Comparing the Intercept Mixture Model with the Slack-Variable Mixture Model Comparación del modelo de mezclas con intercepto con el modelo de mezclas de variable de holgura

Mixture experiments are experiments performed using ingredients whose proportions are restricted. This restriction may result in extremely small range in terms of the mixtures, causing difficulties in model fitting arising from ill-conditioning. The choice of model form is a very important factor in the numerical stability of the information matrix. In this paper, the intercept model is compared against the slack-variable model for mixture experiments. We analyzed if it matter which component is replaced for the constant term in the intercept model, in the sense on numerical stability. We also show by numerical examples that the Correlation Criterion, presented in Kang et al. (2015), does not work for the intercept model. Next, as suggested in the literature, we use linear transformation to alleviate the numerical instability. In addition, we try four transformation methods and choose the best one for the intercept model and the slack-variable model. Finally, we compare the intercept model with the slack-variable model based mainly on the prediction accuracy and numerical stability. Comparing the Intercept Mixture Model with the Slack-Variable Mixture Model Ingeniería Investigación y Tecnología, volumen XVII (número 3), julio-septiembre 2016: 383-393 ISSN 1405-7743 FI-UNAM 384 Introduction A mixture experiment is one in which the response depends only on the relative proportions of the ingredients, or components, present in the mixture, this proportions represent the design variables. In such experiments, by mixing different components, the product is developed. Mixture experiments frequently appear in fields such as chemical, pharmaceutical, food and plastic industries. There are certain type of mixture experiments where the total amount of the mixture, or process variables, are involve too as a design variables (Piepel and Cornell, 1985; Goldfarb et al., 2004). In this paper, we focus on the mixture experiments with the proportions of the components as the only input variables. If xi denotes the proportion of the ith of q components, then xi ≥ 0 for i = 1, 2, ..., q, and