Polinômios de hermite para detecção de oscilações nos efeitos direcionais no espaço simplex em análise sensorial de blends de cafés

Abstract

Mixing experiments are essential in many fields, including chemical, pharmaceutical and consumer product industries such as coffee. Basically, a mixture experiment combines components in various proportions and observes the amounts of one or more responses for each mixture through statistical models.The linear Scheffé model and the Kronecker model are two forms of first-and second-order models, respectively, commonly used to analyze data from experiments of mixtures. A tool to visualize the behavior of the data adjusted by the adopted model are the trace-plot graphs, which allow the study of the average profiles of the components, in such a way that, starting from the budget of a reference mixture and making small increments in one of the components on the Cox directed axes, the effect produced by changing the proportions of the other components and the predicted value obtained by the model is identified. When using the aforementioned models, the effect of each component is interpreted through linear or quadratic traces, represented by the adjustment of the polynomial models. However, in experiments involving coffee blends, for example, external factors such as altitude, type of processing and degree of roasting, can directly influence the functional relationship of the data with the response variable, causing random oscillations and justifying the use of more accurate models. accurate. Following this motivation, this work aims to present a new family of parameterizations of the Scheffé linear model, with the specification of a parameter capable of perturbing the directed effects, which we call the Hermite Model. This model was built using orthogonal Hermite polynomials, where the unitary sum constraint function was applied in combination of different monomials of the Hermite polynomial product. In this study, we propose an improvement of the procedure used in the construction of the trace-plot graph, with Hermite polynomials, in the case study of sensory evaluation of coffee blends. Two correction proposals are also presented in the design matrix of the Hermite model in order to preserve the linear Scheffé model without losing the additional information present in the Hermite model.