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Alternative modeling techniques for the quantal response data in mixture experiments

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Mixture experiments are commonly encountered in many fields including chemical, pharmaceutical and consumer product industries. Due to their wide applications, mixture experiments, a special study of response surface methodology, have been given greater attention in both model building and determination of designs compared with other experimental studies. In this paper, some new approaches are suggested on model building and selection for the analysis of the data in mixture experiments by using a special generalized linear models, logistic regression model, proposed by Chen et al. [7]. Generally, the special mixture models, which do not have a constant term, are highly affected by collinearity in modeling the mixture experiments. For this reason, in order to alleviate the undesired effects of collinearity in the analysis of mixture experiments with logistic regression, a new mixture model is defined with an alternative ratio variable. The deviance analysis table is given for standard mixture polynomial models defined by transformations and special mixture models used as linear predictors. The effects of components on the response in the restricted experimental region are given by using an alternative representation of Cox's direction approach. In addition, odds ratio and the confidence intervals of odds ratio are identified according to the chosen reference and control groups. To compare the suggested models, some model selection criteria, graphical odds ratio and the confidence intervals of the odds ratio are used. The advantage of the suggested approaches is illustrated on tumor incidence data set.
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Keywords: confidence intervals for the odds ratio; experiments with mixture; logistic regression models; model selection; response trace plots; the analysis of deviance table

Document Type: Research Article

Affiliations: 1: Science Faculty, Departments of Mathematics,University of Istanbul, 34134 VeznecilerBeyazit/Istanbul, Turkey 2: Art and Science Faculty, Departments of Statistics,University of Marmara, Goztepe Campus 34722 KuyubasiKadikoy/Istanbul, Turkey

Publication date: November 1, 2011

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