Estimation and variable selection in joint mean and dispersion models applied to mixture experiments

In industrial experiments, controlling variability is of paramount importance to ensure product quality. Classical regression models for mixture experiments are widely used in industry, however, when the assumption of constant variance is not satisfied, the building of procedures that allow minimizing the variability becomes necessary and other methods of statistical modeling should be considered. In this article, we use the class of generalized linear models (GLMs) to build statistical models in mixture experiments. The GLMs class is general and very flexible, generalizing some of the most important probability distributions, and allows modeling the variability through the methodology of the joint modeling of mean and dispersion (JMMD). This paper shows how the JMMD can be used to obtain models for mean and variance in mixture experiments. We give a comprehensive understanding of the procedures for estimating parameters and selecting variables in the JMMD. The variable selection procedure was adapted for the case of mixture experiments, where the verification of constant dispersion is ensured by the existence of only the constant term in the dispersion model; the absence of the constant term or the existence of any other term in the dispersion model implies non-constant dispersion. A simulation study, considering the most common case of Normal distribution, was used to verify the effectiveness of the proposed variable selection procedure. A practical example from the Food Industry was used to illustrate the proposed methodology.