Alternative modeling techniques for the quantal response data in mixture experiments

A simplex dispersion model for improving precision in the odds ratio confidence interval in mixture experiments

“…Data from Akay and Tez (2011) were used. Authors present a mixture experiment to study effects of diets (levels of fat, carbohydrate and fiber) on the expression of mammary gland tumors induced by Dimethylbenzathracene (DMBA) in female rats.…”

“…To solve this problem, inverse terms can be included, producing better fitting, however, this brings a nonlinear impact in Equation 1. Other approaches in literature have been succesfully attemted, as the inclusion of ratio variables, like in the models Equation 4 and 5 of Table 1, where corresponds to the mixture component that causes the border effect (Akay & Tez, 2011). Analysing mixture experiments using Dispersion models Let n independent realizations from a binomial distribution with parameters and .…”

“…Designs for mixture experiments are highly affected by collinearities, which is caused by the constraint in Equation 1. Several alternatives have been proposed in the literature to overcome this problem, such as the use of pseudo-components, inverse terms or ratio variables (Akay & Tez, 2011).…”

Nonlinear logistic regression mixture experiment modeling for binary data using dimensionally reduced components

“…[1][2][3][4][5][6] Despite the limited literature, it is straightforward to model binary response data from mixture experiments using logistic or probit regression 7,8 where the right side of the model is any mixture experiment model linear in the parameters (eg, Scheffé polynomial, Becker model homogeneous of degree one, and Scheffé polynomial with inverse terms). [1][2][3][4][5][6] Despite the limited literature, it is straightforward to model binary response data from mixture experiments using logistic or probit regression 7,8 where the right side of the model is any mixture experiment model linear in the parameters (eg, Scheffé polynomial, Becker model homogeneous of degree one, and Scheffé polynomial with inverse terms).…”

“…The vast majority of examples in the mixture experiment literature involve continuous response variables, with only a few examples that address modeling for binary or multinomial response variables. [1][2][3][4][5][6] Despite the limited literature, it is straightforward to model binary response data from mixture experiments using logistic or probit regression 7,8 where the right side of the model is any mixture experiment model linear in the parameters (eg, Scheffé polynomial, Becker model homogeneous of degree one, and Scheffé polynomial with inverse terms). Cornell 9 discusses each of these classes of mixture experiment models for continuous response variables.…”