Visualization Approaches for Evaluating Ridge Regression Estimators in Mixture and Mixture-Process Experiments

Visualization Approaches for Evaluating Ridge Regression Estimators in Mixture and Mixture-Process Experiments

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Article ID: iaor2016356
Volume: 31
Issue: 8
Start Page Number: 1483
End Page Number: 1494
Publication Date: Dec 2015
Journal: Quality and Reliability Engineering International
Authors: ,
Keywords: experiment, statistics: regression
Abstract:

When the component proportions in mixture experiments are restricted by lower and upper bounds, the input space of a designed experiment space can become an irregular region that can induce multicollinearity problems when estimating the component proportion parameters. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Previous research has focused on using prediction variance as a metric for determining an appropriate value of the ridge constant, k. We use visualization techniques to illustrate and evaluate ridge regression estimators and the robustness of estimation with respect to the variance and the bias. The addition of bias allows better balancing between the stability of the estimators and minimally changing the estimates. We illustrate the graphical methods with mixture and mixture‐process examples from the literature.

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