Abstract
A new approach to data analysis in mixture experiments is proposed using the simplex regression, that is in the class of dispersion models family. The advantages of this approach are illustrated in an experiment studying the mixture effect of fat, carbohydrate, and fiber on tumors’ proportion in mammary glands of rats. Model was evaluated by goodness of fit criteria, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals. The simplex regression model showed better quality of fit and smaller odds ratio confidence intervals.
Highlights
Compared to the results obtained by these authors, this indicates that simplex regression model performs better
We considered three different reference points (0.7, 0.275, 0.025), (0.275, 0.7, 0.025) and (0.332, 0.466, 0.202)
Simplex regression model showed good fit to the analysis of a mixture experiment that evaluated the incidence of mammary tumors in female rats, being a viable option in the analysis of situations where the outcome is limited to the (0,1) interval
Summary
A mixture experiment consists in optimizing a response variable (y) with the constraint that Equation 1: (1) where: We will restrict our discussion to design variables. In this case, E[y] is a function of x's, explanatory variables in a regression approach. The space spanned by design variables takes the form of a (q-1) regular simplex size. Additional restrictions (for economical, physical or practical reasons) are sometimes imposed on individual components, being and , respectively, are the upper and lower limits for x1. In this sense a restricted region as given in Equation 1 arises
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