Seleção de delineamentos em um espaço simplex com efeito de borda em alguns componentes de mistura

Abstract

This study was conducted with the objective of addressing and assessing, via simulation data, the criteria of A- and D-optimality in mixture designs constructed based on a rotational design, considering normal and non-normal models, exploring zero boundary in some of the simplex components and analyzing the use of inverses terms on these components. Given the mathematical restriction imposed over the mixture designs, rotationality property is obtained by using specific algebraic procedure, in order for its inherent characteristic to be preserved, i.e. the prediction variance be constant for all experimental points. In the scenario of mixture problems, when the response presents extreme changes, when part of the components tend to zero border, the models usually used may not be capable or compatible to handle this fact. In this case, the inclusion of inverses terms associated to these components in classical models may be a more suitable alternative, given that these extreme changes occur with lower incidence on the border of the referred components. Considering the evaluated scenarios, we verified that the analysis performed suggest that the precision of the normal linear models with inverses terms was more relevant when analyzing the residual mean square, considering D-optimal mixture designs in detriment of the A-optimal and rotational designs, with greater emphasis when part of the simplex components are close to zero. When considering the response as a count, the use of inverse terms in the simplex components nearing the zero boundary was more effective in analyzing the deviance using the D-optimality property for the Normal model, however adjusting the Poisson model.