A graphical evaluation of logistic ridge estimator in mixture experiments

作者：Akay Kadri Ulas^*

来源：Journal of Applied Statistics, 2014, 41(6): 1217-1232.

DOI：10.1080/02664763.2013.864261

• multicollinearity
• experiments with mixture
• fraction of design space plots
• logistic regression models
• generalized Cox direction
• scaled mean squared error of prediction
• logistic ridge regression

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.

• 出版日期2014-6-3