models obtained with these methods are not always the best model depending on the chosen criteria. As the models obtained with these methods can be affected by collinearity, in this paper, an alternative approach is used for the determination of the models taken into account in the modeling of the mixture surface, which is obtained on the experimental region. This approach depends on the examination of all possible subset regression models obtained for the mixture model. To determine the best subset model, the condition numbers of models and the model control graphs are also taken into account. Then, proposed approach has been investigated on flare data set, which is widely known in literature.
Highlights
In mixture experiments, the measured response is assumed to depend only on the proportions of ingredients present in the mixture and not on the amount of mixture
The models obtained by backward elimination, forward selection and stepwise regression methods are one of the models obtained by all possible subset selection
By using all possible subset selection, we can obtain models according to criteria we want
Summary
The measured response is assumed to depend only on the proportions of ingredients present in the mixture and not on the amount of mixture. The purpose of mixture experiments is to build an appropriate model relating the response(s) to mixture components. All of the work on mixture models has been based on response surface concepts. A model is fitted to data by an experimental design. Various mixture models can be used in the analysis of mixture experiments. The determination of the best model for modeling the mixture system is important in both understanding and interpreting the mixture system since the fitted models are used to screen the components, predict the response(s), determine the effects of components on the response(s), or optimize the response(s) over the experimental region
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