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A graphical evaluation of logistic ridge estimator in mixture experiments

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  • Kadri Ulas Akay

Abstract

In comparison to other experimental studies, multicollinearity appears frequently in mixture experiments, a special study area of response surface methodology, due to the constraints on the components composing the mixture. In the analysis of mixture experiments by using a special generalized linear model, logistic regression model, multicollinearity causes precision problems in the maximum-likelihood logistic regression estimate. Therefore, effects due to multicollinearity can be reduced to a certain extent by using alternative approaches. One of these approaches is to use biased estimators for the estimation of the coefficients. In this paper, we suggest the use of logistic ridge regression (RR) estimator in the cases where there is multicollinearity during the analysis of mixture experiments using logistic regression. Also, for the selection of the biasing parameter, we use fraction of design space plots for evaluating the effect of the logistic RR estimator with respect to the scaled mean squared error of prediction. The suggested graphical approaches are illustrated on the tumor incidence data set.

Suggested Citation

  • Kadri Ulas Akay, 2014. "A graphical evaluation of logistic ridge estimator in mixture experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1217-1232, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1217-1232
    DOI: 10.1080/02664763.2013.864261
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    References listed on IDEAS

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    1. G. Geoffrey Vining & John A. Cornell & Raymond H. Myers, 1993. "A Graphical Approach for Evaluating Mixture Designs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 127-138, March.
    2. Kadri Ulas Akay & Müjgan Tez, 2011. "Alternative modeling techniques for the quantal response data in mixture experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2597-2616, January.
    3. Robinson, Kevin S. & Khuri, Andre I., 2003. "Quantile dispersion graphs for evaluating and comparing designs for logistic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 47-62, May.
    4. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
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